Copyright	(C) 2013-16 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	experimental
Portability	non-portable
Safe Haskell	Safe-Inferred
Language	Haskell2010

Control.Lens.Combinators

Description

This lets the subset of users who vociferously disagree about the full scope and set of operators that should be exported from lens to not have to look at any operator with which they disagree.

import Control.Lens.Combinators

Synopsis

class Contravariant (f :: Type -> Type) where
- contramap :: (a' -> a) -> f a -> f a'
- (>$) :: b -> f b -> f a
class (forall a. Functor (p a)) => Bifunctor (p :: Type -> Type -> Type) where
- bimap :: (a -> b) -> (c -> d) -> p a c -> p b d
class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where
- traverse :: Applicative f => (a -> f b) -> t a -> f (t b)
data (a :: k) :~: (b :: k) where
- Refl :: forall {k} (a :: k). a :~: a
newtype Const a (b :: k) = Const {
- getConst :: a
}
newtype Identity a = Identity {
- runIdentity :: a
}
type IndexedTraversal i s t a b = forall p f. (Indexable i p, Applicative f) => p a (f b) -> s -> f t
class (FunctorWithIndex i t, FoldableWithIndex i t, Traversable t) => TraversableWithIndex i (t :: Type -> Type) | t -> i where
- itraverse :: Applicative f => (i -> a -> f b) -> t a -> f (t b)
class Foldable f => FoldableWithIndex i (f :: Type -> Type) | f -> i where
- ifoldMap :: Monoid m => (i -> a -> m) -> f a -> m
- ifoldMap' :: Monoid m => (i -> a -> m) -> f a -> m
- ifoldr :: (i -> a -> b -> b) -> b -> f a -> b
- ifoldl :: (i -> b -> a -> b) -> b -> f a -> b
- ifoldr' :: (i -> a -> b -> b) -> b -> f a -> b
- ifoldl' :: (i -> b -> a -> b) -> b -> f a -> b
class Functor f => FunctorWithIndex i (f :: Type -> Type) | f -> i where
- imap :: (i -> a -> b) -> f a -> f b
data Sequenced a m
data Traversed a f
class Profunctor (p :: Type -> Type -> Type) where
- dimap :: (a -> b) -> (c -> d) -> p b c -> p a d
- lmap :: (a -> b) -> p b c -> p a c
- rmap :: (b -> c) -> p a b -> p a c
class Profunctor p => Choice (p :: Type -> Type -> Type) where
- left' :: p a b -> p (Either a c) (Either b c)
- right' :: p a b -> p (Either c a) (Either c b)
type Traversing p f s t a b = Over p (BazaarT p f a b) s t a b
type Iso s t a b = forall p f. (Profunctor p, Functor f) => p a (f b) -> p s (f t)
class (Foldable1 t, Traversable t) => Traversable1 (t :: Type -> Type) where
- traverse1 :: Apply f => (a -> f b) -> t a -> f (t b)
type As a = Equality' a a
type Lens s t a b = forall f. Functor f => (a -> f b) -> s -> f t
class Ixed m => At m where
- at :: Index m -> Lens' m (Maybe (IxValue m))
class Cons s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _Cons :: Prism s t (a, s) (b, t)
class Each s t a b | s -> a, t -> b, s b -> t, t a -> s where
- each :: Traversal s t a b
type Equality (s :: k1) (t :: k2) (a :: k1) (b :: k2) = forall k3 (p :: k1 -> k3 -> Type) (f :: k2 -> k3). p a (f b) -> p s (f t)
type Fold s a = forall f. (Contravariant f, Applicative f) => (a -> f a) -> s -> f s
type Getter s a = forall f. (Contravariant f, Functor f) => (a -> f a) -> s -> f s
newtype Indexed i a b = Indexed {
- runIndexed :: i -> a -> b
}
data Level i a
class Plated a where
- plate :: Traversal' a a
type Prism s t a b = forall p f. (Choice p, Applicative f) => p a (f b) -> p s (f t)
type Review t b = forall p f. (Choice p, Bifunctor p, Settable f) => Optic' p f t b
type Setter s t a b = forall f. Settable f => (a -> f b) -> s -> f t
type Traversal s t a b = forall f. Applicative f => (a -> f b) -> s -> f t
class Wrapped s where
- type Unwrapped s :: Type
- _Wrapped' :: Iso' s (Unwrapped s)
class (MonadState s m, MonadState t n) => Zoom m n s t | m -> s, n -> t, m t -> n, n s -> m where
- zoom :: LensLike' (Zoomed m c) t s -> m c -> n c
type family Index (s :: Type) :: Type
type family IxValue (m :: Type) :: Type
class Ixed m where
- ix :: Index m -> Traversal' m (IxValue m)
class Contains m where
- contains :: Index m -> Lens' m Bool
class Snoc s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _Snoc :: Prism s t (s, a) (t, b)
class AsEmpty a where
- _Empty :: Prism' a ()
type Equality' s a = Equality s s a a
type AnEquality s t a b = Identical a (Proxy b) a (Proxy b) -> Identical a (Proxy b) s (Proxy t)
type AnEquality' s a = AnEquality s s a a
data Identical a b s t where
- Identical :: Identical a b a b
type IndexedFold i s a = forall p f. (Indexable i p, Contravariant f, Applicative f) => p a (f a) -> s -> f s
data Leftmost a
data Rightmost a
data Magma i t b a
type IndexedGetter i s a = forall p f. (Indexable i p, Contravariant f, Functor f) => p a (f a) -> s -> f s
type Getting r s a = (a -> Const r a) -> s -> Const r s
type IndexedGetting i m s a = Indexed i a (Const m a) -> s -> Const m s
type Accessing p m s a = p a (Const m a) -> s -> Const m s
class Conjoined p => Indexable i p where
- indexed :: p a b -> i -> a -> b
class (Choice p, Corepresentable p, Comonad (Corep p), Traversable (Corep p), Strong p, Representable p, Monad (Rep p), MonadFix (Rep p), Distributive (Rep p), Costrong p, ArrowLoop p, ArrowApply p, ArrowChoice p, Closed p) => Conjoined p where
- distrib :: Functor f => p a b -> p (f a) (f b)
- conjoined :: (p ~ (->) => q (a -> b) r) -> q (p a b) r -> q (p a b) r
newtype Bazaar p a b t = Bazaar {
- runBazaar :: forall f. Applicative f => p a (f b) -> f t
}
data Context a b t = Context (b -> t) a
type Bazaar' p a = Bazaar p a a
newtype Bazaar1 p a b t = Bazaar1 {
- runBazaar1 :: forall f. Apply f => p a (f b) -> f t
}
type Bazaar1' p a = Bazaar1 p a a
type Context' a = Context a a
data LensRules
type FieldNamer = Name -> [Name] -> Name -> [DefName]
data DefName
- = TopName Name
- | MethodName Name Name
type ClassyNamer = Name -> Maybe (Name, Name)
class Reversing t where
- reversing :: t -> t
class (Profunctor p, Bifunctor p) => Reviewable p
class (Applicative f, Distributive f, Traversable f) => Settable f
type Iso' s a = Iso s s a a
type AnIso s t a b = Exchange a b a (Identity b) -> Exchange a b s (Identity t)
type AnIso' s a = AnIso s s a a
type Lens' s a = Lens s s a a
type IndexedLens i s t a b = forall f p. (Indexable i p, Functor f) => p a (f b) -> s -> f t
type IndexedLens' i s a = IndexedLens i s s a a
type ALens s t a b = LensLike (Pretext (->) a b) s t a b
type ALens' s a = ALens s s a a
type AnIndexedLens i s t a b = Optical (Indexed i) (->) (Pretext (Indexed i) a b) s t a b
type AnIndexedLens' i s a = AnIndexedLens i s s a a
class GPlated a g
class GPlated1 f g
type Prism' s a = Prism s s a a
type APrism s t a b = Market a b a (Identity b) -> Market a b s (Identity t)
type APrism' s a = APrism s s a a
class Prefixed t where
- prefixed :: t -> Prism' t t
class Suffixed t where
- suffixed :: t -> Prism' t t
type Optic p f s t a b = p a (f b) -> p s (f t)
type LensLike f s t a b = (a -> f b) -> s -> f t
type ASetter s t a b = (a -> Identity b) -> s -> Identity t
type ATraversal s t a b = LensLike (Bazaar (->) a b) s t a b
newtype ReifiedLens s t a b = Lens {
- runLens :: Lens s t a b
}
type AReview t b = Optic' Tagged Identity t b
type Setter' s a = Setter s s a a
type IndexedSetter i s t a b = forall f p. (Indexable i p, Settable f) => p a (f b) -> s -> f t
type IndexedSetter' i s a = IndexedSetter i s s a a
type ASetter' s a = ASetter s s a a
type AnIndexedSetter i s t a b = Indexed i a (Identity b) -> s -> Identity t
type AnIndexedSetter' i s a = AnIndexedSetter i s s a a
type Setting p s t a b = p a (Identity b) -> s -> Identity t
type Setting' p s a = Setting p s s a a
type Traversal' s a = Traversal s s a a
type Traversal1 s t a b = forall f. Apply f => (a -> f b) -> s -> f t
type Traversal1' s a = Traversal1 s s a a
type IndexedTraversal' i s a = IndexedTraversal i s s a a
type IndexedTraversal1 i s t a b = forall p f. (Indexable i p, Apply f) => p a (f b) -> s -> f t
type IndexedTraversal1' i s a = IndexedTraversal1 i s s a a
type ATraversal' s a = ATraversal s s a a
type ATraversal1 s t a b = LensLike (Bazaar1 (->) a b) s t a b
type ATraversal1' s a = ATraversal1 s s a a
type AnIndexedTraversal i s t a b = Over (Indexed i) (Bazaar (Indexed i) a b) s t a b
type AnIndexedTraversal' i s a = AnIndexedTraversal i s s a a
type AnIndexedTraversal1 i s t a b = Over (Indexed i) (Bazaar1 (Indexed i) a b) s t a b
type AnIndexedTraversal1' i s a = AnIndexedTraversal1 i s s a a
type Traversing' p f s a = Traversing p f s s a a
type Traversing1 p f s t a b = Over p (BazaarT1 p f a b) s t a b
type Traversing1' p f s a = Traversing1 p f s s a a
class Ord k => TraverseMin k m | m -> k where
- traverseMin :: IndexedTraversal' k (m v) v
class Ord k => TraverseMax k m | m -> k where
- traverseMax :: IndexedTraversal' k (m v) v
class Field1 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _1 :: Lens s t a b
class Field2 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _2 :: Lens s t a b
class Field3 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _3 :: Lens s t a b
class Field4 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _4 :: Lens s t a b
class Field5 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _5 :: Lens s t a b
class Field6 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _6 :: Lens s t a b
class Field7 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _7 :: Lens s t a b
class Field8 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _8 :: Lens s t a b
class Field9 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _9 :: Lens s t a b
class Field10 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _10 :: Lens s t a b
class Field11 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _11 :: Lens s t a b
class Field12 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _12 :: Lens s t a b
class Field13 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _13 :: Lens s t a b
class Field14 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _14 :: Lens s t a b
class Field15 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _15 :: Lens s t a b
class Field16 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _16 :: Lens s t a b
class Field17 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _17 :: Lens s t a b
class Field18 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _18 :: Lens s t a b
class Field19 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _19 :: Lens s t a b
type Fold1 s a = forall f. (Contravariant f, Apply f) => (a -> f a) -> s -> f s
type IndexedFold1 i s a = forall p f. (Indexable i p, Contravariant f, Apply f) => p a (f a) -> s -> f s
type IndexPreservingLens s t a b = forall p f. (Conjoined p, Functor f) => p a (f b) -> p s (f t)
type IndexPreservingLens' s a = IndexPreservingLens s s a a
type IndexPreservingTraversal s t a b = forall p f. (Conjoined p, Applicative f) => p a (f b) -> p s (f t)
type IndexPreservingTraversal' s a = IndexPreservingTraversal s s a a
type IndexPreservingTraversal1 s t a b = forall p f. (Conjoined p, Apply f) => p a (f b) -> p s (f t)
type IndexPreservingTraversal1' s a = IndexPreservingTraversal1 s s a a
type IndexPreservingSetter s t a b = forall p f. (Conjoined p, Settable f) => p a (f b) -> p s (f t)
type IndexPreservingSetter' s a = IndexPreservingSetter s s a a
type IndexPreservingGetter s a = forall p f. (Conjoined p, Contravariant f, Functor f) => p a (f a) -> p s (f s)
type IndexPreservingFold s a = forall p f. (Conjoined p, Contravariant f, Applicative f) => p a (f a) -> p s (f s)
type IndexPreservingFold1 s a = forall p f. (Conjoined p, Contravariant f, Apply f) => p a (f a) -> p s (f s)
type Simple f s a = f s s a a
type LensLike' f s a = LensLike f s s a a
type Over p f s t a b = p a (f b) -> s -> f t
type Over' p f s a = Over p f s s a a
type IndexedLensLike i f s t a b = forall p. Indexable i p => p a (f b) -> s -> f t
type IndexedLensLike' i f s a = IndexedLensLike i f s s a a
type Optical p q f s t a b = p a (f b) -> q s (f t)
type Optical' p q f s a = Optical p q f s s a a
type Optic' p f s a = Optic p f s s a a
class Wrapped s => Rewrapped (s :: Type) (t :: Type)
class (Rewrapped s t, Rewrapped t s) => Rewrapping s t
type family Magnified (m :: Type -> Type) :: Type -> Type -> Type
class (Magnified m ~ Magnified n, MonadReader b m, MonadReader a n) => Magnify m n b a | m -> b, n -> a, m a -> n, n b -> m where
- magnify :: ((Functor (Magnified m c), Contravariant (Magnified m c)) => LensLike' (Magnified m c) a b) -> m c -> n c
type family Zoomed (m :: Type -> Type) :: Type -> Type -> Type
newtype ReifiedTraversal s t a b = Traversal {
- runTraversal :: Traversal s t a b
}
type ReifiedLens' s a = ReifiedLens s s a a
newtype ReifiedIndexedLens i s t a b = IndexedLens {
- runIndexedLens :: IndexedLens i s t a b
}
type ReifiedIndexedLens' i s a = ReifiedIndexedLens i s s a a
newtype ReifiedIndexedTraversal i s t a b = IndexedTraversal {
- runIndexedTraversal :: IndexedTraversal i s t a b
}
type ReifiedIndexedTraversal' i s a = ReifiedIndexedTraversal i s s a a
type ReifiedTraversal' s a = ReifiedTraversal s s a a
newtype ReifiedGetter s a = Getter {
- runGetter :: Getter s a
}
newtype ReifiedIndexedGetter i s a = IndexedGetter {
- runIndexedGetter :: IndexedGetter i s a
}
newtype ReifiedFold s a = Fold {
- runFold :: Fold s a
}
newtype ReifiedIndexedFold i s a = IndexedFold {
- runIndexedFold :: IndexedFold i s a
}
newtype ReifiedSetter s t a b = Setter {
- runSetter :: Setter s t a b
}
type ReifiedSetter' s a = ReifiedSetter s s a a
newtype ReifiedIndexedSetter i s t a b = IndexedSetter {
- runIndexedSetter :: IndexedSetter i s t a b
}
type ReifiedIndexedSetter' i s a = ReifiedIndexedSetter i s s a a
newtype ReifiedIso s t a b = Iso {
- runIso :: Iso s t a b
}
type ReifiedIso' s a = ReifiedIso s s a a
newtype ReifiedPrism s t a b = Prism {
- runPrism :: Prism s t a b
}
type ReifiedPrism' s a = ReifiedPrism s s a a
pattern List :: IsList l => [Item l] -> l
pattern Empty :: AsEmpty s => s
pattern Strict :: Strict s t => t -> s
pattern Lazy :: Strict t s => t -> s
pattern Wrapped :: Rewrapped s s => Unwrapped s -> s
pattern Swapped :: Swap p => p b a -> p a b
pattern Reversed :: Reversing t => t -> t
pattern Unwrapped :: Rewrapped t t => t -> Unwrapped t
strict :: Strict lazy strict => Iso' lazy strict
only :: Eq a => a -> Prism' a ()
index :: (Indexable i p, Eq i, Applicative f) => i -> Optical' p (Indexed i) f a a
indices :: (Indexable i p, Applicative f) => (i -> Bool) -> Optical' p (Indexed i) f a a
lazy :: Strict lazy strict => Iso' strict lazy
uncons :: Cons s s a a => s -> Maybe (a, s)
from :: AnIso s t a b -> Iso b a t s
to :: (Profunctor p, Contravariant f) => (s -> a) -> Optic' p f s a
cons :: Cons s s a a => a -> s -> s
snoc :: Snoc s s a a => s -> a -> s
unsnoc :: Snoc s s a a => s -> Maybe (s, a)
levels :: Applicative f => Traversing (->) f s t a b -> IndexedLensLike Int f s t (Level () a) (Level () b)
chosen :: IndexPreservingLens (Either a a) (Either b b) a b
traverseOf_ :: Functor f => Getting (Traversed r f) s a -> (a -> f r) -> s -> f ()
foldlOf' :: Getting (Endo (Endo r)) s a -> (r -> a -> r) -> r -> s -> r
mapMOf_ :: Monad m => Getting (Sequenced r m) s a -> (a -> m r) -> s -> m ()
ifor :: (TraversableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f (t b)
imapM :: (TraversableWithIndex i t, Monad m) => (i -> a -> m b) -> t a -> m (t b)
iforM :: (TraversableWithIndex i t, Monad m) => t a -> (i -> a -> m b) -> m (t b)
imapAccumR :: TraversableWithIndex i t => (i -> s -> a -> (s, b)) -> s -> t a -> (s, t b)
imapAccumL :: TraversableWithIndex i t => (i -> s -> a -> (s, b)) -> s -> t a -> (s, t b)
iany :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool
iall :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool
inone :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool
none :: Foldable f => (a -> Bool) -> f a -> Bool
itraverse_ :: (FoldableWithIndex i t, Applicative f) => (i -> a -> f b) -> t a -> f ()
ifor_ :: (FoldableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f ()
imapM_ :: (FoldableWithIndex i t, Monad m) => (i -> a -> m b) -> t a -> m ()
iforM_ :: (FoldableWithIndex i t, Monad m) => t a -> (i -> a -> m b) -> m ()
iconcatMap :: FoldableWithIndex i f => (i -> a -> [b]) -> f a -> [b]
ifind :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Maybe (i, a)
ifoldrM :: (FoldableWithIndex i f, Monad m) => (i -> a -> b -> m b) -> b -> f a -> m b
ifoldlM :: (FoldableWithIndex i f, Monad m) => (i -> b -> a -> m b) -> b -> f a -> m b
itoList :: FoldableWithIndex i f => f a -> [(i, a)]
swapped :: Swap p => Iso (p a b) (p c d) (p b a) (p d c)
foldBy :: Foldable t => (a -> a -> a) -> a -> t a -> a
foldMapBy :: Foldable t => (r -> r -> r) -> r -> (a -> r) -> t a -> r
traverseBy :: Traversable t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (a -> f b) -> t a -> f (t b)
sequenceBy :: Traversable t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> t (f a) -> f (t a)
over :: ASetter s t a b -> (a -> b) -> s -> t
elements :: Traversable t => (Int -> Bool) -> IndexedTraversal' Int (t a) a
transform :: Plated a => (a -> a) -> a -> a
set :: ASetter s t a b -> b -> s -> t
sans :: At m => Index m -> m -> m
iat :: At m => Index m -> IndexedLens' (Index m) m (Maybe (IxValue m))
ixAt :: At m => Index m -> Traversal' m (IxValue m)
iix :: Ixed m => Index m -> IndexedTraversal' (Index m) m (IxValue m)
icontains :: Contains m => Index m -> IndexedLens' (Index m) m Bool
_head :: Cons s s a a => Traversal' s a
_tail :: Cons s s a a => Traversal' s s
_init :: Snoc s s a a => Traversal' s s
_last :: Snoc s s a a => Traversal' s a
simply :: forall p f s a rep (r :: TYPE rep). (Optic' p f s a -> r) -> Optic' p f s a -> r
runEq :: AnEquality s t a b -> Identical s t a b
substEq :: forall s t a b rep (r :: TYPE rep). AnEquality s t a b -> ((s ~ a, t ~ b) => r) -> r
mapEq :: forall k1 k2 (s :: k1) (t :: k2) (a :: k1) (b :: k2) (f :: k1 -> Type). AnEquality s t a b -> f s -> f a
fromEq :: AnEquality s t a b -> Equality b a t s
simple :: Equality' a a
equality :: (s :~: a) -> (b :~: t) -> Equality s t a b
equality' :: (a :~: b) -> Equality' a b
withEquality :: forall s t a b rep (r :: TYPE rep). AnEquality s t a b -> ((s :~: a) -> (b :~: t) -> r) -> r
underEquality :: AnEquality s t a b -> p t s -> p b a
overEquality :: AnEquality s t a b -> p a b -> p s t
fromLeibniz :: (Identical a b a b -> Identical a b s t) -> Equality s t a b
fromLeibniz' :: ((s :~: s) -> s :~: a) -> Equality' s a
cloneEquality :: AnEquality s t a b -> Equality s t a b
pre :: Getting (First a) s a -> IndexPreservingGetter s (Maybe a)
ipre :: IndexedGetting i (First (i, a)) s a -> IndexPreservingGetter s (Maybe (i, a))
preview :: MonadReader s m => Getting (First a) s a -> m (Maybe a)
previews :: MonadReader s m => Getting (First r) s a -> (a -> r) -> m (Maybe r)
ipreview :: MonadReader s m => IndexedGetting i (First (i, a)) s a -> m (Maybe (i, a))
ipreviews :: MonadReader s m => IndexedGetting i (First r) s a -> (i -> a -> r) -> m (Maybe r)
preuse :: MonadState s m => Getting (First a) s a -> m (Maybe a)
preuses :: MonadState s m => Getting (First r) s a -> (a -> r) -> m (Maybe r)
ipreuse :: MonadState s m => IndexedGetting i (First (i, a)) s a -> m (Maybe (i, a))
ipreuses :: MonadState s m => IndexedGetting i (First r) s a -> (i -> a -> r) -> m (Maybe r)
has :: Getting Any s a -> s -> Bool
hasn't :: Getting All s a -> s -> Bool
folding :: Foldable f => (s -> f a) -> Fold s a
ifolding :: (Foldable f, Indexable i p, Contravariant g, Applicative g) => (s -> f (i, a)) -> Over p g s t a b
foldring :: (Contravariant f, Applicative f) => ((a -> f a -> f a) -> f a -> s -> f a) -> LensLike f s t a b
ifoldring :: (Indexable i p, Contravariant f, Applicative f) => ((i -> a -> f a -> f a) -> f a -> s -> f a) -> Over p f s t a b
folded :: Foldable f => IndexedFold Int (f a) a
folded64 :: Foldable f => IndexedFold Int64 (f a) a
unfolded :: (b -> Maybe (a, b)) -> Fold b a
iterated :: Apply f => (a -> a) -> LensLike' f a a
filtered :: (Choice p, Applicative f) => (a -> Bool) -> Optic' p f a a
filteredBy :: (Indexable i p, Applicative f) => Getting (First i) a i -> p a (f a) -> a -> f a
backwards :: (Profunctor p, Profunctor q) => Optical p q (Backwards f) s t a b -> Optical p q f s t a b
repeated :: Apply f => LensLike' f a a
replicated :: Int -> Fold a a
cycled :: Apply f => LensLike f s t a b -> LensLike f s t a b
takingWhile :: (Conjoined p, Applicative f) => (a -> Bool) -> Over p (TakingWhile p f a a) s t a a -> Over p f s t a a
droppingWhile :: (Conjoined p, Profunctor q, Applicative f) => (a -> Bool) -> Optical p q (Compose (State Bool) f) s t a a -> Optical p q f s t a a
worded :: Applicative f => IndexedLensLike' Int f String String
lined :: Applicative f => IndexedLensLike' Int f String String
foldMapOf :: Getting r s a -> (a -> r) -> s -> r
foldOf :: Getting a s a -> s -> a
foldrOf :: Getting (Endo r) s a -> (a -> r -> r) -> r -> s -> r
foldlOf :: Getting (Dual (Endo r)) s a -> (r -> a -> r) -> r -> s -> r
toListOf :: Getting (Endo [a]) s a -> s -> [a]
toNonEmptyOf :: Getting (NonEmptyDList a) s a -> s -> NonEmpty a
altOf :: Applicative f => Getting (Alt f a) s a -> s -> f a
anyOf :: Getting Any s a -> (a -> Bool) -> s -> Bool
allOf :: Getting All s a -> (a -> Bool) -> s -> Bool
noneOf :: Getting Any s a -> (a -> Bool) -> s -> Bool
andOf :: Getting All s Bool -> s -> Bool
orOf :: Getting Any s Bool -> s -> Bool
productOf :: Num a => Getting (Endo (Endo a)) s a -> s -> a
sumOf :: Num a => Getting (Endo (Endo a)) s a -> s -> a
forOf_ :: Functor f => Getting (Traversed r f) s a -> s -> (a -> f r) -> f ()
sequenceAOf_ :: Functor f => Getting (Traversed a f) s (f a) -> s -> f ()
traverse1Of_ :: Functor f => Getting (TraversedF r f) s a -> (a -> f r) -> s -> f ()
for1Of_ :: Functor f => Getting (TraversedF r f) s a -> s -> (a -> f r) -> f ()
sequence1Of_ :: Functor f => Getting (TraversedF a f) s (f a) -> s -> f ()
forMOf_ :: Monad m => Getting (Sequenced r m) s a -> s -> (a -> m r) -> m ()
sequenceOf_ :: Monad m => Getting (Sequenced a m) s (m a) -> s -> m ()
asumOf :: Alternative f => Getting (Endo (f a)) s (f a) -> s -> f a
msumOf :: MonadPlus m => Getting (Endo (m a)) s (m a) -> s -> m a
concatMapOf :: Getting [r] s a -> (a -> [r]) -> s -> [r]
concatOf :: Getting [r] s [r] -> s -> [r]
elemOf :: Eq a => Getting Any s a -> a -> s -> Bool
notElemOf :: Eq a => Getting All s a -> a -> s -> Bool
lengthOf :: Getting (Endo (Endo Int)) s a -> s -> Int
nullOf :: Getting All s a -> s -> Bool
notNullOf :: Getting Any s a -> s -> Bool
firstOf :: Getting (Leftmost a) s a -> s -> Maybe a
first1Of :: Getting (First a) s a -> s -> a
lastOf :: Getting (Rightmost a) s a -> s -> Maybe a
last1Of :: Getting (Last a) s a -> s -> a
maximumOf :: Ord a => Getting (Endo (Endo (Maybe a))) s a -> s -> Maybe a
maximum1Of :: Ord a => Getting (Max a) s a -> s -> a
minimumOf :: Ord a => Getting (Endo (Endo (Maybe a))) s a -> s -> Maybe a
minimum1Of :: Ord a => Getting (Min a) s a -> s -> a
maximumByOf :: Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> Ordering) -> s -> Maybe a
minimumByOf :: Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> Ordering) -> s -> Maybe a
findOf :: Getting (Endo (Maybe a)) s a -> (a -> Bool) -> s -> Maybe a
findMOf :: Monad m => Getting (Endo (m (Maybe a))) s a -> (a -> m Bool) -> s -> m (Maybe a)
foldrOf' :: Getting (Dual (Endo (Endo r))) s a -> (a -> r -> r) -> r -> s -> r
foldr1Of :: HasCallStack => Getting (Endo (Maybe a)) s a -> (a -> a -> a) -> s -> a
foldl1Of :: HasCallStack => Getting (Dual (Endo (Maybe a))) s a -> (a -> a -> a) -> s -> a
foldr1Of' :: HasCallStack => Getting (Dual (Endo (Endo (Maybe a)))) s a -> (a -> a -> a) -> s -> a
foldl1Of' :: HasCallStack => Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> a) -> s -> a
foldrMOf :: Monad m => Getting (Dual (Endo (r -> m r))) s a -> (a -> r -> m r) -> r -> s -> m r
foldlMOf :: Monad m => Getting (Endo (r -> m r)) s a -> (r -> a -> m r) -> r -> s -> m r
lookupOf :: Eq k => Getting (Endo (Maybe v)) s (k, v) -> k -> s -> Maybe v
ifoldMapOf :: IndexedGetting i m s a -> (i -> a -> m) -> s -> m
ifoldrOf :: IndexedGetting i (Endo r) s a -> (i -> a -> r -> r) -> r -> s -> r
ifoldlOf :: IndexedGetting i (Dual (Endo r)) s a -> (i -> r -> a -> r) -> r -> s -> r
ianyOf :: IndexedGetting i Any s a -> (i -> a -> Bool) -> s -> Bool
iallOf :: IndexedGetting i All s a -> (i -> a -> Bool) -> s -> Bool
inoneOf :: IndexedGetting i Any s a -> (i -> a -> Bool) -> s -> Bool
itraverseOf_ :: Functor f => IndexedGetting i (Traversed r f) s a -> (i -> a -> f r) -> s -> f ()
iforOf_ :: Functor f => IndexedGetting i (Traversed r f) s a -> s -> (i -> a -> f r) -> f ()
imapMOf_ :: Monad m => IndexedGetting i (Sequenced r m) s a -> (i -> a -> m r) -> s -> m ()
iforMOf_ :: Monad m => IndexedGetting i (Sequenced r m) s a -> s -> (i -> a -> m r) -> m ()
iconcatMapOf :: IndexedGetting i [r] s a -> (i -> a -> [r]) -> s -> [r]
ifindOf :: IndexedGetting i (Endo (Maybe a)) s a -> (i -> a -> Bool) -> s -> Maybe a
ifindMOf :: Monad m => IndexedGetting i (Endo (m (Maybe a))) s a -> (i -> a -> m Bool) -> s -> m (Maybe a)
ifoldrOf' :: IndexedGetting i (Dual (Endo (r -> r))) s a -> (i -> a -> r -> r) -> r -> s -> r
ifoldlOf' :: IndexedGetting i (Endo (r -> r)) s a -> (i -> r -> a -> r) -> r -> s -> r
ifoldrMOf :: Monad m => IndexedGetting i (Dual (Endo (r -> m r))) s a -> (i -> a -> r -> m r) -> r -> s -> m r
ifoldlMOf :: Monad m => IndexedGetting i (Endo (r -> m r)) s a -> (i -> r -> a -> m r) -> r -> s -> m r
itoListOf :: IndexedGetting i (Endo [(i, a)]) s a -> s -> [(i, a)]
elemIndexOf :: Eq a => IndexedGetting i (First i) s a -> a -> s -> Maybe i
elemIndicesOf :: Eq a => IndexedGetting i (Endo [i]) s a -> a -> s -> [i]
findIndexOf :: IndexedGetting i (First i) s a -> (a -> Bool) -> s -> Maybe i
findIndicesOf :: IndexedGetting i (Endo [i]) s a -> (a -> Bool) -> s -> [i]
ifiltered :: (Indexable i p, Applicative f) => (i -> a -> Bool) -> Optical' p (Indexed i) f a a
itakingWhile :: (Indexable i p, Profunctor q, Contravariant f, Applicative f) => (i -> a -> Bool) -> Optical' (Indexed i) q (Const (Endo (f s))) s a -> Optical' p q f s a
idroppingWhile :: (Indexable i p, Profunctor q, Applicative f) => (i -> a -> Bool) -> Optical (Indexed i) q (Compose (State Bool) f) s t a a -> Optical p q f s t a a
foldByOf :: Fold s a -> (a -> a -> a) -> a -> s -> a
foldMapByOf :: Fold s a -> (r -> r -> r) -> r -> (a -> r) -> s -> r
ito :: (Indexable i p, Contravariant f) => (s -> (i, a)) -> Over' p f s a
like :: (Profunctor p, Contravariant f, Functor f) => a -> Optic' p f s a
ilike :: (Indexable i p, Contravariant f, Functor f) => i -> a -> Over' p f s a
view :: MonadReader s m => Getting a s a -> m a
views :: MonadReader s m => LensLike' (Const r) s a -> (a -> r) -> m r
use :: MonadState s m => Getting a s a -> m a
uses :: MonadState s m => LensLike' (Const r) s a -> (a -> r) -> m r
listening :: MonadWriter w m => Getting u w u -> m a -> m (a, u)
listenings :: MonadWriter w m => Getting v w u -> (u -> v) -> m a -> m (a, v)
iview :: MonadReader s m => IndexedGetting i (i, a) s a -> m (i, a)
iviews :: MonadReader s m => IndexedGetting i r s a -> (i -> a -> r) -> m r
iuse :: MonadState s m => IndexedGetting i (i, a) s a -> m (i, a)
iuses :: MonadState s m => IndexedGetting i r s a -> (i -> a -> r) -> m r
ilistening :: MonadWriter w m => IndexedGetting i (i, u) w u -> m a -> m (a, (i, u))
ilistenings :: MonadWriter w m => IndexedGetting i v w u -> (i -> u -> v) -> m a -> m (a, v)
getting :: (Profunctor p, Profunctor q, Functor f, Contravariant f) => Optical p q f s t a b -> Optical' p q f s a
selfIndex :: Indexable a p => p a fb -> a -> fb
reindexed :: Indexable j p => (i -> j) -> (Indexed i a b -> r) -> p a b -> r
icompose :: Indexable p c => (i -> j -> p) -> (Indexed i s t -> r) -> (Indexed j a b -> s -> t) -> c a b -> r
indexing :: Indexable Int p => ((a -> Indexing f b) -> s -> Indexing f t) -> p a (f b) -> s -> f t
indexing64 :: Indexable Int64 p => ((a -> Indexing64 f b) -> s -> Indexing64 f t) -> p a (f b) -> s -> f t
imapped :: FunctorWithIndex i f => IndexedSetter i (f a) (f b) a b
ifolded :: FoldableWithIndex i f => IndexedFold i (f a) a
withIndex :: (Indexable i p, Functor f) => p (i, s) (f (j, t)) -> Indexed i s (f t)
asIndex :: (Indexable i p, Contravariant f, Functor f) => p i (f i) -> Indexed i s (f s)
itraversed :: TraversableWithIndex i t => IndexedTraversal i (t a) (t b) a b
ifoldMapBy :: FoldableWithIndex i t => (r -> r -> r) -> r -> (i -> a -> r) -> t a -> r
ifoldMapByOf :: IndexedFold i t a -> (r -> r -> r) -> r -> (i -> a -> r) -> t -> r
itraverseBy :: TraversableWithIndex i t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (i -> a -> f b) -> t a -> f (t b)
itraverseByOf :: IndexedTraversal i s t a b -> (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (i -> a -> f b) -> s -> f t
makePrisms :: Name -> DecsQ
makeClassyPrisms :: Name -> DecsQ
retagged :: (Profunctor p, Bifunctor p) => p a b -> p s b
iso :: (s -> a) -> (b -> t) -> Iso s t a b
cloneIso :: AnIso s t a b -> Iso s t a b
withIso :: forall s t a b rep (r :: TYPE rep). AnIso s t a b -> ((s -> a) -> (b -> t) -> r) -> r
au :: Functor f => AnIso s t a b -> ((b -> t) -> f s) -> f a
auf :: (Functor f, Functor g) => AnIso s t a b -> (f t -> g s) -> f b -> g a
xplat :: Optic (Costar ((->) s)) g s t a b -> ((s -> a) -> g b) -> g t
xplatf :: Optic (Costar f) g s t a b -> (f a -> g b) -> f s -> g t
under :: AnIso s t a b -> (t -> s) -> b -> a
mapping :: (Functor f, Functor g) => AnIso s t a b -> Iso (f s) (g t) (f a) (g b)
non :: Eq a => a -> Iso' (Maybe a) a
non' :: APrism' a () -> Iso' (Maybe a) a
anon :: a -> (a -> Bool) -> Iso' (Maybe a) a
enum :: Enum a => Iso' Int a
curried :: Iso ((a, b) -> c) ((d, e) -> f) (a -> b -> c) (d -> e -> f)
uncurried :: Iso (a -> b -> c) (d -> e -> f) ((a, b) -> c) ((d, e) -> f)
flipped :: Iso (a -> b -> c) (a' -> b' -> c') (b -> a -> c) (b' -> a' -> c')
reversed :: Reversing a => Iso' a a
involuted :: (a -> a) -> Iso' a a
magma :: LensLike (Mafic a b) s t a b -> Iso s u (Magma Int t b a) (Magma j u c c)
imagma :: Over (Indexed i) (Molten i a b) s t a b -> Iso s t' (Magma i t b a) (Magma j t' c c)
contramapping :: Contravariant f => AnIso s t a b -> Iso (f a) (f b) (f s) (f t)
dimapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> AnIso s' t' a' b' -> Iso (p a s') (q b t') (p s a') (q t b')
lmapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> Iso (p a x) (q b y) (p s x) (q t y)
rmapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> Iso (p x s) (q y t) (p x a) (q y b)
bimapping :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> AnIso s' t' a' b' -> Iso (f s s') (g t t') (f a a') (g b b')
firsting :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> Iso (f s x) (g t y) (f a x) (g b y)
seconding :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> Iso (f x s) (g y t) (f x a) (g y b)
coerced :: forall s t a b. (Coercible s a, Coercible t b) => Iso s t a b
lens :: (s -> a) -> (s -> b -> t) -> Lens s t a b
ilens :: (s -> (i, a)) -> (s -> b -> t) -> IndexedLens i s t a b
iplens :: (s -> a) -> (s -> b -> t) -> IndexPreservingLens s t a b
withLens :: forall s t a b rep (r :: TYPE rep). ALens s t a b -> ((s -> a) -> (s -> b -> t) -> r) -> r
choosing :: Functor f => LensLike f s t a b -> LensLike f s' t' a b -> LensLike f (Either s s') (Either t t') a b
alongside :: LensLike (AlongsideLeft f b') s t a b -> LensLike (AlongsideRight f t) s' t' a' b' -> LensLike f (s, s') (t, t') (a, a') (b, b')
inside :: Corepresentable p => ALens s t a b -> Lens (p e s) (p e t) (p e a) (p e b)
cloneLens :: ALens s t a b -> Lens s t a b
cloneIndexPreservingLens :: ALens s t a b -> IndexPreservingLens s t a b
cloneIndexedLens :: AnIndexedLens i s t a b -> IndexedLens i s t a b
overA :: Arrow ar => LensLike (Context a b) s t a b -> ar a b -> ar s t
storing :: ALens s t a b -> b -> s -> t
devoid :: Over p f Void Void a b
united :: Lens' a ()
head1 :: Traversable1 t => Lens' (t a) a
last1 :: Traversable1 t => Lens' (t a) a
locus :: IndexedComonadStore p => Lens (p a c s) (p b c s) a b
fusing :: Functor f => LensLike (Yoneda f) s t a b -> LensLike f s t a b
ilevels :: Applicative f => Traversing (Indexed i) f s t a b -> IndexedLensLike Int f s t (Level i a) (Level j b)
children :: Plated a => a -> [a]
rewrite :: Plated a => (a -> Maybe a) -> a -> a
rewriteOf :: ASetter a b a b -> (b -> Maybe a) -> a -> b
rewriteOn :: Plated a => ASetter s t a a -> (a -> Maybe a) -> s -> t
rewriteOnOf :: ASetter s t a b -> ASetter a b a b -> (b -> Maybe a) -> s -> t
rewriteM :: (Monad m, Plated a) => (a -> m (Maybe a)) -> a -> m a
rewriteMOf :: Monad m => LensLike (WrappedMonad m) a b a b -> (b -> m (Maybe a)) -> a -> m b
rewriteMOn :: (Monad m, Plated a) => LensLike (WrappedMonad m) s t a a -> (a -> m (Maybe a)) -> s -> m t
rewriteMOnOf :: Monad m => LensLike (WrappedMonad m) s t a b -> LensLike (WrappedMonad m) a b a b -> (b -> m (Maybe a)) -> s -> m t
universe :: Plated a => a -> [a]
universeOf :: Getting (Endo [a]) a a -> a -> [a]
universeOn :: Plated a => Getting (Endo [a]) s a -> s -> [a]
universeOnOf :: Getting (Endo [a]) s a -> Getting (Endo [a]) a a -> s -> [a]
cosmos :: Plated a => Fold a a
cosmosOf :: (Applicative f, Contravariant f) => LensLike' f a a -> LensLike' f a a
cosmosOn :: (Applicative f, Contravariant f, Plated a) => LensLike' f s a -> LensLike' f s a
cosmosOnOf :: (Applicative f, Contravariant f) => LensLike' f s a -> LensLike' f a a -> LensLike' f s a
transformOf :: ASetter a b a b -> (b -> b) -> a -> b
transformOn :: Plated a => ASetter s t a a -> (a -> a) -> s -> t
transformOnOf :: ASetter s t a b -> ASetter a b a b -> (b -> b) -> s -> t
transformM :: (Monad m, Plated a) => (a -> m a) -> a -> m a
transformMOf :: Monad m => LensLike (WrappedMonad m) a b a b -> (b -> m b) -> a -> m b
transformMOn :: (Monad m, Plated a) => LensLike (WrappedMonad m) s t a a -> (a -> m a) -> s -> m t
transformMOnOf :: Monad m => LensLike (WrappedMonad m) s t a b -> LensLike (WrappedMonad m) a b a b -> (b -> m b) -> s -> m t
contexts :: Plated a => a -> [Context a a a]
contextsOf :: ATraversal' a a -> a -> [Context a a a]
contextsOn :: Plated a => ATraversal s t a a -> s -> [Context a a t]
contextsOnOf :: ATraversal s t a a -> ATraversal' a a -> s -> [Context a a t]
holes :: Plated a => a -> [Pretext (->) a a a]
holesOn :: Conjoined p => Over p (Bazaar p a a) s t a a -> s -> [Pretext p a a t]
holesOnOf :: Conjoined p => LensLike (Bazaar p r r) s t a b -> Over p (Bazaar p r r) a b r r -> s -> [Pretext p r r t]
para :: Plated a => (a -> [r] -> r) -> a -> r
paraOf :: Getting (Endo [a]) a a -> (a -> [r] -> r) -> a -> r
deep :: (Conjoined p, Applicative f, Plated s) => Traversing p f s s a b -> Over p f s s a b
composOpFold :: Plated a => b -> (b -> b -> b) -> (a -> b) -> a -> b
parts :: Plated a => Lens' a [a]
gplate :: (Generic a, GPlated a (Rep a)) => Traversal' a a
gplate1 :: (Generic1 f, GPlated1 f (Rep1 f)) => Traversal' (f a) (f a)
prism :: (b -> t) -> (s -> Either t a) -> Prism s t a b
prism' :: (b -> s) -> (s -> Maybe a) -> Prism s s a b
withPrism :: APrism s t a b -> ((b -> t) -> (s -> Either t a) -> r) -> r
clonePrism :: APrism s t a b -> Prism s t a b
outside :: Representable p => APrism s t a b -> Lens (p t r) (p s r) (p b r) (p a r)
aside :: APrism s t a b -> Prism (e, s) (e, t) (e, a) (e, b)
without :: APrism s t a b -> APrism u v c d -> Prism (Either s u) (Either t v) (Either a c) (Either b d)
below :: Traversable f => APrism' s a -> Prism' (f s) (f a)
isn't :: APrism s t a b -> s -> Bool
matching :: APrism s t a b -> s -> Either t a
matching' :: LensLike (Either a) s t a b -> s -> Either t a
_Left :: Prism (Either a c) (Either b c) a b
_Right :: Prism (Either c a) (Either c b) a b
_Just :: Prism (Maybe a) (Maybe b) a b
_Nothing :: Prism' (Maybe a) ()
_Void :: Prism s s a Void
_Show :: (Read a, Show a) => Prism' String a
nearly :: a -> (a -> Bool) -> Prism' a ()
cloneTraversal :: ATraversal s t a b -> Traversal s t a b
ignored :: Applicative f => pafb -> s -> f s
unto :: (Profunctor p, Bifunctor p, Functor f) => (b -> t) -> Optic p f s t a b
un :: (Profunctor p, Bifunctor p, Functor f) => Getting a s a -> Optic' p f a s
re :: AReview t b -> Getter b t
review :: MonadReader b m => AReview t b -> m t
reviews :: MonadReader b m => AReview t b -> (t -> r) -> m r
reuse :: MonadState b m => AReview t b -> m t
reuses :: MonadState b m => AReview t b -> (t -> r) -> m r
reviewing :: (Bifunctor p, Functor f) => Optic Tagged Identity s t a b -> Optic' p f t b
sets :: (Profunctor p, Profunctor q, Settable f) => (p a b -> q s t) -> Optical p q f s t a b
setting :: ((a -> b) -> s -> t) -> IndexPreservingSetter s t a b
cloneSetter :: ASetter s t a b -> Setter s t a b
cloneIndexPreservingSetter :: ASetter s t a b -> IndexPreservingSetter s t a b
cloneIndexedSetter :: AnIndexedSetter i s t a b -> IndexedSetter i s t a b
mapped :: Functor f => Setter (f a) (f b) a b
lifted :: Monad m => Setter (m a) (m b) a b
contramapped :: Contravariant f => Setter (f b) (f a) a b
argument :: Profunctor p => Setter (p b r) (p a r) a b
assign :: MonadState s m => ASetter s s a b -> b -> m ()
modifying :: MonadState s m => ASetter s s a b -> (a -> b) -> m ()
scribe :: (MonadWriter t m, Monoid s) => ASetter s t a b -> b -> m ()
passing :: MonadWriter w m => Setter w w u v -> m (a, u -> v) -> m a
ipassing :: MonadWriter w m => IndexedSetter i w w u v -> m (a, i -> u -> v) -> m a
censoring :: MonadWriter w m => Setter w w u v -> (u -> v) -> m a -> m a
icensoring :: MonadWriter w m => IndexedSetter i w w u v -> (i -> u -> v) -> m a -> m a
locally :: MonadReader s m => ASetter s s a b -> (a -> b) -> m r -> m r
ilocally :: MonadReader s m => AnIndexedSetter i s s a b -> (i -> a -> b) -> m r -> m r
set' :: ASetter' s a -> a -> s -> s
imapOf :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t
iover :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t
iset :: AnIndexedSetter i s t a b -> (i -> b) -> s -> t
imodifying :: MonadState s m => AnIndexedSetter i s s a b -> (i -> a -> b) -> m ()
isets :: ((i -> a -> b) -> s -> t) -> IndexedSetter i s t a b
assignA :: Arrow p => ASetter s t a b -> p s b -> p s t
mapOf :: ASetter s t a b -> (a -> b) -> s -> t
makeLenses :: Name -> DecsQ
makeLensesFor :: [(String, String)] -> Name -> DecsQ
makeClassy :: Name -> DecsQ
makeClassyFor :: String -> String -> [(String, String)] -> Name -> DecsQ
makeClassy_ :: Name -> DecsQ
makeFields :: Name -> DecsQ
makeFieldsNoPrefix :: Name -> DecsQ
makeWrapped :: Name -> DecsQ
declareLenses :: DecsQ -> DecsQ
declareLensesFor :: [(String, String)] -> DecsQ -> DecsQ
declareClassy :: DecsQ -> DecsQ
declareClassyFor :: [(String, (String, String))] -> [(String, String)] -> DecsQ -> DecsQ
declareFields :: DecsQ -> DecsQ
declarePrisms :: DecsQ -> DecsQ
declareWrapped :: DecsQ -> DecsQ
makeLensesWith :: LensRules -> Name -> DecsQ
declareLensesWith :: LensRules -> DecsQ -> DecsQ
lensRules :: LensRules
lensRulesFor :: [(String, String)] -> LensRules
classyRules :: LensRules
classyRules_ :: LensRules
defaultFieldRules :: LensRules
camelCaseFields :: LensRules
classUnderscoreNoPrefixFields :: LensRules
underscoreFields :: LensRules
abbreviatedFields :: LensRules
lensField :: Lens' LensRules FieldNamer
lensClass :: Lens' LensRules ClassyNamer
simpleLenses :: Lens' LensRules Bool
createClass :: Lens' LensRules Bool
generateSignatures :: Lens' LensRules Bool
generateUpdateableOptics :: Lens' LensRules Bool
generateLazyPatterns :: Lens' LensRules Bool
generateRecordSyntax :: Lens' LensRules Bool
underscoreNoPrefixNamer :: FieldNamer
lookingupNamer :: [(String, String)] -> FieldNamer
mappingNamer :: (String -> [String]) -> FieldNamer
camelCaseNamer :: FieldNamer
classUnderscoreNoPrefixNamer :: FieldNamer
underscoreNamer :: FieldNamer
abbreviatedNamer :: FieldNamer
traversal :: ((a -> f b) -> s -> f t) -> LensLike f s t a b
traverseOf :: LensLike f s t a b -> (a -> f b) -> s -> f t
forOf :: LensLike f s t a b -> s -> (a -> f b) -> f t
sequenceAOf :: LensLike f s t (f b) b -> s -> f t
mapMOf :: LensLike (WrappedMonad m) s t a b -> (a -> m b) -> s -> m t
forMOf :: LensLike (WrappedMonad m) s t a b -> s -> (a -> m b) -> m t
sequenceOf :: LensLike (WrappedMonad m) s t (m b) b -> s -> m t
transposeOf :: LensLike ZipList s t [a] a -> s -> [t]
mapAccumLOf :: LensLike (State acc) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
mapAccumROf :: LensLike (Backwards (State acc)) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
scanr1Of :: LensLike (Backwards (State (Maybe a))) s t a a -> (a -> a -> a) -> s -> t
scanl1Of :: LensLike (State (Maybe a)) s t a a -> (a -> a -> a) -> s -> t
failover :: Alternative m => LensLike ((,) Any) s t a b -> (a -> b) -> s -> m t
ifailover :: Alternative m => Over (Indexed i) ((,) Any) s t a b -> (i -> a -> b) -> s -> m t
cloneIndexPreservingTraversal :: ATraversal s t a b -> IndexPreservingTraversal s t a b
cloneIndexedTraversal :: AnIndexedTraversal i s t a b -> IndexedTraversal i s t a b
cloneTraversal1 :: ATraversal1 s t a b -> Traversal1 s t a b
cloneIndexPreservingTraversal1 :: ATraversal1 s t a b -> IndexPreservingTraversal1 s t a b
cloneIndexedTraversal1 :: AnIndexedTraversal1 i s t a b -> IndexedTraversal1 i s t a b
partsOf :: Functor f => Traversing (->) f s t a a -> LensLike f s t [a] [a]
partsOf' :: ATraversal s t a a -> Lens s t [a] [a]
unsafePartsOf :: Functor f => Traversing (->) f s t a b -> LensLike f s t [a] [b]
unsafePartsOf' :: ATraversal s t a b -> Lens s t [a] [b]
holesOf :: Conjoined p => Over p (Bazaar p a a) s t a a -> s -> [Pretext p a a t]
holes1Of :: Conjoined p => Over p (Bazaar1 p a a) s t a a -> s -> NonEmpty (Pretext p a a t)
singular :: (HasCallStack, Conjoined p, Functor f) => Traversing p f s t a a -> Over p f s t a a
unsafeSingular :: (HasCallStack, Conjoined p, Functor f) => Traversing p f s t a b -> Over p f s t a b
both :: Bitraversable r => Traversal (r a a) (r b b) a b
both1 :: Bitraversable1 r => Traversal1 (r a a) (r b b) a b
beside :: (Representable q, Applicative (Rep q), Applicative f, Bitraversable r) => Optical p q f s t a b -> Optical p q f s' t' a b -> Optical p q f (r s s') (r t t') a b
taking :: (Conjoined p, Applicative f) => Int -> Traversing p f s t a a -> Over p f s t a a
dropping :: (Conjoined p, Applicative f) => Int -> Over p (Indexing f) s t a a -> Over p f s t a a
failing :: (Conjoined p, Applicative f) => Traversing p f s t a b -> Over p f s t a b -> Over p f s t a b
deepOf :: (Conjoined p, Applicative f) => LensLike f s t s t -> Traversing p f s t a b -> Over p f s t a b
traversed :: Traversable f => IndexedTraversal Int (f a) (f b) a b
traversed1 :: Traversable1 f => IndexedTraversal1 Int (f a) (f b) a b
traversed64 :: Traversable f => IndexedTraversal Int64 (f a) (f b) a b
elementOf :: Applicative f => LensLike (Indexing f) s t a a -> Int -> IndexedLensLike Int f s t a a
element :: Traversable t => Int -> IndexedTraversal' Int (t a) a
elementsOf :: Applicative f => LensLike (Indexing f) s t a a -> (Int -> Bool) -> IndexedLensLike Int f s t a a
ipartsOf :: forall i p f s t a. (Indexable [i] p, Functor f) => Traversing (Indexed i) f s t a a -> Over p f s t [a] [a]
ipartsOf' :: forall i p f s t a. (Indexable [i] p, Functor f) => Over (Indexed i) (Bazaar' (Indexed i) a) s t a a -> Over p f s t [a] [a]
iunsafePartsOf :: forall i p f s t a b. (Indexable [i] p, Functor f) => Traversing (Indexed i) f s t a b -> Over p f s t [a] [b]
iunsafePartsOf' :: forall i s t a b. Over (Indexed i) (Bazaar (Indexed i) a b) s t a b -> IndexedLens [i] s t [a] [b]
itraverseOf :: (Indexed i a (f b) -> s -> f t) -> (i -> a -> f b) -> s -> f t
iforOf :: (Indexed i a (f b) -> s -> f t) -> s -> (i -> a -> f b) -> f t
imapMOf :: Over (Indexed i) (WrappedMonad m) s t a b -> (i -> a -> m b) -> s -> m t
iforMOf :: (Indexed i a (WrappedMonad m b) -> s -> WrappedMonad m t) -> s -> (i -> a -> m b) -> m t
imapAccumROf :: Over (Indexed i) (Backwards (State acc)) s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
imapAccumLOf :: Over (Indexed i) (State acc) s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
traverseByOf :: Traversal s t a b -> (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (a -> f b) -> s -> f t
sequenceByOf :: Traversal s t (f b) b -> (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> s -> f t
loci :: Traversal (Bazaar (->) a c s) (Bazaar (->) b c s) a b
iloci :: IndexedTraversal i (Bazaar (Indexed i) a c s) (Bazaar (Indexed i) b c s) a b
confusing :: Applicative f => LensLike (Curried (Yoneda f) (Yoneda f)) s t a b -> LensLike f s t a b
_1' :: Field1 s t a b => Lens s t a b
_2' :: Field2 s t a b => Lens s t a b
_3' :: Field3 s t a b => Lens s t a b
_4' :: Field4 s t a b => Lens s t a b
_5' :: Field5 s t a b => Lens s t a b
_6' :: Field6 s t a b => Lens s t a b
_7' :: Field7 s t a b => Lens s t a b
_8' :: Field8 s t a b => Lens s t a b
_9' :: Field9 s t a b => Lens s t a b
_10' :: Field10 s t a b => Lens s t a b
_11' :: Field11 s t a b => Lens s t a b
_12' :: Field12 s t a b => Lens s t a b
_13' :: Field13 s t a b => Lens s t a b
_14' :: Field14 s t a b => Lens s t a b
_15' :: Field15 s t a b => Lens s t a b
_16' :: Field16 s t a b => Lens s t a b
_17' :: Field17 s t a b => Lens s t a b
_18' :: Field18 s t a b => Lens s t a b
_19' :: Field19 s t a b => Lens s t a b
_Unwrapped' :: Wrapped s => Iso' (Unwrapped s) s
_Wrapping' :: Wrapped s => (Unwrapped s -> s) -> Iso' s (Unwrapped s)
_Unwrapping' :: Wrapped s => (Unwrapped s -> s) -> Iso' (Unwrapped s) s
_Wrapped :: Rewrapping s t => Iso s t (Unwrapped s) (Unwrapped t)
_Unwrapped :: Rewrapping s t => Iso (Unwrapped t) (Unwrapped s) t s
_Wrapping :: Rewrapping s t => (Unwrapped s -> s) -> Iso s t (Unwrapped s) (Unwrapped t)
_Unwrapping :: Rewrapping s t => (Unwrapped s -> s) -> Iso (Unwrapped t) (Unwrapped s) t s
op :: Wrapped s => (Unwrapped s -> s) -> s -> Unwrapped s
ala :: (Functor f, Rewrapping s t) => (Unwrapped s -> s) -> ((Unwrapped t -> t) -> f s) -> f (Unwrapped s)
alaf :: (Functor f, Functor g, Rewrapping s t) => (Unwrapped s -> s) -> (f t -> g s) -> f (Unwrapped t) -> g (Unwrapped s)
_GWrapped' :: (Generic s, D1 d (C1 c (S1 s' (Rec0 a))) ~ Rep s, Unwrapped s ~ GUnwrapped (Rep s)) => Iso' s (Unwrapped s)

Documentation

class Contravariant (f :: Type -> Type) where #

The class of contravariant functors.

Whereas in Haskell, one can think of a Functor as containing or producing values, a contravariant functor is a functor that can be thought of as consuming values.

As an example, consider the type of predicate functions a -> Bool. One such predicate might be negative x = x < 0, which classifies integers as to whether they are negative. However, given this predicate, we can re-use it in other situations, providing we have a way to map values to integers. For instance, we can use the negative predicate on a person's bank balance to work out if they are currently overdrawn:

newtype Predicate a = Predicate { getPredicate :: a -> Bool }

instance Contravariant Predicate where
  contramap :: (a' -> a) -> (Predicate a -> Predicate a')
  contramap f (Predicate p) = Predicate (p . f)
                                         |   `- First, map the input...
                                         `----- then apply the predicate.

overdrawn :: Predicate Person
overdrawn = contramap personBankBalance negative

Any instance should be subject to the following laws:

Identity: contramap id = id
Composition: contramap (g . f) = contramap f . contramap g

Note, that the second law follows from the free theorem of the type of contramap and the first law, so you need only check that the former condition holds.

Minimal complete definition

contramap

Methods

contramap :: (a' -> a) -> f a -> f a' #

(>$) :: b -> f b -> f a infixl 4 #

Replace all locations in the output with the same value. The default definition is contramap . const, but this may be overridden with a more efficient version.

Instances

Instances details

Contravariant Comparison	A `Comparison` is a `Contravariant` `Functor`, because `contramap` can apply its function argument to each input of the comparison function.
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a' -> a) -> Comparison a -> Comparison a' # (>$) :: b -> Comparison b -> Comparison a #
Contravariant Equivalence	Equivalence relations are `Contravariant`, because you can apply the contramapped function to each input to the equivalence relation.
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a' -> a) -> Equivalence a -> Equivalence a' # (>$) :: b -> Equivalence b -> Equivalence a #
Contravariant Predicate	A `Predicate` is a `Contravariant` `Functor`, because `contramap` can apply its function argument to the input of the predicate. Without newtypes `contramap f` equals precomposing with `f` (= `(. f)`). contramap :: (a' -> a) -> (Predicate a -> Predicate a') contramap f (Predicate g) = Predicate (g . f)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a' -> a) -> Predicate a -> Predicate a' # (>$) :: b -> Predicate b -> Predicate a #
Contravariant (Op a)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a' -> a0) -> Op a a0 -> Op a a' # (>$) :: b -> Op a b -> Op a a0 #
Contravariant (Proxy :: Type -> Type)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a' -> a) -> Proxy a -> Proxy a' # (>$) :: b -> Proxy b -> Proxy a #
Contravariant (U1 :: Type -> Type)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a' -> a) -> U1 a -> U1 a' # (>$) :: b -> U1 b -> U1 a #
Contravariant (V1 :: Type -> Type)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a' -> a) -> V1 a -> V1 a' # (>$) :: b -> V1 b -> V1 a #
Contravariant f => Contravariant (Indexing f) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods contramap :: (a' -> a) -> Indexing f a -> Indexing f a' # (>$) :: b -> Indexing f b -> Indexing f a #
Contravariant f => Contravariant (Indexing64 f) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods contramap :: (a' -> a) -> Indexing64 f a -> Indexing64 f a' # (>$) :: b -> Indexing64 f b -> Indexing64 f a #
Contravariant m => Contravariant (MaybeT m)
Instance details Defined in Control.Monad.Trans.Maybe Methods contramap :: (a' -> a) -> MaybeT m a -> MaybeT m a' # (>$) :: b -> MaybeT m b -> MaybeT m a #
Contravariant (Const a :: Type -> Type)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a' -> a0) -> Const a a0 -> Const a a' # (>$) :: b -> Const a b -> Const a a0 #
Contravariant f => Contravariant (Alt f)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a' -> a) -> Alt f a -> Alt f a' # (>$) :: b -> Alt f b -> Alt f a #
Contravariant f => Contravariant (Rec1 f)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a' -> a) -> Rec1 f a -> Rec1 f a' # (>$) :: b -> Rec1 f b -> Rec1 f a #
(Contravariant f, Functor g) => Contravariant (ComposeCF f g)
Instance details Defined in Data.Functor.Contravariant.Compose Methods contramap :: (a' -> a) -> ComposeCF f g a -> ComposeCF f g a' # (>$) :: b -> ComposeCF f g b -> ComposeCF f g a #
(Functor f, Contravariant g) => Contravariant (ComposeFC f g)
Instance details Defined in Data.Functor.Contravariant.Compose Methods contramap :: (a' -> a) -> ComposeFC f g a -> ComposeFC f g a' # (>$) :: b -> ComposeFC f g b -> ComposeFC f g a #
Contravariant f => Contravariant (AlongsideLeft f b) Source #
Instance details Defined in Control.Lens.Internal.Getter Methods contramap :: (a' -> a) -> AlongsideLeft f b a -> AlongsideLeft f b a' # (>$) :: b0 -> AlongsideLeft f b b0 -> AlongsideLeft f b a #
Contravariant f => Contravariant (AlongsideRight f a) Source #
Instance details Defined in Control.Lens.Internal.Getter Methods contramap :: (a' -> a0) -> AlongsideRight f a a0 -> AlongsideRight f a a' # (>$) :: b -> AlongsideRight f a b -> AlongsideRight f a a0 #
Contravariant (Effect m r) Source #
Instance details Defined in Control.Lens.Internal.Zoom Methods contramap :: (a' -> a) -> Effect m r a -> Effect m r a' # (>$) :: b -> Effect m r b -> Effect m r a #
Contravariant f => Contravariant (Backwards f)	Derived instance.
Instance details Defined in Control.Applicative.Backwards Methods contramap :: (a' -> a) -> Backwards f a -> Backwards f a' # (>$) :: b -> Backwards f b -> Backwards f a #
Contravariant m => Contravariant (ExceptT e m)
Instance details Defined in Control.Monad.Trans.Except Methods contramap :: (a' -> a) -> ExceptT e m a -> ExceptT e m a' # (>$) :: b -> ExceptT e m b -> ExceptT e m a #
Contravariant f => Contravariant (IdentityT f)
Instance details Defined in Control.Monad.Trans.Identity Methods contramap :: (a' -> a) -> IdentityT f a -> IdentityT f a' # (>$) :: b -> IdentityT f b -> IdentityT f a #
Contravariant m => Contravariant (ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods contramap :: (a' -> a) -> ReaderT r m a -> ReaderT r m a' # (>$) :: b -> ReaderT r m b -> ReaderT r m a #
Contravariant m => Contravariant (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Lazy Methods contramap :: (a' -> a) -> StateT s m a -> StateT s m a' # (>$) :: b -> StateT s m b -> StateT s m a #
Contravariant m => Contravariant (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Strict Methods contramap :: (a' -> a) -> StateT s m a -> StateT s m a' # (>$) :: b -> StateT s m b -> StateT s m a #
Contravariant m => Contravariant (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods contramap :: (a' -> a) -> WriterT w m a -> WriterT w m a' # (>$) :: b -> WriterT w m b -> WriterT w m a #
Contravariant m => Contravariant (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods contramap :: (a' -> a) -> WriterT w m a -> WriterT w m a' # (>$) :: b -> WriterT w m b -> WriterT w m a #
Contravariant (Constant a :: Type -> Type)
Instance details Defined in Data.Functor.Constant Methods contramap :: (a' -> a0) -> Constant a a0 -> Constant a a' # (>$) :: b -> Constant a b -> Constant a a0 #
Contravariant f => Contravariant (Reverse f)	Derived instance.
Instance details Defined in Data.Functor.Reverse Methods contramap :: (a' -> a) -> Reverse f a -> Reverse f a' # (>$) :: b -> Reverse f b -> Reverse f a #
(Contravariant f, Contravariant g) => Contravariant (Product f g)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a' -> a) -> Product f g a -> Product f g a' # (>$) :: b -> Product f g b -> Product f g a #
(Contravariant f, Contravariant g) => Contravariant (Sum f g)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a' -> a) -> Sum f g a -> Sum f g a' # (>$) :: b -> Sum f g b -> Sum f g a #
(Contravariant f, Contravariant g) => Contravariant (f :*: g)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a' -> a) -> (f :: g) a -> (f :: g) a' # (>$) :: b -> (f :: g) b -> (f :: g) a #
(Contravariant f, Contravariant g) => Contravariant (f :+: g)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a' -> a) -> (f :+: g) a -> (f :+: g) a' # (>$) :: b -> (f :+: g) b -> (f :+: g) a #
Contravariant (K1 i c :: Type -> Type)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a' -> a) -> K1 i c a -> K1 i c a' # (>$) :: b -> K1 i c b -> K1 i c a #
Contravariant (Forget r a :: Type -> Type)
Instance details Defined in Data.Profunctor.Types Methods contramap :: (a' -> a0) -> Forget r a a0 -> Forget r a a' # (>$) :: b -> Forget r a b -> Forget r a a0 #
Contravariant f => Contravariant (Star f a)
Instance details Defined in Data.Profunctor.Types Methods contramap :: (a' -> a0) -> Star f a a0 -> Star f a a' # (>$) :: b -> Star f a b -> Star f a a0 #
(Functor f, Contravariant g) => Contravariant (Compose f g)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a' -> a) -> Compose f g a -> Compose f g a' # (>$) :: b -> Compose f g b -> Compose f g a #
(Functor f, Contravariant g) => Contravariant (f :.: g)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a' -> a) -> (f :.: g) a -> (f :.: g) a' # (>$) :: b -> (f :.: g) b -> (f :.: g) a #
Contravariant f => Contravariant (M1 i c f)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a' -> a) -> M1 i c f a -> M1 i c f a' # (>$) :: b -> M1 i c f b -> M1 i c f a #
(Profunctor p, Contravariant g) => Contravariant (BazaarT p g a b) Source #
Instance details Defined in Control.Lens.Internal.Bazaar Methods contramap :: (a' -> a0) -> BazaarT p g a b a0 -> BazaarT p g a b a' # (>$) :: b0 -> BazaarT p g a b b0 -> BazaarT p g a b a0 #
(Profunctor p, Contravariant g) => Contravariant (BazaarT1 p g a b) Source #
Instance details Defined in Control.Lens.Internal.Bazaar Methods contramap :: (a' -> a0) -> BazaarT1 p g a b a0 -> BazaarT1 p g a b a' # (>$) :: b0 -> BazaarT1 p g a b b0 -> BazaarT1 p g a b a0 #
(Profunctor p, Contravariant g) => Contravariant (PretextT p g a b) Source #
Instance details Defined in Control.Lens.Internal.Context Methods contramap :: (a' -> a0) -> PretextT p g a b a0 -> PretextT p g a b a' # (>$) :: b0 -> PretextT p g a b b0 -> PretextT p g a b a0 #
Contravariant f => Contravariant (TakingWhile p f a b) Source #
Instance details Defined in Control.Lens.Internal.Magma Methods contramap :: (a' -> a0) -> TakingWhile p f a b a0 -> TakingWhile p f a b a' # (>$) :: b0 -> TakingWhile p f a b b0 -> TakingWhile p f a b a0 #
Contravariant (EffectRWS w st m s) Source #
Instance details Defined in Control.Lens.Internal.Zoom Methods contramap :: (a' -> a) -> EffectRWS w st m s a -> EffectRWS w st m s a' # (>$) :: b -> EffectRWS w st m s b -> EffectRWS w st m s a #
Contravariant m => Contravariant (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Lazy Methods contramap :: (a' -> a) -> RWST r w s m a -> RWST r w s m a' # (>$) :: b -> RWST r w s m b -> RWST r w s m a #
Contravariant m => Contravariant (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Strict Methods contramap :: (a' -> a) -> RWST r w s m a -> RWST r w s m a' # (>$) :: b -> RWST r w s m b -> RWST r w s m a #

class (forall a. Functor (p a)) => Bifunctor (p :: Type -> Type -> Type) where #

A bifunctor is a type constructor that takes two type arguments and is a functor in both arguments. That is, unlike with Functor, a type constructor such as Either does not need to be partially applied for a Bifunctor instance, and the methods in this class permit mapping functions over the Left value or the Right value, or both at the same time.

Formally, the class Bifunctor represents a bifunctor from Hask -> Hask.

Intuitively it is a bifunctor where both the first and second arguments are covariant.

You can define a Bifunctor by either defining bimap or by defining both first and second. A partially applied Bifunctor must be a Functor and the second method must agree with fmap. From this it follows that:

second id = id

If you supply bimap, you should ensure that:

bimap id id ≡ id

If you supply first and second, ensure:

first id ≡ id
second id ≡ id

If you supply both, you should also ensure:

bimap f g ≡ first f . second g

These ensure by parametricity:

bimap  (f . g) (h . i) ≡ bimap f h . bimap g i
first  (f . g) ≡ first  f . first  g
second (f . g) ≡ second f . second g

Since 4.18.0.0 Functor is a superclass of 'Bifunctor.

Since: base-4.8.0.0

Minimal complete definition

bimap | first, second

Methods

bimap :: (a -> b) -> (c -> d) -> p a c -> p b d #

Map over both arguments at the same time.

bimap f g ≡ first f . second g

Examples

Expand

>>> bimap toUpper (+1) ('j', 3)
('J',4)

>>> bimap toUpper (+1) (Left 'j')
Left 'J'

>>> bimap toUpper (+1) (Right 3)
Right 4

Instances

Instances details

Bifunctor Either	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> Either a c -> Either b d # first :: (a -> b) -> Either a c -> Either b c # second :: (b -> c) -> Either a b -> Either a c #
Bifunctor Arg	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods bimap :: (a -> b) -> (c -> d) -> Arg a c -> Arg b d # first :: (a -> b) -> Arg a c -> Arg b c # second :: (b -> c) -> Arg a b -> Arg a c #
Bifunctor Either
Instance details Defined in Data.Strict.Either Methods bimap :: (a -> b) -> (c -> d) -> Either a c -> Either b d # first :: (a -> b) -> Either a c -> Either b c # second :: (b -> c) -> Either a b -> Either a c #
Bifunctor These
Instance details Defined in Data.Strict.These Methods bimap :: (a -> b) -> (c -> d) -> These a c -> These b d # first :: (a -> b) -> These a c -> These b c # second :: (b -> c) -> These a b -> These a c #
Bifunctor Pair
Instance details Defined in Data.Strict.Tuple Methods bimap :: (a -> b) -> (c -> d) -> Pair a c -> Pair b d # first :: (a -> b) -> Pair a c -> Pair b c # second :: (b -> c) -> Pair a b -> Pair a c #
Bifunctor These
Instance details Defined in Data.These Methods bimap :: (a -> b) -> (c -> d) -> These a c -> These b d # first :: (a -> b) -> These a c -> These b c # second :: (b -> c) -> These a b -> These a c #
Bifunctor (,)	Class laws for tuples hold only up to laziness. Both `first` `id` and `second` `id` are lazier than `id` (and `fmap` `id`): `>>>` first id (undefined :: (Int, Word)) `seq` ()() `>>>` second id (undefined :: (Int, Word)) `seq` ()() `>>>` id (undefined :: (Int, Word)) `seq` ()*** Exception: Prelude.undefined Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> (a, c) -> (b, d) # first :: (a -> b) -> (a, c) -> (b, c) # second :: (b -> c) -> (a, b) -> (a, c) #
Bifunctor (Const :: Type -> Type -> Type)	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> Const a c -> Const b d # first :: (a -> b) -> Const a c -> Const b c # second :: (b -> c) -> Const a b -> Const a c #
Functor f => Bifunctor (CofreeF f)
Instance details Defined in Control.Comonad.Trans.Cofree Methods bimap :: (a -> b) -> (c -> d) -> CofreeF f a c -> CofreeF f b d # first :: (a -> b) -> CofreeF f a c -> CofreeF f b c # second :: (b -> c) -> CofreeF f a b -> CofreeF f a c #
Functor f => Bifunctor (FreeF f)
Instance details Defined in Control.Monad.Trans.Free Methods bimap :: (a -> b) -> (c -> d) -> FreeF f a c -> FreeF f b d # first :: (a -> b) -> FreeF f a c -> FreeF f b c # second :: (b -> c) -> FreeF f a b -> FreeF f a c #
Functor f => Bifunctor (AlongsideLeft f) Source #
Instance details Defined in Control.Lens.Internal.Getter Methods bimap :: (a -> b) -> (c -> d) -> AlongsideLeft f a c -> AlongsideLeft f b d # first :: (a -> b) -> AlongsideLeft f a c -> AlongsideLeft f b c # second :: (b -> c) -> AlongsideLeft f a b -> AlongsideLeft f a c #
Functor f => Bifunctor (AlongsideRight f) Source #
Instance details Defined in Control.Lens.Internal.Getter Methods bimap :: (a -> b) -> (c -> d) -> AlongsideRight f a c -> AlongsideRight f b d # first :: (a -> b) -> AlongsideRight f a c -> AlongsideRight f b c # second :: (b -> c) -> AlongsideRight f a b -> AlongsideRight f a c #
Bifunctor (Tagged :: Type -> Type -> Type)
Instance details Defined in Data.Tagged Methods bimap :: (a -> b) -> (c -> d) -> Tagged a c -> Tagged b d # first :: (a -> b) -> Tagged a c -> Tagged b c # second :: (b -> c) -> Tagged a b -> Tagged a c #
Bifunctor (Constant :: Type -> Type -> Type)
Instance details Defined in Data.Functor.Constant Methods bimap :: (a -> b) -> (c -> d) -> Constant a c -> Constant b d # first :: (a -> b) -> Constant a c -> Constant b c # second :: (b -> c) -> Constant a b -> Constant a c #
Bifunctor ((,,) x1)	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> (x1, a, c) -> (x1, b, d) # first :: (a -> b) -> (x1, a, c) -> (x1, b, c) # second :: (b -> c) -> (x1, a, b) -> (x1, a, c) #
Bifunctor (K1 i :: Type -> Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> K1 i a c -> K1 i b d # first :: (a -> b) -> K1 i a c -> K1 i b c # second :: (b -> c) -> K1 i a b -> K1 i a c #
Bifunctor ((,,,) x1 x2)	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> (x1, x2, a, c) -> (x1, x2, b, d) # first :: (a -> b) -> (x1, x2, a, c) -> (x1, x2, b, c) # second :: (b -> c) -> (x1, x2, a, b) -> (x1, x2, a, c) #
Functor f => Bifunctor (Clown f :: Type -> Type -> Type)
Instance details Defined in Data.Bifunctor.Clown Methods bimap :: (a -> b) -> (c -> d) -> Clown f a c -> Clown f b d # first :: (a -> b) -> Clown f a c -> Clown f b c # second :: (b -> c) -> Clown f a b -> Clown f a c #
Bifunctor p => Bifunctor (Flip p)
Instance details Defined in Data.Bifunctor.Flip Methods bimap :: (a -> b) -> (c -> d) -> Flip p a c -> Flip p b d # first :: (a -> b) -> Flip p a c -> Flip p b c # second :: (b -> c) -> Flip p a b -> Flip p a c #
Functor g => Bifunctor (Joker g :: Type -> Type -> Type)
Instance details Defined in Data.Bifunctor.Joker Methods bimap :: (a -> b) -> (c -> d) -> Joker g a c -> Joker g b d # first :: (a -> b) -> Joker g a c -> Joker g b c # second :: (b -> c) -> Joker g a b -> Joker g a c #
Bifunctor p => Bifunctor (WrappedBifunctor p)
Instance details Defined in Data.Bifunctor.Wrapped Methods bimap :: (a -> b) -> (c -> d) -> WrappedBifunctor p a c -> WrappedBifunctor p b d # first :: (a -> b) -> WrappedBifunctor p a c -> WrappedBifunctor p b c # second :: (b -> c) -> WrappedBifunctor p a b -> WrappedBifunctor p a c #
Bifunctor ((,,,,) x1 x2 x3)	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, a, c) -> (x1, x2, x3, b, d) # first :: (a -> b) -> (x1, x2, x3, a, c) -> (x1, x2, x3, b, c) # second :: (b -> c) -> (x1, x2, x3, a, b) -> (x1, x2, x3, a, c) #
(Bifunctor f, Bifunctor g) => Bifunctor (Product f g)
Instance details Defined in Data.Bifunctor.Product Methods bimap :: (a -> b) -> (c -> d) -> Product f g a c -> Product f g b d # first :: (a -> b) -> Product f g a c -> Product f g b c # second :: (b -> c) -> Product f g a b -> Product f g a c #
(Bifunctor p, Bifunctor q) => Bifunctor (Sum p q)
Instance details Defined in Data.Bifunctor.Sum Methods bimap :: (a -> b) -> (c -> d) -> Sum p q a c -> Sum p q b d # first :: (a -> b) -> Sum p q a c -> Sum p q b c # second :: (b -> c) -> Sum p q a b -> Sum p q a c #
Bifunctor ((,,,,,) x1 x2 x3 x4)	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, x4, a, c) -> (x1, x2, x3, x4, b, d) # first :: (a -> b) -> (x1, x2, x3, x4, a, c) -> (x1, x2, x3, x4, b, c) # second :: (b -> c) -> (x1, x2, x3, x4, a, b) -> (x1, x2, x3, x4, a, c) #
(Functor f, Bifunctor p) => Bifunctor (Tannen f p)
Instance details Defined in Data.Bifunctor.Tannen Methods bimap :: (a -> b) -> (c -> d) -> Tannen f p a c -> Tannen f p b d # first :: (a -> b) -> Tannen f p a c -> Tannen f p b c # second :: (b -> c) -> Tannen f p a b -> Tannen f p a c #
Bifunctor ((,,,,,,) x1 x2 x3 x4 x5)	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, x4, x5, a, c) -> (x1, x2, x3, x4, x5, b, d) # first :: (a -> b) -> (x1, x2, x3, x4, x5, a, c) -> (x1, x2, x3, x4, x5, b, c) # second :: (b -> c) -> (x1, x2, x3, x4, x5, a, b) -> (x1, x2, x3, x4, x5, a, c) #
(Bifunctor p, Functor f, Functor g) => Bifunctor (Biff p f g)
Instance details Defined in Data.Bifunctor.Biff Methods bimap :: (a -> b) -> (c -> d) -> Biff p f g a c -> Biff p f g b d # first :: (a -> b) -> Biff p f g a c -> Biff p f g b c # second :: (b -> c) -> Biff p f g a b -> Biff p f g a c #

class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where #

Functors representing data structures that can be transformed to structures of the same shape by performing an Applicative (or, therefore, Monad) action on each element from left to right.

A more detailed description of what same shape means, the various methods, how traversals are constructed, and example advanced use-cases can be found in the Overview section of Data.Traversable.

For the class laws see the Laws section of Data.Traversable.

Minimal complete definition

traverse | sequenceA

Methods

traverse :: Applicative f => (a -> f b) -> t a -> f (t b) #

Map each element of a structure to an action, evaluate these actions from left to right, and collect the results. For a version that ignores the results see traverse_.

Examples

Expand

Basic usage:

In the first two examples we show each evaluated action mapping to the output structure.

>>> traverse Just [1,2,3,4]
Just [1,2,3,4]

>>> traverse id [Right 1, Right 2, Right 3, Right 4]
Right [1,2,3,4]

In the next examples, we show that Nothing and Left values short circuit the created structure.

>>> traverse (const Nothing) [1,2,3,4]
Nothing

>>> traverse (\x -> if odd x then Just x else Nothing)  [1,2,3,4]
Nothing

>>> traverse id [Right 1, Right 2, Right 3, Right 4, Left 0]
Left 0

Instances

Instances details

Traversable ZipList	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> ZipList a -> f (ZipList b) # sequenceA :: Applicative f => ZipList (f a) -> f (ZipList a) # mapM :: Monad m => (a -> m b) -> ZipList a -> m (ZipList b) # sequence :: Monad m => ZipList (m a) -> m (ZipList a) #
Traversable Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods traverse :: Applicative f => (a -> f b) -> Complex a -> f (Complex b) # sequenceA :: Applicative f => Complex (f a) -> f (Complex a) # mapM :: Monad m => (a -> m b) -> Complex a -> m (Complex b) # sequence :: Monad m => Complex (m a) -> m (Complex a) #
Traversable Identity	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Identity a -> f (Identity b) # sequenceA :: Applicative f => Identity (f a) -> f (Identity a) # mapM :: Monad m => (a -> m b) -> Identity a -> m (Identity b) # sequence :: Monad m => Identity (m a) -> m (Identity a) #
Traversable First	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> First a -> f (First b) # sequenceA :: Applicative f => First (f a) -> f (First a) # mapM :: Monad m => (a -> m b) -> First a -> m (First b) # sequence :: Monad m => First (m a) -> m (First a) #
Traversable Last	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) # sequenceA :: Applicative f => Last (f a) -> f (Last a) # mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) # sequence :: Monad m => Last (m a) -> m (Last a) #
Traversable Down	Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Down a -> f (Down b) # sequenceA :: Applicative f => Down (f a) -> f (Down a) # mapM :: Monad m => (a -> m b) -> Down a -> m (Down b) # sequence :: Monad m => Down (m a) -> m (Down a) #
Traversable First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> First a -> f (First b) # sequenceA :: Applicative f => First (f a) -> f (First a) # mapM :: Monad m => (a -> m b) -> First a -> m (First b) # sequence :: Monad m => First (m a) -> m (First a) #
Traversable Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) # sequenceA :: Applicative f => Last (f a) -> f (Last a) # mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) # sequence :: Monad m => Last (m a) -> m (Last a) #
Traversable Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Max a -> f (Max b) # sequenceA :: Applicative f => Max (f a) -> f (Max a) # mapM :: Monad m => (a -> m b) -> Max a -> m (Max b) # sequence :: Monad m => Max (m a) -> m (Max a) #
Traversable Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Min a -> f (Min b) # sequenceA :: Applicative f => Min (f a) -> f (Min a) # mapM :: Monad m => (a -> m b) -> Min a -> m (Min b) # sequence :: Monad m => Min (m a) -> m (Min a) #
Traversable Dual	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b) # sequenceA :: Applicative f => Dual (f a) -> f (Dual a) # mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b) # sequence :: Monad m => Dual (m a) -> m (Dual a) #
Traversable Product	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b) # sequenceA :: Applicative f => Product (f a) -> f (Product a) # mapM :: Monad m => (a -> m b) -> Product a -> m (Product b) # sequence :: Monad m => Product (m a) -> m (Product a) #
Traversable Sum	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b) # sequenceA :: Applicative f => Sum (f a) -> f (Sum a) # mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b) # sequence :: Monad m => Sum (m a) -> m (Sum a) #
Traversable NonEmpty	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> NonEmpty a -> f (NonEmpty b) # sequenceA :: Applicative f => NonEmpty (f a) -> f (NonEmpty a) # mapM :: Monad m => (a -> m b) -> NonEmpty a -> m (NonEmpty b) # sequence :: Monad m => NonEmpty (m a) -> m (NonEmpty a) #
Traversable Par1	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Par1 a -> f (Par1 b) # sequenceA :: Applicative f => Par1 (f a) -> f (Par1 a) # mapM :: Monad m => (a -> m b) -> Par1 a -> m (Par1 b) # sequence :: Monad m => Par1 (m a) -> m (Par1 a) #
Traversable IntMap	Traverses in order of increasing key.
Instance details Defined in Data.IntMap.Internal Methods traverse :: Applicative f => (a -> f b) -> IntMap a -> f (IntMap b) # sequenceA :: Applicative f => IntMap (f a) -> f (IntMap a) # mapM :: Monad m => (a -> m b) -> IntMap a -> m (IntMap b) # sequence :: Monad m => IntMap (m a) -> m (IntMap a) #
Traversable Digit
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Digit a -> f (Digit b) # sequenceA :: Applicative f => Digit (f a) -> f (Digit a) # mapM :: Monad m => (a -> m b) -> Digit a -> m (Digit b) # sequence :: Monad m => Digit (m a) -> m (Digit a) #
Traversable Elem
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Elem a -> f (Elem b) # sequenceA :: Applicative f => Elem (f a) -> f (Elem a) # mapM :: Monad m => (a -> m b) -> Elem a -> m (Elem b) # sequence :: Monad m => Elem (m a) -> m (Elem a) #
Traversable FingerTree
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> FingerTree a -> f (FingerTree b) # sequenceA :: Applicative f => FingerTree (f a) -> f (FingerTree a) # mapM :: Monad m => (a -> m b) -> FingerTree a -> m (FingerTree b) # sequence :: Monad m => FingerTree (m a) -> m (FingerTree a) #
Traversable Node
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Node a -> f (Node b) # sequenceA :: Applicative f => Node (f a) -> f (Node a) # mapM :: Monad m => (a -> m b) -> Node a -> m (Node b) # sequence :: Monad m => Node (m a) -> m (Node a) #
Traversable Seq
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Seq a -> f (Seq b) # sequenceA :: Applicative f => Seq (f a) -> f (Seq a) # mapM :: Monad m => (a -> m b) -> Seq a -> m (Seq b) # sequence :: Monad m => Seq (m a) -> m (Seq a) #
Traversable ViewL
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> ViewL a -> f (ViewL b) # sequenceA :: Applicative f => ViewL (f a) -> f (ViewL a) # mapM :: Monad m => (a -> m b) -> ViewL a -> m (ViewL b) # sequence :: Monad m => ViewL (m a) -> m (ViewL a) #
Traversable ViewR
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> ViewR a -> f (ViewR b) # sequenceA :: Applicative f => ViewR (f a) -> f (ViewR a) # mapM :: Monad m => (a -> m b) -> ViewR a -> m (ViewR b) # sequence :: Monad m => ViewR (m a) -> m (ViewR a) #
Traversable Tree
Instance details Defined in Data.Tree Methods traverse :: Applicative f => (a -> f b) -> Tree a -> f (Tree b) # sequenceA :: Applicative f => Tree (f a) -> f (Tree a) # mapM :: Monad m => (a -> m b) -> Tree a -> m (Tree b) # sequence :: Monad m => Tree (m a) -> m (Tree a) #
Traversable Deque Source #
Instance details Defined in Control.Lens.Internal.Deque Methods traverse :: Applicative f => (a -> f b) -> Deque a -> f (Deque b) # sequenceA :: Applicative f => Deque (f a) -> f (Deque a) # mapM :: Monad m => (a -> m b) -> Deque a -> m (Deque b) # sequence :: Monad m => Deque (m a) -> m (Deque a) #
Traversable Array
Instance details Defined in Data.Primitive.Array Methods traverse :: Applicative f => (a -> f b) -> Array a -> f (Array b) # sequenceA :: Applicative f => Array (f a) -> f (Array a) # mapM :: Monad m => (a -> m b) -> Array a -> m (Array b) # sequence :: Monad m => Array (m a) -> m (Array a) #
Traversable SmallArray
Instance details Defined in Data.Primitive.SmallArray Methods traverse :: Applicative f => (a -> f b) -> SmallArray a -> f (SmallArray b) # sequenceA :: Applicative f => SmallArray (f a) -> f (SmallArray a) # mapM :: Monad m => (a -> m b) -> SmallArray a -> m (SmallArray b) # sequence :: Monad m => SmallArray (m a) -> m (SmallArray a) #
Traversable Maybe
Instance details Defined in Data.Strict.Maybe Methods traverse :: Applicative f => (a -> f b) -> Maybe a -> f (Maybe b) # sequenceA :: Applicative f => Maybe (f a) -> f (Maybe a) # mapM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b) # sequence :: Monad m => Maybe (m a) -> m (Maybe a) #
Traversable Vector
Instance details Defined in Data.Vector Methods traverse :: Applicative f => (a -> f b) -> Vector a -> f (Vector b) # sequenceA :: Applicative f => Vector (f a) -> f (Vector a) # mapM :: Monad m => (a -> m b) -> Vector a -> m (Vector b) # sequence :: Monad m => Vector (m a) -> m (Vector a) #
Traversable Maybe	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Maybe a -> f (Maybe b) # sequenceA :: Applicative f => Maybe (f a) -> f (Maybe a) # mapM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b) # sequence :: Monad m => Maybe (m a) -> m (Maybe a) #
Traversable Solo	Since: base-4.15
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Solo a -> f (Solo b) # sequenceA :: Applicative f => Solo (f a) -> f (Solo a) # mapM :: Monad m => (a -> m b) -> Solo a -> m (Solo b) # sequence :: Monad m => Solo (m a) -> m (Solo a) #
Traversable List	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> [a] -> f [b] # sequenceA :: Applicative f => [f a] -> f [a] # mapM :: Monad m => (a -> m b) -> [a] -> m [b] # sequence :: Monad m => [m a] -> m [a] #
Traversable (Either a)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> Either a a0 -> f (Either a b) # sequenceA :: Applicative f => Either a (f a0) -> f (Either a a0) # mapM :: Monad m => (a0 -> m b) -> Either a a0 -> m (Either a b) # sequence :: Monad m => Either a (m a0) -> m (Either a a0) #
Traversable (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Proxy a -> f (Proxy b) # sequenceA :: Applicative f => Proxy (f a) -> f (Proxy a) # mapM :: Monad m => (a -> m b) -> Proxy a -> m (Proxy b) # sequence :: Monad m => Proxy (m a) -> m (Proxy a) #
Traversable (Arg a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a0 -> f b) -> Arg a a0 -> f (Arg a b) # sequenceA :: Applicative f => Arg a (f a0) -> f (Arg a a0) # mapM :: Monad m => (a0 -> m b) -> Arg a a0 -> m (Arg a b) # sequence :: Monad m => Arg a (m a0) -> m (Arg a a0) #
Ix i => Traversable (Array i)	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Array i a -> f (Array i b) # sequenceA :: Applicative f => Array i (f a) -> f (Array i a) # mapM :: Monad m => (a -> m b) -> Array i a -> m (Array i b) # sequence :: Monad m => Array i (m a) -> m (Array i a) #
Traversable (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> U1 a -> f (U1 b) # sequenceA :: Applicative f => U1 (f a) -> f (U1 a) # mapM :: Monad m => (a -> m b) -> U1 a -> m (U1 b) # sequence :: Monad m => U1 (m a) -> m (U1 a) #
Traversable (UAddr :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> UAddr a -> f (UAddr b) # sequenceA :: Applicative f => UAddr (f a) -> f (UAddr a) # mapM :: Monad m => (a -> m b) -> UAddr a -> m (UAddr b) # sequence :: Monad m => UAddr (m a) -> m (UAddr a) #
Traversable (UChar :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> UChar a -> f (UChar b) # sequenceA :: Applicative f => UChar (f a) -> f (UChar a) # mapM :: Monad m => (a -> m b) -> UChar a -> m (UChar b) # sequence :: Monad m => UChar (m a) -> m (UChar a) #
Traversable (UDouble :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> UDouble a -> f (UDouble b) # sequenceA :: Applicative f => UDouble (f a) -> f (UDouble a) # mapM :: Monad m => (a -> m b) -> UDouble a -> m (UDouble b) # sequence :: Monad m => UDouble (m a) -> m (UDouble a) #
Traversable (UFloat :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> UFloat a -> f (UFloat b) # sequenceA :: Applicative f => UFloat (f a) -> f (UFloat a) # mapM :: Monad m => (a -> m b) -> UFloat a -> m (UFloat b) # sequence :: Monad m => UFloat (m a) -> m (UFloat a) #
Traversable (UInt :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> UInt a -> f (UInt b) # sequenceA :: Applicative f => UInt (f a) -> f (UInt a) # mapM :: Monad m => (a -> m b) -> UInt a -> m (UInt b) # sequence :: Monad m => UInt (m a) -> m (UInt a) #
Traversable (UWord :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> UWord a -> f (UWord b) # sequenceA :: Applicative f => UWord (f a) -> f (UWord a) # mapM :: Monad m => (a -> m b) -> UWord a -> m (UWord b) # sequence :: Monad m => UWord (m a) -> m (UWord a) #
Traversable (V1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> V1 a -> f (V1 b) # sequenceA :: Applicative f => V1 (f a) -> f (V1 a) # mapM :: Monad m => (a -> m b) -> V1 a -> m (V1 b) # sequence :: Monad m => V1 (m a) -> m (V1 a) #
Traversable (Map k)	Traverses in order of increasing key.
Instance details Defined in Data.Map.Internal Methods traverse :: Applicative f => (a -> f b) -> Map k a -> f (Map k b) # sequenceA :: Applicative f => Map k (f a) -> f (Map k a) # mapM :: Monad m => (a -> m b) -> Map k a -> m (Map k b) # sequence :: Monad m => Map k (m a) -> m (Map k a) #
(Monad m, Traversable m) => Traversable (CatchT m)
Instance details Defined in Control.Monad.Catch.Pure Methods traverse :: Applicative f => (a -> f b) -> CatchT m a -> f (CatchT m b) # sequenceA :: Applicative f => CatchT m (f a) -> f (CatchT m a) # mapM :: Monad m0 => (a -> m0 b) -> CatchT m a -> m0 (CatchT m b) # sequence :: Monad m0 => CatchT m (m0 a) -> m0 (CatchT m a) #
Traversable f => Traversable (Cofree f)
Instance details Defined in Control.Comonad.Cofree Methods traverse :: Applicative f0 => (a -> f0 b) -> Cofree f a -> f0 (Cofree f b) # sequenceA :: Applicative f0 => Cofree f (f0 a) -> f0 (Cofree f a) # mapM :: Monad m => (a -> m b) -> Cofree f a -> m (Cofree f b) # sequence :: Monad m => Cofree f (m a) -> m (Cofree f a) #
Traversable w => Traversable (CoiterT w)
Instance details Defined in Control.Comonad.Trans.Coiter Methods traverse :: Applicative f => (a -> f b) -> CoiterT w a -> f (CoiterT w b) # sequenceA :: Applicative f => CoiterT w (f a) -> f (CoiterT w a) # mapM :: Monad m => (a -> m b) -> CoiterT w a -> m (CoiterT w b) # sequence :: Monad m => CoiterT w (m a) -> m (CoiterT w a) #
Traversable f => Traversable (Free f)
Instance details Defined in Control.Monad.Free Methods traverse :: Applicative f0 => (a -> f0 b) -> Free f a -> f0 (Free f b) # sequenceA :: Applicative f0 => Free f (f0 a) -> f0 (Free f a) # mapM :: Monad m => (a -> m b) -> Free f a -> m (Free f b) # sequence :: Monad m => Free f (m a) -> m (Free f a) #
Traversable f => Traversable (F f)
Instance details Defined in Control.Monad.Free.Church Methods traverse :: Applicative f0 => (a -> f0 b) -> F f a -> f0 (F f b) # sequenceA :: Applicative f0 => F f (f0 a) -> f0 (F f a) # mapM :: Monad m => (a -> m b) -> F f a -> m (F f b) # sequence :: Monad m => F f (m a) -> m (F f a) #
(Monad m, Traversable m) => Traversable (IterT m)
Instance details Defined in Control.Monad.Trans.Iter Methods traverse :: Applicative f => (a -> f b) -> IterT m a -> f (IterT m b) # sequenceA :: Applicative f => IterT m (f a) -> f (IterT m a) # mapM :: Monad m0 => (a -> m0 b) -> IterT m a -> m0 (IterT m b) # sequence :: Monad m0 => IterT m (m0 a) -> m0 (IterT m a) #
Traversable f => Traversable (Yoneda f)
Instance details Defined in Data.Functor.Yoneda Methods traverse :: Applicative f0 => (a -> f0 b) -> Yoneda f a -> f0 (Yoneda f b) # sequenceA :: Applicative f0 => Yoneda f (f0 a) -> f0 (Yoneda f a) # mapM :: Monad m => (a -> m b) -> Yoneda f a -> m (Yoneda f b) # sequence :: Monad m => Yoneda f (m a) -> m (Yoneda f a) #
Traversable (Level i) Source #
Instance details Defined in Control.Lens.Internal.Level Methods traverse :: Applicative f => (a -> f b) -> Level i a -> f (Level i b) # sequenceA :: Applicative f => Level i (f a) -> f (Level i a) # mapM :: Monad m => (a -> m b) -> Level i a -> m (Level i b) # sequence :: Monad m => Level i (m a) -> m (Level i a) #
Traversable (Either e)
Instance details Defined in Data.Strict.Either Methods traverse :: Applicative f => (a -> f b) -> Either e a -> f (Either e b) # sequenceA :: Applicative f => Either e (f a) -> f (Either e a) # mapM :: Monad m => (a -> m b) -> Either e a -> m (Either e b) # sequence :: Monad m => Either e (m a) -> m (Either e a) #
Traversable (These a)
Instance details Defined in Data.Strict.These Methods traverse :: Applicative f => (a0 -> f b) -> These a a0 -> f (These a b) # sequenceA :: Applicative f => These a (f a0) -> f (These a a0) # mapM :: Monad m => (a0 -> m b) -> These a a0 -> m (These a b) # sequence :: Monad m => These a (m a0) -> m (These a a0) #
Traversable (Pair e)
Instance details Defined in Data.Strict.Tuple Methods traverse :: Applicative f => (a -> f b) -> Pair e a -> f (Pair e b) # sequenceA :: Applicative f => Pair e (f a) -> f (Pair e a) # mapM :: Monad m => (a -> m b) -> Pair e a -> m (Pair e b) # sequence :: Monad m => Pair e (m a) -> m (Pair e a) #
Traversable (These a)
Instance details Defined in Data.These Methods traverse :: Applicative f => (a0 -> f b) -> These a a0 -> f (These a b) # sequenceA :: Applicative f => These a (f a0) -> f (These a a0) # mapM :: Monad m => (a0 -> m b) -> These a a0 -> m (These a b) # sequence :: Monad m => These a (m a0) -> m (These a a0) #
Traversable f => Traversable (Lift f)
Instance details Defined in Control.Applicative.Lift Methods traverse :: Applicative f0 => (a -> f0 b) -> Lift f a -> f0 (Lift f b) # sequenceA :: Applicative f0 => Lift f (f0 a) -> f0 (Lift f a) # mapM :: Monad m => (a -> m b) -> Lift f a -> m (Lift f b) # sequence :: Monad m => Lift f (m a) -> m (Lift f a) #
Traversable f => Traversable (MaybeT f)
Instance details Defined in Control.Monad.Trans.Maybe Methods traverse :: Applicative f0 => (a -> f0 b) -> MaybeT f a -> f0 (MaybeT f b) # sequenceA :: Applicative f0 => MaybeT f (f0 a) -> f0 (MaybeT f a) # mapM :: Monad m => (a -> m b) -> MaybeT f a -> m (MaybeT f b) # sequence :: Monad m => MaybeT f (m a) -> m (MaybeT f a) #
Traversable (HashMap k)
Instance details Defined in Data.HashMap.Internal Methods traverse :: Applicative f => (a -> f b) -> HashMap k a -> f (HashMap k b) # sequenceA :: Applicative f => HashMap k (f a) -> f (HashMap k a) # mapM :: Monad m => (a -> m b) -> HashMap k a -> m (HashMap k b) # sequence :: Monad m => HashMap k (m a) -> m (HashMap k a) #
Traversable ((,) a)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> (a, a0) -> f (a, b) # sequenceA :: Applicative f => (a, f a0) -> f (a, a0) # mapM :: Monad m => (a0 -> m b) -> (a, a0) -> m (a, b) # sequence :: Monad m => (a, m a0) -> m (a, a0) #
Traversable (Const m :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Const m a -> f (Const m b) # sequenceA :: Applicative f => Const m (f a) -> f (Const m a) # mapM :: Monad m0 => (a -> m0 b) -> Const m a -> m0 (Const m b) # sequence :: Monad m0 => Const m (m0 a) -> m0 (Const m a) #
Traversable f => Traversable (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Ap f a -> f0 (Ap f b) # sequenceA :: Applicative f0 => Ap f (f0 a) -> f0 (Ap f a) # mapM :: Monad m => (a -> m b) -> Ap f a -> m (Ap f b) # sequence :: Monad m => Ap f (m a) -> m (Ap f a) #
Traversable f => Traversable (Alt f)	Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Alt f a -> f0 (Alt f b) # sequenceA :: Applicative f0 => Alt f (f0 a) -> f0 (Alt f a) # mapM :: Monad m => (a -> m b) -> Alt f a -> m (Alt f b) # sequence :: Monad m => Alt f (m a) -> m (Alt f a) #
Traversable f => Traversable (Rec1 f)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Rec1 f a -> f0 (Rec1 f b) # sequenceA :: Applicative f0 => Rec1 f (f0 a) -> f0 (Rec1 f a) # mapM :: Monad m => (a -> m b) -> Rec1 f a -> m (Rec1 f b) # sequence :: Monad m => Rec1 f (m a) -> m (Rec1 f a) #
Bitraversable p => Traversable (Fix p)
Instance details Defined in Data.Bifunctor.Fix Methods traverse :: Applicative f => (a -> f b) -> Fix p a -> f (Fix p b) # sequenceA :: Applicative f => Fix p (f a) -> f (Fix p a) # mapM :: Monad m => (a -> m b) -> Fix p a -> m (Fix p b) # sequence :: Monad m => Fix p (m a) -> m (Fix p a) #
Bitraversable p => Traversable (Join p)
Instance details Defined in Data.Bifunctor.Join Methods traverse :: Applicative f => (a -> f b) -> Join p a -> f (Join p b) # sequenceA :: Applicative f => Join p (f a) -> f (Join p a) # mapM :: Monad m => (a -> m b) -> Join p a -> m (Join p b) # sequence :: Monad m => Join p (m a) -> m (Join p a) #
Traversable f => Traversable (CofreeF f a)
Instance details Defined in Control.Comonad.Trans.Cofree Methods traverse :: Applicative f0 => (a0 -> f0 b) -> CofreeF f a a0 -> f0 (CofreeF f a b) # sequenceA :: Applicative f0 => CofreeF f a (f0 a0) -> f0 (CofreeF f a a0) # mapM :: Monad m => (a0 -> m b) -> CofreeF f a a0 -> m (CofreeF f a b) # sequence :: Monad m => CofreeF f a (m a0) -> m (CofreeF f a a0) #
(Traversable f, Traversable w) => Traversable (CofreeT f w)
Instance details Defined in Control.Comonad.Trans.Cofree Methods traverse :: Applicative f0 => (a -> f0 b) -> CofreeT f w a -> f0 (CofreeT f w b) # sequenceA :: Applicative f0 => CofreeT f w (f0 a) -> f0 (CofreeT f w a) # mapM :: Monad m => (a -> m b) -> CofreeT f w a -> m (CofreeT f w b) # sequence :: Monad m => CofreeT f w (m a) -> m (CofreeT f w a) #
Traversable f => Traversable (FreeF f a)
Instance details Defined in Control.Monad.Trans.Free Methods traverse :: Applicative f0 => (a0 -> f0 b) -> FreeF f a a0 -> f0 (FreeF f a b) # sequenceA :: Applicative f0 => FreeF f a (f0 a0) -> f0 (FreeF f a a0) # mapM :: Monad m => (a0 -> m b) -> FreeF f a a0 -> m (FreeF f a b) # sequence :: Monad m => FreeF f a (m a0) -> m (FreeF f a a0) #
(Monad m, Traversable m, Traversable f) => Traversable (FreeT f m)
Instance details Defined in Control.Monad.Trans.Free Methods traverse :: Applicative f0 => (a -> f0 b) -> FreeT f m a -> f0 (FreeT f m b) # sequenceA :: Applicative f0 => FreeT f m (f0 a) -> f0 (FreeT f m a) # mapM :: Monad m0 => (a -> m0 b) -> FreeT f m a -> m0 (FreeT f m b) # sequence :: Monad m0 => FreeT f m (m0 a) -> m0 (FreeT f m a) #
Traversable f => Traversable (AlongsideLeft f b) Source #
Instance details Defined in Control.Lens.Internal.Getter Methods traverse :: Applicative f0 => (a -> f0 b0) -> AlongsideLeft f b a -> f0 (AlongsideLeft f b b0) # sequenceA :: Applicative f0 => AlongsideLeft f b (f0 a) -> f0 (AlongsideLeft f b a) # mapM :: Monad m => (a -> m b0) -> AlongsideLeft f b a -> m (AlongsideLeft f b b0) # sequence :: Monad m => AlongsideLeft f b (m a) -> m (AlongsideLeft f b a) #
Traversable f => Traversable (AlongsideRight f a) Source #
Instance details Defined in Control.Lens.Internal.Getter Methods traverse :: Applicative f0 => (a0 -> f0 b) -> AlongsideRight f a a0 -> f0 (AlongsideRight f a b) # sequenceA :: Applicative f0 => AlongsideRight f a (f0 a0) -> f0 (AlongsideRight f a a0) # mapM :: Monad m => (a0 -> m b) -> AlongsideRight f a a0 -> m (AlongsideRight f a b) # sequence :: Monad m => AlongsideRight f a (m a0) -> m (AlongsideRight f a a0) #
Traversable (Baz t b)
Instance details Defined in Data.Profunctor.Traversing Methods traverse :: Applicative f => (a -> f b0) -> Baz t b a -> f (Baz t b b0) # sequenceA :: Applicative f => Baz t b (f a) -> f (Baz t b a) # mapM :: Monad m => (a -> m b0) -> Baz t b a -> m (Baz t b b0) # sequence :: Monad m => Baz t b (m a) -> m (Baz t b a) #
Traversable (Tagged s)
Instance details Defined in Data.Tagged Methods traverse :: Applicative f => (a -> f b) -> Tagged s a -> f (Tagged s b) # sequenceA :: Applicative f => Tagged s (f a) -> f (Tagged s a) # mapM :: Monad m => (a -> m b) -> Tagged s a -> m (Tagged s b) # sequence :: Monad m => Tagged s (m a) -> m (Tagged s a) #
Traversable f => Traversable (Backwards f)	Derived instance.
Instance details Defined in Control.Applicative.Backwards Methods traverse :: Applicative f0 => (a -> f0 b) -> Backwards f a -> f0 (Backwards f b) # sequenceA :: Applicative f0 => Backwards f (f0 a) -> f0 (Backwards f a) # mapM :: Monad m => (a -> m b) -> Backwards f a -> m (Backwards f b) # sequence :: Monad m => Backwards f (m a) -> m (Backwards f a) #
Traversable f => Traversable (ExceptT e f)
Instance details Defined in Control.Monad.Trans.Except Methods traverse :: Applicative f0 => (a -> f0 b) -> ExceptT e f a -> f0 (ExceptT e f b) # sequenceA :: Applicative f0 => ExceptT e f (f0 a) -> f0 (ExceptT e f a) # mapM :: Monad m => (a -> m b) -> ExceptT e f a -> m (ExceptT e f b) # sequence :: Monad m => ExceptT e f (m a) -> m (ExceptT e f a) #
Traversable f => Traversable (IdentityT f)
Instance details Defined in Control.Monad.Trans.Identity Methods traverse :: Applicative f0 => (a -> f0 b) -> IdentityT f a -> f0 (IdentityT f b) # sequenceA :: Applicative f0 => IdentityT f (f0 a) -> f0 (IdentityT f a) # mapM :: Monad m => (a -> m b) -> IdentityT f a -> m (IdentityT f b) # sequence :: Monad m => IdentityT f (m a) -> m (IdentityT f a) #
Traversable f => Traversable (WriterT w f)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods traverse :: Applicative f0 => (a -> f0 b) -> WriterT w f a -> f0 (WriterT w f b) # sequenceA :: Applicative f0 => WriterT w f (f0 a) -> f0 (WriterT w f a) # mapM :: Monad m => (a -> m b) -> WriterT w f a -> m (WriterT w f b) # sequence :: Monad m => WriterT w f (m a) -> m (WriterT w f a) #
Traversable f => Traversable (WriterT w f)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods traverse :: Applicative f0 => (a -> f0 b) -> WriterT w f a -> f0 (WriterT w f b) # sequenceA :: Applicative f0 => WriterT w f (f0 a) -> f0 (WriterT w f a) # mapM :: Monad m => (a -> m b) -> WriterT w f a -> m (WriterT w f b) # sequence :: Monad m => WriterT w f (m a) -> m (WriterT w f a) #
Traversable (Constant a :: Type -> Type)
Instance details Defined in Data.Functor.Constant Methods traverse :: Applicative f => (a0 -> f b) -> Constant a a0 -> f (Constant a b) # sequenceA :: Applicative f => Constant a (f a0) -> f (Constant a a0) # mapM :: Monad m => (a0 -> m b) -> Constant a a0 -> m (Constant a b) # sequence :: Monad m => Constant a (m a0) -> m (Constant a a0) #
Traversable f => Traversable (Reverse f)	Traverse from right to left.
Instance details Defined in Data.Functor.Reverse Methods traverse :: Applicative f0 => (a -> f0 b) -> Reverse f a -> f0 (Reverse f b) # sequenceA :: Applicative f0 => Reverse f (f0 a) -> f0 (Reverse f a) # mapM :: Monad m => (a -> m b) -> Reverse f a -> m (Reverse f b) # sequence :: Monad m => Reverse f (m a) -> m (Reverse f a) #
(Traversable f, Traversable g) => Traversable (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods traverse :: Applicative f0 => (a -> f0 b) -> Product f g a -> f0 (Product f g b) # sequenceA :: Applicative f0 => Product f g (f0 a) -> f0 (Product f g a) # mapM :: Monad m => (a -> m b) -> Product f g a -> m (Product f g b) # sequence :: Monad m => Product f g (m a) -> m (Product f g a) #
(Traversable f, Traversable g) => Traversable (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods traverse :: Applicative f0 => (a -> f0 b) -> Sum f g a -> f0 (Sum f g b) # sequenceA :: Applicative f0 => Sum f g (f0 a) -> f0 (Sum f g a) # mapM :: Monad m => (a -> m b) -> Sum f g a -> m (Sum f g b) # sequence :: Monad m => Sum f g (m a) -> m (Sum f g a) #
(Traversable f, Traversable g) => Traversable (f :*: g)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :: g) a -> f0 ((f :: g) b) # sequenceA :: Applicative f0 => (f :: g) (f0 a) -> f0 ((f :: g) a) # mapM :: Monad m => (a -> m b) -> (f :: g) a -> m ((f :: g) b) # sequence :: Monad m => (f :: g) (m a) -> m ((f :: g) a) #
(Traversable f, Traversable g) => Traversable (f :+: g)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b) # sequenceA :: Applicative f0 => (f :+: g) (f0 a) -> f0 ((f :+: g) a) # mapM :: Monad m => (a -> m b) -> (f :+: g) a -> m ((f :+: g) b) # sequence :: Monad m => (f :+: g) (m a) -> m ((f :+: g) a) #
Traversable (K1 i c :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> K1 i c a -> f (K1 i c b) # sequenceA :: Applicative f => K1 i c (f a) -> f (K1 i c a) # mapM :: Monad m => (a -> m b) -> K1 i c a -> m (K1 i c b) # sequence :: Monad m => K1 i c (m a) -> m (K1 i c a) #
Traversable (Magma i t b) Source #
Instance details Defined in Control.Lens.Internal.Magma Methods traverse :: Applicative f => (a -> f b0) -> Magma i t b a -> f (Magma i t b b0) # sequenceA :: Applicative f => Magma i t b (f a) -> f (Magma i t b a) # mapM :: Monad m => (a -> m b0) -> Magma i t b a -> m (Magma i t b b0) # sequence :: Monad m => Magma i t b (m a) -> m (Magma i t b a) #
Traversable (Forget r a :: Type -> Type)
Instance details Defined in Data.Profunctor.Types Methods traverse :: Applicative f => (a0 -> f b) -> Forget r a a0 -> f (Forget r a b) # sequenceA :: Applicative f => Forget r a (f a0) -> f (Forget r a a0) # mapM :: Monad m => (a0 -> m b) -> Forget r a a0 -> m (Forget r a b) # sequence :: Monad m => Forget r a (m a0) -> m (Forget r a a0) #
(Traversable f, Traversable g) => Traversable (Compose f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods traverse :: Applicative f0 => (a -> f0 b) -> Compose f g a -> f0 (Compose f g b) # sequenceA :: Applicative f0 => Compose f g (f0 a) -> f0 (Compose f g a) # mapM :: Monad m => (a -> m b) -> Compose f g a -> m (Compose f g b) # sequence :: Monad m => Compose f g (m a) -> m (Compose f g a) #
(Traversable f, Traversable g) => Traversable (f :.: g)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b) # sequenceA :: Applicative f0 => (f :.: g) (f0 a) -> f0 ((f :.: g) a) # mapM :: Monad m => (a -> m b) -> (f :.: g) a -> m ((f :.: g) b) # sequence :: Monad m => (f :.: g) (m a) -> m ((f :.: g) a) #
Traversable f => Traversable (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> M1 i c f a -> f0 (M1 i c f b) # sequenceA :: Applicative f0 => M1 i c f (f0 a) -> f0 (M1 i c f a) # mapM :: Monad m => (a -> m b) -> M1 i c f a -> m (M1 i c f b) # sequence :: Monad m => M1 i c f (m a) -> m (M1 i c f a) #
Traversable (Clown f a :: Type -> Type)
Instance details Defined in Data.Bifunctor.Clown Methods traverse :: Applicative f0 => (a0 -> f0 b) -> Clown f a a0 -> f0 (Clown f a b) # sequenceA :: Applicative f0 => Clown f a (f0 a0) -> f0 (Clown f a a0) # mapM :: Monad m => (a0 -> m b) -> Clown f a a0 -> m (Clown f a b) # sequence :: Monad m => Clown f a (m a0) -> m (Clown f a a0) #
Bitraversable p => Traversable (Flip p a)
Instance details Defined in Data.Bifunctor.Flip Methods traverse :: Applicative f => (a0 -> f b) -> Flip p a a0 -> f (Flip p a b) # sequenceA :: Applicative f => Flip p a (f a0) -> f (Flip p a a0) # mapM :: Monad m => (a0 -> m b) -> Flip p a a0 -> m (Flip p a b) # sequence :: Monad m => Flip p a (m a0) -> m (Flip p a a0) #
Traversable g => Traversable (Joker g a)
Instance details Defined in Data.Bifunctor.Joker Methods traverse :: Applicative f => (a0 -> f b) -> Joker g a a0 -> f (Joker g a b) # sequenceA :: Applicative f => Joker g a (f a0) -> f (Joker g a a0) # mapM :: Monad m => (a0 -> m b) -> Joker g a a0 -> m (Joker g a b) # sequence :: Monad m => Joker g a (m a0) -> m (Joker g a a0) #
Bitraversable p => Traversable (WrappedBifunctor p a)
Instance details Defined in Data.Bifunctor.Wrapped Methods traverse :: Applicative f => (a0 -> f b) -> WrappedBifunctor p a a0 -> f (WrappedBifunctor p a b) # sequenceA :: Applicative f => WrappedBifunctor p a (f a0) -> f (WrappedBifunctor p a a0) # mapM :: Monad m => (a0 -> m b) -> WrappedBifunctor p a a0 -> m (WrappedBifunctor p a b) # sequence :: Monad m => WrappedBifunctor p a (m a0) -> m (WrappedBifunctor p a a0) #
(Traversable (f a), Traversable (g a)) => Traversable (Product f g a)
Instance details Defined in Data.Bifunctor.Product Methods traverse :: Applicative f0 => (a0 -> f0 b) -> Product f g a a0 -> f0 (Product f g a b) # sequenceA :: Applicative f0 => Product f g a (f0 a0) -> f0 (Product f g a a0) # mapM :: Monad m => (a0 -> m b) -> Product f g a a0 -> m (Product f g a b) # sequence :: Monad m => Product f g a (m a0) -> m (Product f g a a0) #
(Traversable (f a), Traversable (g a)) => Traversable (Sum f g a)
Instance details Defined in Data.Bifunctor.Sum Methods traverse :: Applicative f0 => (a0 -> f0 b) -> Sum f g a a0 -> f0 (Sum f g a b) # sequenceA :: Applicative f0 => Sum f g a (f0 a0) -> f0 (Sum f g a a0) # mapM :: Monad m => (a0 -> m b) -> Sum f g a a0 -> m (Sum f g a b) # sequence :: Monad m => Sum f g a (m a0) -> m (Sum f g a a0) #
(Traversable f, Bitraversable p) => Traversable (Tannen f p a)
Instance details Defined in Data.Bifunctor.Tannen Methods traverse :: Applicative f0 => (a0 -> f0 b) -> Tannen f p a a0 -> f0 (Tannen f p a b) # sequenceA :: Applicative f0 => Tannen f p a (f0 a0) -> f0 (Tannen f p a a0) # mapM :: Monad m => (a0 -> m b) -> Tannen f p a a0 -> m (Tannen f p a b) # sequence :: Monad m => Tannen f p a (m a0) -> m (Tannen f p a a0) #
(Bitraversable p, Traversable g) => Traversable (Biff p f g a)
Instance details Defined in Data.Bifunctor.Biff Methods traverse :: Applicative f0 => (a0 -> f0 b) -> Biff p f g a a0 -> f0 (Biff p f g a b) # sequenceA :: Applicative f0 => Biff p f g a (f0 a0) -> f0 (Biff p f g a a0) # mapM :: Monad m => (a0 -> m b) -> Biff p f g a a0 -> m (Biff p f g a b) # sequence :: Monad m => Biff p f g a (m a0) -> m (Biff p f g a a0) #

data (a :: k) :~: (b :: k) where infix 4 #

Propositional equality. If a :~: b is inhabited by some terminating value, then the type a is the same as the type b. To use this equality in practice, pattern-match on the a :~: b to get out the Refl constructor; in the body of the pattern-match, the compiler knows that a ~ b.

Since: base-4.7.0.0

Constructors

Refl :: forall {k} (a :: k). a :~: a

Instances

Instances details

Category ((:~:) :: k -> k -> Type)	Since: base-4.7.0.0
Instance details Defined in Control.Category Methods id :: forall (a :: k0). a :~: a # (.) :: forall (b :: k0) (c :: k0) (a :: k0). (b :~: c) -> (a :~: b) -> a :~: c #
Semigroupoid ((:~:) :: k -> k -> Type)
Instance details Defined in Data.Semigroupoid Methods o :: forall (j :: k0) (k1 :: k0) (i :: k0). (j :~: k1) -> (i :~: j) -> i :~: k1 #
TestEquality ((:~:) a :: k -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods testEquality :: forall (a0 :: k0) (b :: k0). (a :~: a0) -> (a :~: b) -> Maybe (a0 :~: b) #
NFData2 ((:~:) :: Type -> Type -> Type)	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf2 :: (a -> ()) -> (b -> ()) -> (a :~: b) -> () #
NFData1 ((:~:) a)	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf :: (a0 -> ()) -> (a :~: a0) -> () #
(a ~ b, Data a) => Data (a :~: b)	Since: base-4.7.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> (a :~: b) -> c (a :~: b) # gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (a :~: b) # toConstr :: (a :~: b) -> Constr # dataTypeOf :: (a :~: b) -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (a :~: b)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (a :~: b)) # gmapT :: (forall b0. Data b0 => b0 -> b0) -> (a :~: b) -> a :~: b # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> (a :~: b) -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> (a :~: b) -> r # gmapQ :: (forall d. Data d => d -> u) -> (a :~: b) -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> (a :~: b) -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> (a :~: b) -> m (a :~: b) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> (a :~: b) -> m (a :~: b) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> (a :~: b) -> m (a :~: b) #
a ~ b => Bounded (a :~: b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods minBound :: a :~: b # maxBound :: a :~: b #
a ~ b => Enum (a :~: b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods succ :: (a :~: b) -> a :~: b # pred :: (a :~: b) -> a :~: b # toEnum :: Int -> a :~: b # fromEnum :: (a :~: b) -> Int # enumFrom :: (a :~: b) -> [a :~: b] # enumFromThen :: (a :~: b) -> (a :~: b) -> [a :~: b] # enumFromTo :: (a :~: b) -> (a :~: b) -> [a :~: b] # enumFromThenTo :: (a :~: b) -> (a :~: b) -> (a :~: b) -> [a :~: b] #
a ~ b => Read (a :~: b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods readsPrec :: Int -> ReadS (a :~: b) # readList :: ReadS [a :~: b] # readPrec :: ReadPrec (a :~: b) # readListPrec :: ReadPrec [a :~: b] #
Show (a :~: b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods showsPrec :: Int -> (a :~: b) -> ShowS # show :: (a :~: b) -> String # showList :: [a :~: b] -> ShowS #
NFData (a :~: b)	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods rnf :: (a :~: b) -> () #
Eq (a :~: b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods (==) :: (a :~: b) -> (a :~: b) -> Bool # (/=) :: (a :~: b) -> (a :~: b) -> Bool #
Ord (a :~: b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods compare :: (a :~: b) -> (a :~: b) -> Ordering # (<) :: (a :~: b) -> (a :~: b) -> Bool # (<=) :: (a :~: b) -> (a :~: b) -> Bool # (>) :: (a :~: b) -> (a :~: b) -> Bool # (>=) :: (a :~: b) -> (a :~: b) -> Bool # max :: (a :~: b) -> (a :~: b) -> a :~: b # min :: (a :~: b) -> (a :~: b) -> a :~: b #

newtype Const a (b :: k) #

The Const functor.

Constructors

Const
Fields getConst :: a

Instances

Instances details

Semigroupoid (Const :: Type -> Type -> Type)
Instance details Defined in Data.Semigroupoid Methods o :: forall (j :: k) (k1 :: k) (i :: k). Const j k1 -> Const i j -> Const i k1 #
Generic1 (Const a :: k -> Type)
Instance details Defined in Data.Functor.Const Associated Types type Rep1 (Const a) :: k -> Type # Methods from1 :: forall (a0 :: k0). Const a a0 -> Rep1 (Const a) a0 # to1 :: forall (a0 :: k0). Rep1 (Const a) a0 -> Const a a0 #
FoldableWithIndex Void (Const e :: Type -> Type)
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (Void -> a -> m) -> Const e a -> m # ifoldMap' :: Monoid m => (Void -> a -> m) -> Const e a -> m # ifoldr :: (Void -> a -> b -> b) -> b -> Const e a -> b # ifoldl :: (Void -> b -> a -> b) -> b -> Const e a -> b # ifoldr' :: (Void -> a -> b -> b) -> b -> Const e a -> b # ifoldl' :: (Void -> b -> a -> b) -> b -> Const e a -> b #
FunctorWithIndex Void (Const e :: Type -> Type)
Instance details Defined in WithIndex Methods imap :: (Void -> a -> b) -> Const e a -> Const e b #
TraversableWithIndex Void (Const e :: Type -> Type)
Instance details Defined in WithIndex Methods itraverse :: Applicative f => (Void -> a -> f b) -> Const e a -> f (Const e b) #
Unbox a => Vector Vector (Const a b)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: Mutable Vector s (Const a b) -> ST s (Vector (Const a b)) # basicUnsafeThaw :: Vector (Const a b) -> ST s (Mutable Vector s (Const a b)) # basicLength :: Vector (Const a b) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (Const a b) -> Vector (Const a b) # basicUnsafeIndexM :: Vector (Const a b) -> Int -> Box (Const a b) # basicUnsafeCopy :: Mutable Vector s (Const a b) -> Vector (Const a b) -> ST s () # elemseq :: Vector (Const a b) -> Const a b -> b0 -> b0 #
Unbox a => MVector MVector (Const a b)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s (Const a b) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (Const a b) -> MVector s (Const a b) # basicOverlaps :: MVector s (Const a b) -> MVector s (Const a b) -> Bool # basicUnsafeNew :: Int -> ST s (MVector s (Const a b)) # basicInitialize :: MVector s (Const a b) -> ST s () # basicUnsafeReplicate :: Int -> Const a b -> ST s (MVector s (Const a b)) # basicUnsafeRead :: MVector s (Const a b) -> Int -> ST s (Const a b) # basicUnsafeWrite :: MVector s (Const a b) -> Int -> Const a b -> ST s () # basicClear :: MVector s (Const a b) -> ST s () # basicSet :: MVector s (Const a b) -> Const a b -> ST s () # basicUnsafeCopy :: MVector s (Const a b) -> MVector s (Const a b) -> ST s () # basicUnsafeMove :: MVector s (Const a b) -> MVector s (Const a b) -> ST s () # basicUnsafeGrow :: MVector s (Const a b) -> Int -> ST s (MVector s (Const a b)) #
Bifoldable (Const :: Type -> Type -> Type)	Since: base-4.10.0.0
Instance details Defined in Data.Bifoldable Methods bifold :: Monoid m => Const m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Const a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Const a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Const a b -> c #
Bifoldable1 (Const :: Type -> Type -> Type)
Instance details Defined in Data.Bifoldable1 Methods bifold1 :: Semigroup m => Const m m -> m # bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> Const a b -> m #
Bifunctor (Const :: Type -> Type -> Type)	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> Const a c -> Const b d # first :: (a -> b) -> Const a c -> Const b c # second :: (b -> c) -> Const a b -> Const a c #
Bitraversable (Const :: Type -> Type -> Type)	Since: base-4.10.0.0
Instance details Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Const a b -> f (Const c d) #
NFData2 (Const :: Type -> Type -> Type)	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf2 :: (a -> ()) -> (b -> ()) -> Const a b -> () #
Hashable2 (Const :: Type -> Type -> Type)
Instance details Defined in Data.Hashable.Class Methods liftHashWithSalt2 :: (Int -> a -> Int) -> (Int -> b -> Int) -> Int -> Const a b -> Int #
Biapply (Const :: Type -> Type -> Type)
Instance details Defined in Data.Functor.Bind.Class Methods (<<.>>) :: Const (a -> b) (c -> d) -> Const a c -> Const b d # (.>>) :: Const a b -> Const c d -> Const c d # (<<.) :: Const a b -> Const c d -> Const a b #
Bitraversable1 (Const :: Type -> Type -> Type)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> Const a c -> f (Const b d) # bisequence1 :: Apply f => Const (f a) (f b) -> f (Const a b) #
Foldable (Const m :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Functor.Const Methods fold :: Monoid m0 => Const m m0 -> m0 # foldMap :: Monoid m0 => (a -> m0) -> Const m a -> m0 # foldMap' :: Monoid m0 => (a -> m0) -> Const m a -> m0 # foldr :: (a -> b -> b) -> b -> Const m a -> b # foldr' :: (a -> b -> b) -> b -> Const m a -> b # foldl :: (b -> a -> b) -> b -> Const m a -> b # foldl' :: (b -> a -> b) -> b -> Const m a -> b # foldr1 :: (a -> a -> a) -> Const m a -> a # foldl1 :: (a -> a -> a) -> Const m a -> a # toList :: Const m a -> [a] # null :: Const m a -> Bool # length :: Const m a -> Int # elem :: Eq a => a -> Const m a -> Bool # maximum :: Ord a => Const m a -> a # minimum :: Ord a => Const m a -> a # sum :: Num a => Const m a -> a # product :: Num a => Const m a -> a #
Contravariant (Const a :: Type -> Type)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a' -> a0) -> Const a a0 -> Const a a' # (>$) :: b -> Const a b -> Const a a0 #
Traversable (Const m :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Const m a -> f (Const m b) # sequenceA :: Applicative f => Const m (f a) -> f (Const m a) # mapM :: Monad m0 => (a -> m0 b) -> Const m a -> m0 (Const m b) # sequence :: Monad m0 => Const m (m0 a) -> m0 (Const m a) #
Monoid m => Applicative (Const m :: Type -> Type)	Since: base-2.0.1
Instance details Defined in Data.Functor.Const Methods pure :: a -> Const m a # (<>) :: Const m (a -> b) -> Const m a -> Const m b # liftA2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c # (>) :: Const m a -> Const m b -> Const m b # (<*) :: Const m a -> Const m b -> Const m a #
Functor (Const m :: Type -> Type)	Since: base-2.1
Instance details Defined in Data.Functor.Const Methods fmap :: (a -> b) -> Const m a -> Const m b # (<$) :: a -> Const m b -> Const m a #
NFData a => NFData1 (Const a :: Type -> Type)	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf :: (a0 -> ()) -> Const a a0 -> () #
Hashable a => Hashable1 (Const a :: Type -> Type)
Instance details Defined in Data.Hashable.Class Methods liftHashWithSalt :: (Int -> a0 -> Int) -> Int -> Const a a0 -> Int #
Semigroup m => Apply (Const m :: Type -> Type)	A `Const m` is not `Applicative` unless its `m` is a `Monoid`, but it is an instance of `Apply`
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Const m (a -> b) -> Const m a -> Const m b # (.>) :: Const m a -> Const m b -> Const m b # (<.) :: Const m a -> Const m b -> Const m a # liftF2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c #
ComonadCofree (Const b :: Type -> Type) ((,) b)
Instance details Defined in Control.Comonad.Cofree.Class Methods unwrap :: (b, a) -> Const b (b, a) #
Sieve (Forget r :: Type -> Type -> Type) (Const r :: Type -> Type)
Instance details Defined in Data.Profunctor.Sieve Methods sieve :: Forget r a b -> a -> Const r b #
(Typeable k, Data a, Typeable b) => Data (Const a b)	Since: base-4.10.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Const a b -> c (Const a b) # gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Const a b) # toConstr :: Const a b -> Constr # dataTypeOf :: Const a b -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Const a b)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Const a b)) # gmapT :: (forall b0. Data b0 => b0 -> b0) -> Const a b -> Const a b # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Const a b -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Const a b -> r # gmapQ :: (forall d. Data d => d -> u) -> Const a b -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Const a b -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Const a b -> m (Const a b) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Const a b -> m (Const a b) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Const a b -> m (Const a b) #
Storable a => Storable (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods sizeOf :: Const a b -> Int # alignment :: Const a b -> Int # peekElemOff :: Ptr (Const a b) -> Int -> IO (Const a b) # pokeElemOff :: Ptr (Const a b) -> Int -> Const a b -> IO () # peekByteOff :: Ptr b0 -> Int -> IO (Const a b) # pokeByteOff :: Ptr b0 -> Int -> Const a b -> IO () # peek :: Ptr (Const a b) -> IO (Const a b) # poke :: Ptr (Const a b) -> Const a b -> IO () #
Monoid a => Monoid (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods mempty :: Const a b # mappend :: Const a b -> Const a b -> Const a b # mconcat :: [Const a b] -> Const a b #
Semigroup a => Semigroup (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (<>) :: Const a b -> Const a b -> Const a b # sconcat :: NonEmpty (Const a b) -> Const a b # stimes :: Integral b0 => b0 -> Const a b -> Const a b #
Bits a => Bits (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (.&.) :: Const a b -> Const a b -> Const a b # (.\|.) :: Const a b -> Const a b -> Const a b # xor :: Const a b -> Const a b -> Const a b # complement :: Const a b -> Const a b # shift :: Const a b -> Int -> Const a b # rotate :: Const a b -> Int -> Const a b # zeroBits :: Const a b # bit :: Int -> Const a b # setBit :: Const a b -> Int -> Const a b # clearBit :: Const a b -> Int -> Const a b # complementBit :: Const a b -> Int -> Const a b # testBit :: Const a b -> Int -> Bool # bitSizeMaybe :: Const a b -> Maybe Int # bitSize :: Const a b -> Int # isSigned :: Const a b -> Bool # shiftL :: Const a b -> Int -> Const a b # unsafeShiftL :: Const a b -> Int -> Const a b # shiftR :: Const a b -> Int -> Const a b # unsafeShiftR :: Const a b -> Int -> Const a b # rotateL :: Const a b -> Int -> Const a b # rotateR :: Const a b -> Int -> Const a b # popCount :: Const a b -> Int #
FiniteBits a => FiniteBits (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods finiteBitSize :: Const a b -> Int # countLeadingZeros :: Const a b -> Int # countTrailingZeros :: Const a b -> Int #
Bounded a => Bounded (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods minBound :: Const a b # maxBound :: Const a b #
Enum a => Enum (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods succ :: Const a b -> Const a b # pred :: Const a b -> Const a b # toEnum :: Int -> Const a b # fromEnum :: Const a b -> Int # enumFrom :: Const a b -> [Const a b] # enumFromThen :: Const a b -> Const a b -> [Const a b] # enumFromTo :: Const a b -> Const a b -> [Const a b] # enumFromThenTo :: Const a b -> Const a b -> Const a b -> [Const a b] #
Floating a => Floating (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods pi :: Const a b # exp :: Const a b -> Const a b # log :: Const a b -> Const a b # sqrt :: Const a b -> Const a b # (**) :: Const a b -> Const a b -> Const a b # logBase :: Const a b -> Const a b -> Const a b # sin :: Const a b -> Const a b # cos :: Const a b -> Const a b # tan :: Const a b -> Const a b # asin :: Const a b -> Const a b # acos :: Const a b -> Const a b # atan :: Const a b -> Const a b # sinh :: Const a b -> Const a b # cosh :: Const a b -> Const a b # tanh :: Const a b -> Const a b # asinh :: Const a b -> Const a b # acosh :: Const a b -> Const a b # atanh :: Const a b -> Const a b # log1p :: Const a b -> Const a b # expm1 :: Const a b -> Const a b # log1pexp :: Const a b -> Const a b # log1mexp :: Const a b -> Const a b #
RealFloat a => RealFloat (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods floatRadix :: Const a b -> Integer # floatDigits :: Const a b -> Int # floatRange :: Const a b -> (Int, Int) # decodeFloat :: Const a b -> (Integer, Int) # encodeFloat :: Integer -> Int -> Const a b # exponent :: Const a b -> Int # significand :: Const a b -> Const a b # scaleFloat :: Int -> Const a b -> Const a b # isNaN :: Const a b -> Bool # isInfinite :: Const a b -> Bool # isDenormalized :: Const a b -> Bool # isNegativeZero :: Const a b -> Bool # isIEEE :: Const a b -> Bool # atan2 :: Const a b -> Const a b -> Const a b #
Generic (Const a b)
Instance details Defined in Data.Functor.Const Associated Types type Rep (Const a b) :: Type -> Type # Methods from :: Const a b -> Rep (Const a b) x # to :: Rep (Const a b) x -> Const a b #
Ix a => Ix (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods range :: (Const a b, Const a b) -> [Const a b] # index :: (Const a b, Const a b) -> Const a b -> Int # unsafeIndex :: (Const a b, Const a b) -> Const a b -> Int # inRange :: (Const a b, Const a b) -> Const a b -> Bool # rangeSize :: (Const a b, Const a b) -> Int # unsafeRangeSize :: (Const a b, Const a b) -> Int #
Num a => Num (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (+) :: Const a b -> Const a b -> Const a b # (-) :: Const a b -> Const a b -> Const a b # (*) :: Const a b -> Const a b -> Const a b # negate :: Const a b -> Const a b # abs :: Const a b -> Const a b # signum :: Const a b -> Const a b # fromInteger :: Integer -> Const a b #
Read a => Read (Const a b)	This instance would be equivalent to the derived instances of the `Const` newtype if the `getConst` field were removed Since: base-4.8.0.0
Instance details Defined in Data.Functor.Const Methods readsPrec :: Int -> ReadS (Const a b) # readList :: ReadS [Const a b] # readPrec :: ReadPrec (Const a b) # readListPrec :: ReadPrec [Const a b] #
Fractional a => Fractional (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (/) :: Const a b -> Const a b -> Const a b # recip :: Const a b -> Const a b # fromRational :: Rational -> Const a b #
Integral a => Integral (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods quot :: Const a b -> Const a b -> Const a b # rem :: Const a b -> Const a b -> Const a b # div :: Const a b -> Const a b -> Const a b # mod :: Const a b -> Const a b -> Const a b # quotRem :: Const a b -> Const a b -> (Const a b, Const a b) # divMod :: Const a b -> Const a b -> (Const a b, Const a b) # toInteger :: Const a b -> Integer #
Real a => Real (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods toRational :: Const a b -> Rational #
RealFrac a => RealFrac (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods properFraction :: Integral b0 => Const a b -> (b0, Const a b) # truncate :: Integral b0 => Const a b -> b0 # round :: Integral b0 => Const a b -> b0 # ceiling :: Integral b0 => Const a b -> b0 # floor :: Integral b0 => Const a b -> b0 #
Show a => Show (Const a b)	This instance would be equivalent to the derived instances of the `Const` newtype if the `getConst` field were removed Since: base-4.8.0.0
Instance details Defined in Data.Functor.Const Methods showsPrec :: Int -> Const a b -> ShowS # show :: Const a b -> String # showList :: [Const a b] -> ShowS #
NFData a => NFData (Const a b)	Since: deepseq-1.4.0.0
Instance details Defined in Control.DeepSeq Methods rnf :: Const a b -> () #
Eq a => Eq (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (==) :: Const a b -> Const a b -> Bool # (/=) :: Const a b -> Const a b -> Bool #
Ord a => Ord (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods compare :: Const a b -> Const a b -> Ordering # (<) :: Const a b -> Const a b -> Bool # (<=) :: Const a b -> Const a b -> Bool # (>) :: Const a b -> Const a b -> Bool # (>=) :: Const a b -> Const a b -> Bool # max :: Const a b -> Const a b -> Const a b # min :: Const a b -> Const a b -> Const a b #
Hashable a => Hashable (Const a b)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Const a b -> Int # hash :: Const a b -> Int #
Wrapped (Const a x) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Const a x) Source # Methods _Wrapped' :: Iso' (Const a x) (Unwrapped (Const a x)) Source #
Prim a => Prim (Const a b)	Since: primitive-0.6.5.0
Instance details Defined in Data.Primitive.Types Methods sizeOf# :: Const a b -> Int# # alignment# :: Const a b -> Int# # indexByteArray# :: ByteArray# -> Int# -> Const a b # readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Const a b #) # writeByteArray# :: MutableByteArray# s -> Int# -> Const a b -> State# s -> State# s # setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Const a b -> State# s -> State# s # indexOffAddr# :: Addr# -> Int# -> Const a b # readOffAddr# :: Addr# -> Int# -> State# s -> (# State# s, Const a b #) # writeOffAddr# :: Addr# -> Int# -> Const a b -> State# s -> State# s # setOffAddr# :: Addr# -> Int# -> Int# -> Const a b -> State# s -> State# s #
Unbox a => Unbox (Const a b)
Instance details Defined in Data.Vector.Unboxed.Base
t ~ Const a' x' => Rewrapped (Const a x) t Source #
Instance details Defined in Control.Lens.Wrapped
type Rep1 (Const a :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const type Rep1 (Const a :: k -> Type) = D1 ('MetaData "Const" "Data.Functor.Const" "base" 'True) (C1 ('MetaCons "Const" 'PrefixI 'True) (S1 ('MetaSel ('Just "getConst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
newtype MVector s (Const a b)
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s (Const a b) = MV_Const (MVector s a)
type Rep (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const type Rep (Const a b) = D1 ('MetaData "Const" "Data.Functor.Const" "base" 'True) (C1 ('MetaCons "Const" 'PrefixI 'True) (S1 ('MetaSel ('Just "getConst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Unwrapped (Const a x) Source #
Instance details Defined in Control.Lens.Wrapped type Unwrapped (Const a x) = a
newtype Vector (Const a b)
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector (Const a b) = V_Const (Vector a)

newtype Identity a #

Identity functor and monad. (a non-strict monad)

Since: base-4.8.0.0

Constructors

Identity
Fields runIdentity :: a

Instances

Instances details

Representable Identity
Instance details Defined in Data.Functor.Rep Associated Types type Rep Identity # Methods tabulate :: (Rep Identity -> a) -> Identity a # index :: Identity a -> Rep Identity -> a #
MonadFix Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods mfix :: (a -> Identity a) -> Identity a #
Foldable Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods fold :: Monoid m => Identity m -> m # foldMap :: Monoid m => (a -> m) -> Identity a -> m # foldMap' :: Monoid m => (a -> m) -> Identity a -> m # foldr :: (a -> b -> b) -> b -> Identity a -> b # foldr' :: (a -> b -> b) -> b -> Identity a -> b # foldl :: (b -> a -> b) -> b -> Identity a -> b # foldl' :: (b -> a -> b) -> b -> Identity a -> b # foldr1 :: (a -> a -> a) -> Identity a -> a # foldl1 :: (a -> a -> a) -> Identity a -> a # toList :: Identity a -> [a] # null :: Identity a -> Bool # length :: Identity a -> Int # elem :: Eq a => a -> Identity a -> Bool # maximum :: Ord a => Identity a -> a # minimum :: Ord a => Identity a -> a # sum :: Num a => Identity a -> a # product :: Num a => Identity a -> a #
Foldable1 Identity	Since: base-4.18.0.0
Instance details Defined in Data.Foldable1 Methods fold1 :: Semigroup m => Identity m -> m # foldMap1 :: Semigroup m => (a -> m) -> Identity a -> m # foldMap1' :: Semigroup m => (a -> m) -> Identity a -> m # toNonEmpty :: Identity a -> NonEmpty a # maximum :: Ord a => Identity a -> a # minimum :: Ord a => Identity a -> a # head :: Identity a -> a # last :: Identity a -> a # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Identity a -> b # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Identity a -> b # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Identity a -> b # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Identity a -> b #
Traversable Identity	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Identity a -> f (Identity b) # sequenceA :: Applicative f => Identity (f a) -> f (Identity a) # mapM :: Monad m => (a -> m b) -> Identity a -> m (Identity b) # sequence :: Monad m => Identity (m a) -> m (Identity a) #
Applicative Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods pure :: a -> Identity a # (<>) :: Identity (a -> b) -> Identity a -> Identity b # liftA2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c # (>) :: Identity a -> Identity b -> Identity b # (<*) :: Identity a -> Identity b -> Identity a #
Functor Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods fmap :: (a -> b) -> Identity a -> Identity b # (<$) :: a -> Identity b -> Identity a #
Monad Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods (>>=) :: Identity a -> (a -> Identity b) -> Identity b # (>>) :: Identity a -> Identity b -> Identity b # return :: a -> Identity a #
Comonad Identity
Instance details Defined in Control.Comonad Methods extract :: Identity a -> a # duplicate :: Identity a -> Identity (Identity a) # extend :: (Identity a -> b) -> Identity a -> Identity b #
ComonadApply Identity
Instance details Defined in Control.Comonad Methods (<@>) :: Identity (a -> b) -> Identity a -> Identity b # (@>) :: Identity a -> Identity b -> Identity b # (<@) :: Identity a -> Identity b -> Identity a #
NFData1 Identity	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf :: (a -> ()) -> Identity a -> () #
Distributive Identity
Instance details Defined in Data.Distributive Methods distribute :: Functor f => f (Identity a) -> Identity (f a) # collect :: Functor f => (a -> Identity b) -> f a -> Identity (f b) # distributeM :: Monad m => m (Identity a) -> Identity (m a) # collectM :: Monad m => (a -> Identity b) -> m a -> Identity (m b) #
Hashable1 Identity
Instance details Defined in Data.Hashable.Class Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> Identity a -> Int #
Settable Identity Source #	So you can pass our `Setter` into combinators from other lens libraries.
Instance details Defined in Control.Lens.Internal.Setter Methods untainted :: Identity a -> a Source # untaintedDot :: Profunctor p => p a (Identity b) -> p a b Source # taintedDot :: Profunctor p => p a b -> p a (Identity b) Source #
Alt Identity	Choose the first option every time. While 'choose the last option' every time is also valid, this instance satisfies more laws. Since: semigroupoids-5.3.6
Instance details Defined in Data.Functor.Alt Methods (<!>) :: Identity a -> Identity a -> Identity a # some :: Applicative Identity => Identity a -> Identity [a] # many :: Applicative Identity => Identity a -> Identity [a] #
Apply Identity
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Identity (a -> b) -> Identity a -> Identity b # (.>) :: Identity a -> Identity b -> Identity b # (<.) :: Identity a -> Identity b -> Identity a # liftF2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c #
Bind Identity
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Identity a -> (a -> Identity b) -> Identity b # join :: Identity (Identity a) -> Identity a #
Extend Identity
Instance details Defined in Data.Functor.Extend Methods duplicated :: Identity a -> Identity (Identity a) # extended :: (Identity a -> b) -> Identity a -> Identity b #
Traversable1 Identity
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Identity a -> f (Identity b) # sequence1 :: Apply f => Identity (f b) -> f (Identity b) #
Generic1 Identity
Instance details Defined in Data.Functor.Identity Associated Types type Rep1 Identity :: k -> Type # Methods from1 :: forall (a :: k). Identity a -> Rep1 Identity a # to1 :: forall (a :: k). Rep1 Identity a -> Identity a #
FoldableWithIndex () Identity
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (() -> a -> m) -> Identity a -> m # ifoldMap' :: Monoid m => (() -> a -> m) -> Identity a -> m # ifoldr :: (() -> a -> b -> b) -> b -> Identity a -> b # ifoldl :: (() -> b -> a -> b) -> b -> Identity a -> b # ifoldr' :: (() -> a -> b -> b) -> b -> Identity a -> b # ifoldl' :: (() -> b -> a -> b) -> b -> Identity a -> b #
FunctorWithIndex () Identity
Instance details Defined in WithIndex Methods imap :: (() -> a -> b) -> Identity a -> Identity b #
TraversableWithIndex () Identity
Instance details Defined in WithIndex Methods itraverse :: Applicative f => (() -> a -> f b) -> Identity a -> f (Identity b) #
Cosieve ReifiedGetter Identity Source #
Instance details Defined in Control.Lens.Reified Methods cosieve :: ReifiedGetter a b -> Identity a -> b #
Sieve ReifiedGetter Identity Source #
Instance details Defined in Control.Lens.Reified Methods sieve :: ReifiedGetter a b -> a -> Identity b #
Comonad w => ComonadCofree Identity (CoiterT w)
Instance details Defined in Control.Comonad.Trans.Coiter Methods unwrap :: CoiterT w a -> Identity (CoiterT w a) #
Monad m => MonadFree Identity (IterT m)
Instance details Defined in Control.Monad.Trans.Iter Methods wrap :: Identity (IterT m a) -> IterT m a #
Unbox a => Vector Vector (Identity a)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: Mutable Vector s (Identity a) -> ST s (Vector (Identity a)) # basicUnsafeThaw :: Vector (Identity a) -> ST s (Mutable Vector s (Identity a)) # basicLength :: Vector (Identity a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (Identity a) -> Vector (Identity a) # basicUnsafeIndexM :: Vector (Identity a) -> Int -> Box (Identity a) # basicUnsafeCopy :: Mutable Vector s (Identity a) -> Vector (Identity a) -> ST s () # elemseq :: Vector (Identity a) -> Identity a -> b -> b #
Unbox a => MVector MVector (Identity a)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s (Identity a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (Identity a) -> MVector s (Identity a) # basicOverlaps :: MVector s (Identity a) -> MVector s (Identity a) -> Bool # basicUnsafeNew :: Int -> ST s (MVector s (Identity a)) # basicInitialize :: MVector s (Identity a) -> ST s () # basicUnsafeReplicate :: Int -> Identity a -> ST s (MVector s (Identity a)) # basicUnsafeRead :: MVector s (Identity a) -> Int -> ST s (Identity a) # basicUnsafeWrite :: MVector s (Identity a) -> Int -> Identity a -> ST s () # basicClear :: MVector s (Identity a) -> ST s () # basicSet :: MVector s (Identity a) -> Identity a -> ST s () # basicUnsafeCopy :: MVector s (Identity a) -> MVector s (Identity a) -> ST s () # basicUnsafeMove :: MVector s (Identity a) -> MVector s (Identity a) -> ST s () # basicUnsafeGrow :: MVector s (Identity a) -> Int -> ST s (MVector s (Identity a)) #
Data a => Data (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Identity a -> c (Identity a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Identity a) # toConstr :: Identity a -> Constr # dataTypeOf :: Identity a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Identity a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Identity a)) # gmapT :: (forall b. Data b => b -> b) -> Identity a -> Identity a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Identity a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Identity a -> r # gmapQ :: (forall d. Data d => d -> u) -> Identity a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Identity a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Identity a -> m (Identity a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Identity a -> m (Identity a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Identity a -> m (Identity a) #
Storable a => Storable (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods sizeOf :: Identity a -> Int # alignment :: Identity a -> Int # peekElemOff :: Ptr (Identity a) -> Int -> IO (Identity a) # pokeElemOff :: Ptr (Identity a) -> Int -> Identity a -> IO () # peekByteOff :: Ptr b -> Int -> IO (Identity a) # pokeByteOff :: Ptr b -> Int -> Identity a -> IO () # peek :: Ptr (Identity a) -> IO (Identity a) # poke :: Ptr (Identity a) -> Identity a -> IO () #
Monoid a => Monoid (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods mempty :: Identity a # mappend :: Identity a -> Identity a -> Identity a # mconcat :: [Identity a] -> Identity a #
Semigroup a => Semigroup (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods (<>) :: Identity a -> Identity a -> Identity a # sconcat :: NonEmpty (Identity a) -> Identity a # stimes :: Integral b => b -> Identity a -> Identity a #
Bits a => Bits (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods (.&.) :: Identity a -> Identity a -> Identity a # (.\|.) :: Identity a -> Identity a -> Identity a # xor :: Identity a -> Identity a -> Identity a # complement :: Identity a -> Identity a # shift :: Identity a -> Int -> Identity a # rotate :: Identity a -> Int -> Identity a # zeroBits :: Identity a # bit :: Int -> Identity a # setBit :: Identity a -> Int -> Identity a # clearBit :: Identity a -> Int -> Identity a # complementBit :: Identity a -> Int -> Identity a # testBit :: Identity a -> Int -> Bool # bitSizeMaybe :: Identity a -> Maybe Int # bitSize :: Identity a -> Int # isSigned :: Identity a -> Bool # shiftL :: Identity a -> Int -> Identity a # unsafeShiftL :: Identity a -> Int -> Identity a # shiftR :: Identity a -> Int -> Identity a # unsafeShiftR :: Identity a -> Int -> Identity a # rotateL :: Identity a -> Int -> Identity a # rotateR :: Identity a -> Int -> Identity a # popCount :: Identity a -> Int #
FiniteBits a => FiniteBits (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods finiteBitSize :: Identity a -> Int # countLeadingZeros :: Identity a -> Int # countTrailingZeros :: Identity a -> Int #
Bounded a => Bounded (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods minBound :: Identity a # maxBound :: Identity a #
Enum a => Enum (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods succ :: Identity a -> Identity a # pred :: Identity a -> Identity a # toEnum :: Int -> Identity a # fromEnum :: Identity a -> Int # enumFrom :: Identity a -> [Identity a] # enumFromThen :: Identity a -> Identity a -> [Identity a] # enumFromTo :: Identity a -> Identity a -> [Identity a] # enumFromThenTo :: Identity a -> Identity a -> Identity a -> [Identity a] #
Floating a => Floating (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods pi :: Identity a # exp :: Identity a -> Identity a # log :: Identity a -> Identity a # sqrt :: Identity a -> Identity a # (**) :: Identity a -> Identity a -> Identity a # logBase :: Identity a -> Identity a -> Identity a # sin :: Identity a -> Identity a # cos :: Identity a -> Identity a # tan :: Identity a -> Identity a # asin :: Identity a -> Identity a # acos :: Identity a -> Identity a # atan :: Identity a -> Identity a # sinh :: Identity a -> Identity a # cosh :: Identity a -> Identity a # tanh :: Identity a -> Identity a # asinh :: Identity a -> Identity a # acosh :: Identity a -> Identity a # atanh :: Identity a -> Identity a # log1p :: Identity a -> Identity a # expm1 :: Identity a -> Identity a # log1pexp :: Identity a -> Identity a # log1mexp :: Identity a -> Identity a #
RealFloat a => RealFloat (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods floatRadix :: Identity a -> Integer # floatDigits :: Identity a -> Int # floatRange :: Identity a -> (Int, Int) # decodeFloat :: Identity a -> (Integer, Int) # encodeFloat :: Integer -> Int -> Identity a # exponent :: Identity a -> Int # significand :: Identity a -> Identity a # scaleFloat :: Int -> Identity a -> Identity a # isNaN :: Identity a -> Bool # isInfinite :: Identity a -> Bool # isDenormalized :: Identity a -> Bool # isNegativeZero :: Identity a -> Bool # isIEEE :: Identity a -> Bool # atan2 :: Identity a -> Identity a -> Identity a #
Generic (Identity a)
Instance details Defined in Data.Functor.Identity Associated Types type Rep (Identity a) :: Type -> Type # Methods from :: Identity a -> Rep (Identity a) x # to :: Rep (Identity a) x -> Identity a #
Ix a => Ix (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods range :: (Identity a, Identity a) -> [Identity a] # index :: (Identity a, Identity a) -> Identity a -> Int # unsafeIndex :: (Identity a, Identity a) -> Identity a -> Int # inRange :: (Identity a, Identity a) -> Identity a -> Bool # rangeSize :: (Identity a, Identity a) -> Int # unsafeRangeSize :: (Identity a, Identity a) -> Int #
Num a => Num (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods (+) :: Identity a -> Identity a -> Identity a # (-) :: Identity a -> Identity a -> Identity a # (*) :: Identity a -> Identity a -> Identity a # negate :: Identity a -> Identity a # abs :: Identity a -> Identity a # signum :: Identity a -> Identity a # fromInteger :: Integer -> Identity a #
Read a => Read (Identity a)	This instance would be equivalent to the derived instances of the `Identity` newtype if the `runIdentity` field were removed Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods readsPrec :: Int -> ReadS (Identity a) # readList :: ReadS [Identity a] # readPrec :: ReadPrec (Identity a) # readListPrec :: ReadPrec [Identity a] #
Fractional a => Fractional (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods (/) :: Identity a -> Identity a -> Identity a # recip :: Identity a -> Identity a # fromRational :: Rational -> Identity a #
Integral a => Integral (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods quot :: Identity a -> Identity a -> Identity a # rem :: Identity a -> Identity a -> Identity a # div :: Identity a -> Identity a -> Identity a # mod :: Identity a -> Identity a -> Identity a # quotRem :: Identity a -> Identity a -> (Identity a, Identity a) # divMod :: Identity a -> Identity a -> (Identity a, Identity a) # toInteger :: Identity a -> Integer #
Real a => Real (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods toRational :: Identity a -> Rational #
RealFrac a => RealFrac (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods properFraction :: Integral b => Identity a -> (b, Identity a) # truncate :: Integral b => Identity a -> b # round :: Integral b => Identity a -> b # ceiling :: Integral b => Identity a -> b # floor :: Integral b => Identity a -> b #
Show a => Show (Identity a)	This instance would be equivalent to the derived instances of the `Identity` newtype if the `runIdentity` field were removed Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods showsPrec :: Int -> Identity a -> ShowS # show :: Identity a -> String # showList :: [Identity a] -> ShowS #
NFData a => NFData (Identity a)	Since: deepseq-1.4.0.0
Instance details Defined in Control.DeepSeq Methods rnf :: Identity a -> () #
Eq a => Eq (Identity a)	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods (==) :: Identity a -> Identity a -> Bool # (/=) :: Identity a -> Identity a -> Bool #
Ord a => Ord (Identity a)	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods compare :: Identity a -> Identity a -> Ordering # (<) :: Identity a -> Identity a -> Bool # (<=) :: Identity a -> Identity a -> Bool # (>) :: Identity a -> Identity a -> Bool # (>=) :: Identity a -> Identity a -> Bool # max :: Identity a -> Identity a -> Identity a # min :: Identity a -> Identity a -> Identity a #
Hashable a => Hashable (Identity a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Identity a -> Int # hash :: Identity a -> Int #
Ixed (Identity a) Source #
Instance details Defined in Control.Lens.At Methods ix :: Index (Identity a) -> Traversal' (Identity a) (IxValue (Identity a)) Source #
Wrapped (Identity a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Identity a) Source # Methods _Wrapped' :: Iso' (Identity a) (Unwrapped (Identity a)) Source #
Prim a => Prim (Identity a)	Since: primitive-0.6.5.0
Instance details Defined in Data.Primitive.Types Methods sizeOf# :: Identity a -> Int# # alignment# :: Identity a -> Int# # indexByteArray# :: ByteArray# -> Int# -> Identity a # readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Identity a #) # writeByteArray# :: MutableByteArray# s -> Int# -> Identity a -> State# s -> State# s # setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Identity a -> State# s -> State# s # indexOffAddr# :: Addr# -> Int# -> Identity a # readOffAddr# :: Addr# -> Int# -> State# s -> (# State# s, Identity a #) # writeOffAddr# :: Addr# -> Int# -> Identity a -> State# s -> State# s # setOffAddr# :: Addr# -> Int# -> Int# -> Identity a -> State# s -> State# s #
Unbox a => Unbox (Identity a)
Instance details Defined in Data.Vector.Unboxed.Base
t ~ Identity b => Rewrapped (Identity a) t Source #
Instance details Defined in Control.Lens.Wrapped
Each (Identity a) (Identity b) a b Source #	`each` :: `Traversal` (`Identity` a) (`Identity` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Identity a) (Identity b) a b Source #
Field1 (Identity a) (Identity b) a b Source #
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (Identity a) (Identity b) a b Source #
Cosieve (->) Identity
Instance details Defined in Data.Profunctor.Sieve Methods cosieve :: (a -> b) -> Identity a -> b #
Sieve (->) Identity
Instance details Defined in Data.Profunctor.Sieve Methods sieve :: (a -> b) -> a -> Identity b #
type Rep Identity
Instance details Defined in Data.Functor.Rep type Rep Identity = ()
type Rep1 Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity type Rep1 Identity = D1 ('MetaData "Identity" "Data.Functor.Identity" "base" 'True) (C1 ('MetaCons "Identity" 'PrefixI 'True) (S1 ('MetaSel ('Just "runIdentity") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
newtype MVector s (Identity a)
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s (Identity a) = MV_Identity (MVector s a)
type Rep (Identity a)	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity type Rep (Identity a) = D1 ('MetaData "Identity" "Data.Functor.Identity" "base" 'True) (C1 ('MetaCons "Identity" 'PrefixI 'True) (S1 ('MetaSel ('Just "runIdentity") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Index (Identity a) Source #
Instance details Defined in Control.Lens.At type Index (Identity a) = ()
type IxValue (Identity a) Source #
Instance details Defined in Control.Lens.At type IxValue (Identity a) = a
type Unwrapped (Identity a) Source #
Instance details Defined in Control.Lens.Wrapped type Unwrapped (Identity a) = a
newtype Vector (Identity a)
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector (Identity a) = V_Identity (Vector a)

type IndexedTraversal i s t a b = forall p f. (Indexable i p, Applicative f) => p a (f b) -> s -> f t Source #

Every IndexedTraversal is a valid Traversal or IndexedFold.

The Indexed constraint is used to allow an IndexedTraversal to be used directly as a Traversal.

The Traversal laws are still required to hold.

In addition, the index i should satisfy the requirement that it stays unchanged even when modifying the value a, otherwise traversals like indices break the Traversal laws.

class (FunctorWithIndex i t, FoldableWithIndex i t, Traversable t) => TraversableWithIndex i (t :: Type -> Type) | t -> i where #

A Traversable with an additional index.

An instance must satisfy a (modified) form of the Traversable laws:

itraverse (const Identity) ≡ Identity
fmap (itraverse f) . itraverse g ≡ getCompose . itraverse (\i -> Compose . fmap (f i) . g i)

Minimal complete definition

Nothing

Methods

itraverse :: Applicative f => (i -> a -> f b) -> t a -> f (t b) #

Traverse an indexed container.

itraverse ≡ itraverseOf itraversed

Instances

Instances details

TraversableWithIndex () Identity
Instance details Defined in WithIndex Methods itraverse :: Applicative f => (() -> a -> f b) -> Identity a -> f (Identity b) #
TraversableWithIndex () Par1
Instance details Defined in WithIndex Methods itraverse :: Applicative f => (() -> a -> f b) -> Par1 a -> f (Par1 b) #
TraversableWithIndex () Maybe
Instance details Defined in WithIndex Methods itraverse :: Applicative f => (() -> a -> f b) -> Maybe a -> f (Maybe b) #
TraversableWithIndex Int ZipList
Instance details Defined in WithIndex Methods itraverse :: Applicative f => (Int -> a -> f b) -> ZipList a -> f (ZipList b) #
TraversableWithIndex Int NonEmpty
Instance details Defined in WithIndex Methods itraverse :: Applicative f => (Int -> a -> f b) -> NonEmpty a -> f (NonEmpty b) #
TraversableWithIndex Int IntMap
Instance details Defined in WithIndex Methods itraverse :: Applicative f => (Int -> a -> f b) -> IntMap a -> f (IntMap b) #
TraversableWithIndex Int Seq
Instance details Defined in WithIndex Methods itraverse :: Applicative f => (Int -> a -> f b) -> Seq a -> f (Seq b) #
TraversableWithIndex Int Deque Source #
Instance details Defined in Control.Lens.Internal.Deque Methods itraverse :: Applicative f => (Int -> a -> f b) -> Deque a -> f (Deque b) #
TraversableWithIndex Int List
Instance details Defined in WithIndex Methods itraverse :: Applicative f => (Int -> a -> f b) -> [a] -> f [b] #
TraversableWithIndex Void (Proxy :: Type -> Type)
Instance details Defined in WithIndex Methods itraverse :: Applicative f => (Void -> a -> f b) -> Proxy a -> f (Proxy b) #
TraversableWithIndex Void (U1 :: Type -> Type)
Instance details Defined in WithIndex Methods itraverse :: Applicative f => (Void -> a -> f b) -> U1 a -> f (U1 b) #
TraversableWithIndex Void (V1 :: Type -> Type)
Instance details Defined in WithIndex Methods itraverse :: Applicative f => (Void -> a -> f b) -> V1 a -> f (V1 b) #
Ix i => TraversableWithIndex i (Array i)
Instance details Defined in WithIndex Methods itraverse :: Applicative f => (i -> a -> f b) -> Array i a -> f (Array i b) #
TraversableWithIndex i (Level i) Source #
Instance details Defined in Control.Lens.Internal.Level Methods itraverse :: Applicative f => (i -> a -> f b) -> Level i a -> f (Level i b) #
TraversableWithIndex k (Map k)
Instance details Defined in WithIndex Methods itraverse :: Applicative f => (k -> a -> f b) -> Map k a -> f (Map k b) #
TraversableWithIndex k ((,) k)
Instance details Defined in WithIndex Methods itraverse :: Applicative f => (k -> a -> f b) -> (k, a) -> f (k, b) #
TraversableWithIndex Void (Const e :: Type -> Type)
Instance details Defined in WithIndex Methods itraverse :: Applicative f => (Void -> a -> f b) -> Const e a -> f (Const e b) #
TraversableWithIndex Void (Constant e :: Type -> Type)
Instance details Defined in WithIndex Methods itraverse :: Applicative f => (Void -> a -> f b) -> Constant e a -> f (Constant e b) #
TraversableWithIndex i f => TraversableWithIndex i (Rec1 f)
Instance details Defined in WithIndex Methods itraverse :: Applicative f0 => (i -> a -> f0 b) -> Rec1 f a -> f0 (Rec1 f b) #
TraversableWithIndex i f => TraversableWithIndex i (Backwards f)
Instance details Defined in WithIndex Methods itraverse :: Applicative f0 => (i -> a -> f0 b) -> Backwards f a -> f0 (Backwards f b) #
TraversableWithIndex i m => TraversableWithIndex i (IdentityT m)
Instance details Defined in WithIndex Methods itraverse :: Applicative f => (i -> a -> f b) -> IdentityT m a -> f (IdentityT m b) #
TraversableWithIndex i f => TraversableWithIndex i (Reverse f)
Instance details Defined in WithIndex Methods itraverse :: Applicative f0 => (i -> a -> f0 b) -> Reverse f a -> f0 (Reverse f b) #
TraversableWithIndex Void (K1 i c :: Type -> Type)
Instance details Defined in WithIndex Methods itraverse :: Applicative f => (Void -> a -> f b) -> K1 i c a -> f (K1 i c b) #
TraversableWithIndex i (Magma i t b) Source #
Instance details Defined in Control.Lens.Internal.Magma Methods itraverse :: Applicative f => (i -> a -> f b0) -> Magma i t b a -> f (Magma i t b b0) #
TraversableWithIndex [Int] Tree
Instance details Defined in WithIndex Methods itraverse :: Applicative f => ([Int] -> a -> f b) -> Tree a -> f (Tree b) #
TraversableWithIndex i f => TraversableWithIndex [i] (Cofree f)
Instance details Defined in Control.Comonad.Cofree Methods itraverse :: Applicative f0 => ([i] -> a -> f0 b) -> Cofree f a -> f0 (Cofree f b) #
TraversableWithIndex i f => TraversableWithIndex [i] (Free f)
Instance details Defined in Control.Monad.Free Methods itraverse :: Applicative f0 => ([i] -> a -> f0 b) -> Free f a -> f0 (Free f b) #
(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (Product f g)
Instance details Defined in WithIndex Methods itraverse :: Applicative f0 => (Either i j -> a -> f0 b) -> Product f g a -> f0 (Product f g b) #
(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (Sum f g)
Instance details Defined in WithIndex Methods itraverse :: Applicative f0 => (Either i j -> a -> f0 b) -> Sum f g a -> f0 (Sum f g b) #
(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (f :*: g)
Instance details Defined in WithIndex Methods itraverse :: Applicative f0 => (Either i j -> a -> f0 b) -> (f :: g) a -> f0 ((f :: g) b) #
(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (f :+: g)
Instance details Defined in WithIndex Methods itraverse :: Applicative f0 => (Either i j -> a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b) #
(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (i, j) (Compose f g)
Instance details Defined in WithIndex Methods itraverse :: Applicative f0 => ((i, j) -> a -> f0 b) -> Compose f g a -> f0 (Compose f g b) #
(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (i, j) (f :.: g)
Instance details Defined in WithIndex Methods itraverse :: Applicative f0 => ((i, j) -> a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b) #

class Foldable f => FoldableWithIndex i (f :: Type -> Type) | f -> i where #

A container that supports folding with an additional index.

Minimal complete definition

Nothing

Methods

ifoldMap :: Monoid m => (i -> a -> m) -> f a -> m #

Fold a container by mapping value to an arbitrary Monoid with access to the index i.

When you don't need access to the index then foldMap is more flexible in what it accepts.

foldMap ≡ ifoldMap . const

ifoldMap' :: Monoid m => (i -> a -> m) -> f a -> m #

A variant of ifoldMap that is strict in the accumulator.

When you don't need access to the index then foldMap' is more flexible in what it accepts.

foldMap' ≡ ifoldMap' . const

ifoldr :: (i -> a -> b -> b) -> b -> f a -> b #

Right-associative fold of an indexed container with access to the index i.

When you don't need access to the index then foldr is more flexible in what it accepts.

foldr ≡ ifoldr . const

ifoldl :: (i -> b -> a -> b) -> b -> f a -> b #

Left-associative fold of an indexed container with access to the index i.

When you don't need access to the index then foldl is more flexible in what it accepts.

foldl ≡ ifoldl . const

ifoldr' :: (i -> a -> b -> b) -> b -> f a -> b #

Strictly fold right over the elements of a structure with access to the index i.

When you don't need access to the index then foldr' is more flexible in what it accepts.

foldr' ≡ ifoldr' . const

ifoldl' :: (i -> b -> a -> b) -> b -> f a -> b #

Fold over the elements of a structure with an index, associating to the left, but strictly.

When you don't need access to the index then foldlOf' is more flexible in what it accepts.

foldl' l ≡ ifoldl' l . const

Instances

Instances details

FoldableWithIndex () Identity
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (() -> a -> m) -> Identity a -> m # ifoldMap' :: Monoid m => (() -> a -> m) -> Identity a -> m # ifoldr :: (() -> a -> b -> b) -> b -> Identity a -> b # ifoldl :: (() -> b -> a -> b) -> b -> Identity a -> b # ifoldr' :: (() -> a -> b -> b) -> b -> Identity a -> b # ifoldl' :: (() -> b -> a -> b) -> b -> Identity a -> b #
FoldableWithIndex () Par1
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (() -> a -> m) -> Par1 a -> m # ifoldMap' :: Monoid m => (() -> a -> m) -> Par1 a -> m # ifoldr :: (() -> a -> b -> b) -> b -> Par1 a -> b # ifoldl :: (() -> b -> a -> b) -> b -> Par1 a -> b # ifoldr' :: (() -> a -> b -> b) -> b -> Par1 a -> b # ifoldl' :: (() -> b -> a -> b) -> b -> Par1 a -> b #
FoldableWithIndex () Maybe
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (() -> a -> m) -> Maybe a -> m # ifoldMap' :: Monoid m => (() -> a -> m) -> Maybe a -> m # ifoldr :: (() -> a -> b -> b) -> b -> Maybe a -> b # ifoldl :: (() -> b -> a -> b) -> b -> Maybe a -> b # ifoldr' :: (() -> a -> b -> b) -> b -> Maybe a -> b # ifoldl' :: (() -> b -> a -> b) -> b -> Maybe a -> b #
FoldableWithIndex Int ZipList
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (Int -> a -> m) -> ZipList a -> m # ifoldMap' :: Monoid m => (Int -> a -> m) -> ZipList a -> m # ifoldr :: (Int -> a -> b -> b) -> b -> ZipList a -> b # ifoldl :: (Int -> b -> a -> b) -> b -> ZipList a -> b # ifoldr' :: (Int -> a -> b -> b) -> b -> ZipList a -> b # ifoldl' :: (Int -> b -> a -> b) -> b -> ZipList a -> b #
FoldableWithIndex Int NonEmpty
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (Int -> a -> m) -> NonEmpty a -> m # ifoldMap' :: Monoid m => (Int -> a -> m) -> NonEmpty a -> m # ifoldr :: (Int -> a -> b -> b) -> b -> NonEmpty a -> b # ifoldl :: (Int -> b -> a -> b) -> b -> NonEmpty a -> b # ifoldr' :: (Int -> a -> b -> b) -> b -> NonEmpty a -> b # ifoldl' :: (Int -> b -> a -> b) -> b -> NonEmpty a -> b #
FoldableWithIndex Int IntMap
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (Int -> a -> m) -> IntMap a -> m # ifoldMap' :: Monoid m => (Int -> a -> m) -> IntMap a -> m # ifoldr :: (Int -> a -> b -> b) -> b -> IntMap a -> b # ifoldl :: (Int -> b -> a -> b) -> b -> IntMap a -> b # ifoldr' :: (Int -> a -> b -> b) -> b -> IntMap a -> b # ifoldl' :: (Int -> b -> a -> b) -> b -> IntMap a -> b #
FoldableWithIndex Int Seq
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (Int -> a -> m) -> Seq a -> m # ifoldMap' :: Monoid m => (Int -> a -> m) -> Seq a -> m # ifoldr :: (Int -> a -> b -> b) -> b -> Seq a -> b # ifoldl :: (Int -> b -> a -> b) -> b -> Seq a -> b # ifoldr' :: (Int -> a -> b -> b) -> b -> Seq a -> b # ifoldl' :: (Int -> b -> a -> b) -> b -> Seq a -> b #
FoldableWithIndex Int Deque Source #
Instance details Defined in Control.Lens.Internal.Deque Methods ifoldMap :: Monoid m => (Int -> a -> m) -> Deque a -> m # ifoldMap' :: Monoid m => (Int -> a -> m) -> Deque a -> m # ifoldr :: (Int -> a -> b -> b) -> b -> Deque a -> b # ifoldl :: (Int -> b -> a -> b) -> b -> Deque a -> b # ifoldr' :: (Int -> a -> b -> b) -> b -> Deque a -> b # ifoldl' :: (Int -> b -> a -> b) -> b -> Deque a -> b #
FoldableWithIndex Int List
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (Int -> a -> m) -> [a] -> m # ifoldMap' :: Monoid m => (Int -> a -> m) -> [a] -> m # ifoldr :: (Int -> a -> b -> b) -> b -> [a] -> b # ifoldl :: (Int -> b -> a -> b) -> b -> [a] -> b # ifoldr' :: (Int -> a -> b -> b) -> b -> [a] -> b # ifoldl' :: (Int -> b -> a -> b) -> b -> [a] -> b #
FoldableWithIndex Void (Proxy :: Type -> Type)
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (Void -> a -> m) -> Proxy a -> m # ifoldMap' :: Monoid m => (Void -> a -> m) -> Proxy a -> m # ifoldr :: (Void -> a -> b -> b) -> b -> Proxy a -> b # ifoldl :: (Void -> b -> a -> b) -> b -> Proxy a -> b # ifoldr' :: (Void -> a -> b -> b) -> b -> Proxy a -> b # ifoldl' :: (Void -> b -> a -> b) -> b -> Proxy a -> b #
FoldableWithIndex Void (U1 :: Type -> Type)
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (Void -> a -> m) -> U1 a -> m # ifoldMap' :: Monoid m => (Void -> a -> m) -> U1 a -> m # ifoldr :: (Void -> a -> b -> b) -> b -> U1 a -> b # ifoldl :: (Void -> b -> a -> b) -> b -> U1 a -> b # ifoldr' :: (Void -> a -> b -> b) -> b -> U1 a -> b # ifoldl' :: (Void -> b -> a -> b) -> b -> U1 a -> b #
FoldableWithIndex Void (V1 :: Type -> Type)
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (Void -> a -> m) -> V1 a -> m # ifoldMap' :: Monoid m => (Void -> a -> m) -> V1 a -> m # ifoldr :: (Void -> a -> b -> b) -> b -> V1 a -> b # ifoldl :: (Void -> b -> a -> b) -> b -> V1 a -> b # ifoldr' :: (Void -> a -> b -> b) -> b -> V1 a -> b # ifoldl' :: (Void -> b -> a -> b) -> b -> V1 a -> b #
Ix i => FoldableWithIndex i (Array i)
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (i -> a -> m) -> Array i a -> m # ifoldMap' :: Monoid m => (i -> a -> m) -> Array i a -> m # ifoldr :: (i -> a -> b -> b) -> b -> Array i a -> b # ifoldl :: (i -> b -> a -> b) -> b -> Array i a -> b # ifoldr' :: (i -> a -> b -> b) -> b -> Array i a -> b # ifoldl' :: (i -> b -> a -> b) -> b -> Array i a -> b #
FoldableWithIndex i (Level i) Source #
Instance details Defined in Control.Lens.Internal.Level Methods ifoldMap :: Monoid m => (i -> a -> m) -> Level i a -> m # ifoldMap' :: Monoid m => (i -> a -> m) -> Level i a -> m # ifoldr :: (i -> a -> b -> b) -> b -> Level i a -> b # ifoldl :: (i -> b -> a -> b) -> b -> Level i a -> b # ifoldr' :: (i -> a -> b -> b) -> b -> Level i a -> b # ifoldl' :: (i -> b -> a -> b) -> b -> Level i a -> b #
FoldableWithIndex k (Map k)
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (k -> a -> m) -> Map k a -> m # ifoldMap' :: Monoid m => (k -> a -> m) -> Map k a -> m # ifoldr :: (k -> a -> b -> b) -> b -> Map k a -> b # ifoldl :: (k -> b -> a -> b) -> b -> Map k a -> b # ifoldr' :: (k -> a -> b -> b) -> b -> Map k a -> b # ifoldl' :: (k -> b -> a -> b) -> b -> Map k a -> b #
FoldableWithIndex k ((,) k)
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (k -> a -> m) -> (k, a) -> m # ifoldMap' :: Monoid m => (k -> a -> m) -> (k, a) -> m # ifoldr :: (k -> a -> b -> b) -> b -> (k, a) -> b # ifoldl :: (k -> b -> a -> b) -> b -> (k, a) -> b # ifoldr' :: (k -> a -> b -> b) -> b -> (k, a) -> b # ifoldl' :: (k -> b -> a -> b) -> b -> (k, a) -> b #
FoldableWithIndex Void (Const e :: Type -> Type)
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (Void -> a -> m) -> Const e a -> m # ifoldMap' :: Monoid m => (Void -> a -> m) -> Const e a -> m # ifoldr :: (Void -> a -> b -> b) -> b -> Const e a -> b # ifoldl :: (Void -> b -> a -> b) -> b -> Const e a -> b # ifoldr' :: (Void -> a -> b -> b) -> b -> Const e a -> b # ifoldl' :: (Void -> b -> a -> b) -> b -> Const e a -> b #
FoldableWithIndex Void (Constant e :: Type -> Type)
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (Void -> a -> m) -> Constant e a -> m # ifoldMap' :: Monoid m => (Void -> a -> m) -> Constant e a -> m # ifoldr :: (Void -> a -> b -> b) -> b -> Constant e a -> b # ifoldl :: (Void -> b -> a -> b) -> b -> Constant e a -> b # ifoldr' :: (Void -> a -> b -> b) -> b -> Constant e a -> b # ifoldl' :: (Void -> b -> a -> b) -> b -> Constant e a -> b #
FoldableWithIndex i f => FoldableWithIndex i (Rec1 f)
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (i -> a -> m) -> Rec1 f a -> m # ifoldMap' :: Monoid m => (i -> a -> m) -> Rec1 f a -> m # ifoldr :: (i -> a -> b -> b) -> b -> Rec1 f a -> b # ifoldl :: (i -> b -> a -> b) -> b -> Rec1 f a -> b # ifoldr' :: (i -> a -> b -> b) -> b -> Rec1 f a -> b # ifoldl' :: (i -> b -> a -> b) -> b -> Rec1 f a -> b #
FoldableWithIndex i f => FoldableWithIndex i (Backwards f)
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (i -> a -> m) -> Backwards f a -> m # ifoldMap' :: Monoid m => (i -> a -> m) -> Backwards f a -> m # ifoldr :: (i -> a -> b -> b) -> b -> Backwards f a -> b # ifoldl :: (i -> b -> a -> b) -> b -> Backwards f a -> b # ifoldr' :: (i -> a -> b -> b) -> b -> Backwards f a -> b # ifoldl' :: (i -> b -> a -> b) -> b -> Backwards f a -> b #
FoldableWithIndex i m => FoldableWithIndex i (IdentityT m)
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m0 => (i -> a -> m0) -> IdentityT m a -> m0 # ifoldMap' :: Monoid m0 => (i -> a -> m0) -> IdentityT m a -> m0 # ifoldr :: (i -> a -> b -> b) -> b -> IdentityT m a -> b # ifoldl :: (i -> b -> a -> b) -> b -> IdentityT m a -> b # ifoldr' :: (i -> a -> b -> b) -> b -> IdentityT m a -> b # ifoldl' :: (i -> b -> a -> b) -> b -> IdentityT m a -> b #
FoldableWithIndex i f => FoldableWithIndex i (Reverse f)
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (i -> a -> m) -> Reverse f a -> m # ifoldMap' :: Monoid m => (i -> a -> m) -> Reverse f a -> m # ifoldr :: (i -> a -> b -> b) -> b -> Reverse f a -> b # ifoldl :: (i -> b -> a -> b) -> b -> Reverse f a -> b # ifoldr' :: (i -> a -> b -> b) -> b -> Reverse f a -> b # ifoldl' :: (i -> b -> a -> b) -> b -> Reverse f a -> b #
FoldableWithIndex Void (K1 i c :: Type -> Type)
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (Void -> a -> m) -> K1 i c a -> m # ifoldMap' :: Monoid m => (Void -> a -> m) -> K1 i c a -> m # ifoldr :: (Void -> a -> b -> b) -> b -> K1 i c a -> b # ifoldl :: (Void -> b -> a -> b) -> b -> K1 i c a -> b # ifoldr' :: (Void -> a -> b -> b) -> b -> K1 i c a -> b # ifoldl' :: (Void -> b -> a -> b) -> b -> K1 i c a -> b #
FoldableWithIndex i (Magma i t b) Source #
Instance details Defined in Control.Lens.Internal.Magma Methods ifoldMap :: Monoid m => (i -> a -> m) -> Magma i t b a -> m # ifoldMap' :: Monoid m => (i -> a -> m) -> Magma i t b a -> m # ifoldr :: (i -> a -> b0 -> b0) -> b0 -> Magma i t b a -> b0 # ifoldl :: (i -> b0 -> a -> b0) -> b0 -> Magma i t b a -> b0 # ifoldr' :: (i -> a -> b0 -> b0) -> b0 -> Magma i t b a -> b0 # ifoldl' :: (i -> b0 -> a -> b0) -> b0 -> Magma i t b a -> b0 #
FoldableWithIndex [Int] Tree
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => ([Int] -> a -> m) -> Tree a -> m # ifoldMap' :: Monoid m => ([Int] -> a -> m) -> Tree a -> m # ifoldr :: ([Int] -> a -> b -> b) -> b -> Tree a -> b # ifoldl :: ([Int] -> b -> a -> b) -> b -> Tree a -> b # ifoldr' :: ([Int] -> a -> b -> b) -> b -> Tree a -> b # ifoldl' :: ([Int] -> b -> a -> b) -> b -> Tree a -> b #
FoldableWithIndex i f => FoldableWithIndex [i] (Cofree f)
Instance details Defined in Control.Comonad.Cofree Methods ifoldMap :: Monoid m => ([i] -> a -> m) -> Cofree f a -> m # ifoldMap' :: Monoid m => ([i] -> a -> m) -> Cofree f a -> m # ifoldr :: ([i] -> a -> b -> b) -> b -> Cofree f a -> b # ifoldl :: ([i] -> b -> a -> b) -> b -> Cofree f a -> b # ifoldr' :: ([i] -> a -> b -> b) -> b -> Cofree f a -> b # ifoldl' :: ([i] -> b -> a -> b) -> b -> Cofree f a -> b #
FoldableWithIndex i f => FoldableWithIndex [i] (Free f)
Instance details Defined in Control.Monad.Free Methods ifoldMap :: Monoid m => ([i] -> a -> m) -> Free f a -> m # ifoldMap' :: Monoid m => ([i] -> a -> m) -> Free f a -> m # ifoldr :: ([i] -> a -> b -> b) -> b -> Free f a -> b # ifoldl :: ([i] -> b -> a -> b) -> b -> Free f a -> b # ifoldr' :: ([i] -> a -> b -> b) -> b -> Free f a -> b # ifoldl' :: ([i] -> b -> a -> b) -> b -> Free f a -> b #
(FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (Either i j) (Product f g)
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (Either i j -> a -> m) -> Product f g a -> m # ifoldMap' :: Monoid m => (Either i j -> a -> m) -> Product f g a -> m # ifoldr :: (Either i j -> a -> b -> b) -> b -> Product f g a -> b # ifoldl :: (Either i j -> b -> a -> b) -> b -> Product f g a -> b # ifoldr' :: (Either i j -> a -> b -> b) -> b -> Product f g a -> b # ifoldl' :: (Either i j -> b -> a -> b) -> b -> Product f g a -> b #
(FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (Either i j) (Sum f g)
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (Either i j -> a -> m) -> Sum f g a -> m # ifoldMap' :: Monoid m => (Either i j -> a -> m) -> Sum f g a -> m # ifoldr :: (Either i j -> a -> b -> b) -> b -> Sum f g a -> b # ifoldl :: (Either i j -> b -> a -> b) -> b -> Sum f g a -> b # ifoldr' :: (Either i j -> a -> b -> b) -> b -> Sum f g a -> b # ifoldl' :: (Either i j -> b -> a -> b) -> b -> Sum f g a -> b #
(FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (Either i j) (f :*: g)
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (Either i j -> a -> m) -> (f :: g) a -> m # ifoldMap' :: Monoid m => (Either i j -> a -> m) -> (f :: g) a -> m # ifoldr :: (Either i j -> a -> b -> b) -> b -> (f :: g) a -> b # ifoldl :: (Either i j -> b -> a -> b) -> b -> (f :: g) a -> b # ifoldr' :: (Either i j -> a -> b -> b) -> b -> (f :: g) a -> b # ifoldl' :: (Either i j -> b -> a -> b) -> b -> (f :: g) a -> b #
(FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (Either i j) (f :+: g)
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => (Either i j -> a -> m) -> (f :+: g) a -> m # ifoldMap' :: Monoid m => (Either i j -> a -> m) -> (f :+: g) a -> m # ifoldr :: (Either i j -> a -> b -> b) -> b -> (f :+: g) a -> b # ifoldl :: (Either i j -> b -> a -> b) -> b -> (f :+: g) a -> b # ifoldr' :: (Either i j -> a -> b -> b) -> b -> (f :+: g) a -> b # ifoldl' :: (Either i j -> b -> a -> b) -> b -> (f :+: g) a -> b #
(FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (i, j) (Compose f g)
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => ((i, j) -> a -> m) -> Compose f g a -> m # ifoldMap' :: Monoid m => ((i, j) -> a -> m) -> Compose f g a -> m # ifoldr :: ((i, j) -> a -> b -> b) -> b -> Compose f g a -> b # ifoldl :: ((i, j) -> b -> a -> b) -> b -> Compose f g a -> b # ifoldr' :: ((i, j) -> a -> b -> b) -> b -> Compose f g a -> b # ifoldl' :: ((i, j) -> b -> a -> b) -> b -> Compose f g a -> b #
(FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (i, j) (f :.: g)
Instance details Defined in WithIndex Methods ifoldMap :: Monoid m => ((i, j) -> a -> m) -> (f :.: g) a -> m # ifoldMap' :: Monoid m => ((i, j) -> a -> m) -> (f :.: g) a -> m # ifoldr :: ((i, j) -> a -> b -> b) -> b -> (f :.: g) a -> b # ifoldl :: ((i, j) -> b -> a -> b) -> b -> (f :.: g) a -> b # ifoldr' :: ((i, j) -> a -> b -> b) -> b -> (f :.: g) a -> b # ifoldl' :: ((i, j) -> b -> a -> b) -> b -> (f :.: g) a -> b #

class Functor f => FunctorWithIndex i (f :: Type -> Type) | f -> i where #

A Functor with an additional index.

Instances must satisfy a modified form of the Functor laws:

imap f . imap g ≡ imap (\i -> f i . g i)
imap (\_ a -> a) ≡ id

Minimal complete definition

Nothing

Methods

imap :: (i -> a -> b) -> f a -> f b #

Map with access to the index.

Instances

Instances details

FunctorWithIndex () Identity
Instance details Defined in WithIndex Methods imap :: (() -> a -> b) -> Identity a -> Identity b #
FunctorWithIndex () Par1
Instance details Defined in WithIndex Methods imap :: (() -> a -> b) -> Par1 a -> Par1 b #
FunctorWithIndex () Maybe
Instance details Defined in WithIndex Methods imap :: (() -> a -> b) -> Maybe a -> Maybe b #
FunctorWithIndex Int ZipList	Same instance as for `[]`.
Instance details Defined in WithIndex Methods imap :: (Int -> a -> b) -> ZipList a -> ZipList b #
FunctorWithIndex Int NonEmpty
Instance details Defined in WithIndex Methods imap :: (Int -> a -> b) -> NonEmpty a -> NonEmpty b #
FunctorWithIndex Int IntMap
Instance details Defined in WithIndex Methods imap :: (Int -> a -> b) -> IntMap a -> IntMap b #
FunctorWithIndex Int Seq	The position in the `Seq` is available as the index.
Instance details Defined in WithIndex Methods imap :: (Int -> a -> b) -> Seq a -> Seq b #
FunctorWithIndex Int Deque Source #
Instance details Defined in Control.Lens.Internal.Deque Methods imap :: (Int -> a -> b) -> Deque a -> Deque b #
FunctorWithIndex Int List	The position in the list is available as the index.
Instance details Defined in WithIndex Methods imap :: (Int -> a -> b) -> [a] -> [b] #
FunctorWithIndex Void (Proxy :: Type -> Type)
Instance details Defined in WithIndex Methods imap :: (Void -> a -> b) -> Proxy a -> Proxy b #
FunctorWithIndex Void (U1 :: Type -> Type)
Instance details Defined in WithIndex Methods imap :: (Void -> a -> b) -> U1 a -> U1 b #
FunctorWithIndex Void (V1 :: Type -> Type)
Instance details Defined in WithIndex Methods imap :: (Void -> a -> b) -> V1 a -> V1 b #
Ix i => FunctorWithIndex i (Array i)
Instance details Defined in WithIndex Methods imap :: (i -> a -> b) -> Array i a -> Array i b #
FunctorWithIndex i (Level i) Source #
Instance details Defined in Control.Lens.Internal.Level Methods imap :: (i -> a -> b) -> Level i a -> Level i b #
FunctorWithIndex k (Map k)
Instance details Defined in WithIndex Methods imap :: (k -> a -> b) -> Map k a -> Map k b #
FunctorWithIndex k ((,) k)
Instance details Defined in WithIndex Methods imap :: (k -> a -> b) -> (k, a) -> (k, b) #
FunctorWithIndex Void (Const e :: Type -> Type)
Instance details Defined in WithIndex Methods imap :: (Void -> a -> b) -> Const e a -> Const e b #
FunctorWithIndex Void (Constant e :: Type -> Type)
Instance details Defined in WithIndex Methods imap :: (Void -> a -> b) -> Constant e a -> Constant e b #
FunctorWithIndex i f => FunctorWithIndex i (Rec1 f)
Instance details Defined in WithIndex Methods imap :: (i -> a -> b) -> Rec1 f a -> Rec1 f b #
FunctorWithIndex i f => FunctorWithIndex i (Backwards f)
Instance details Defined in WithIndex Methods imap :: (i -> a -> b) -> Backwards f a -> Backwards f b #
FunctorWithIndex i m => FunctorWithIndex i (IdentityT m)
Instance details Defined in WithIndex Methods imap :: (i -> a -> b) -> IdentityT m a -> IdentityT m b #
FunctorWithIndex i f => FunctorWithIndex i (Reverse f)
Instance details Defined in WithIndex Methods imap :: (i -> a -> b) -> Reverse f a -> Reverse f b #
FunctorWithIndex Void (K1 i c :: Type -> Type)
Instance details Defined in WithIndex Methods imap :: (Void -> a -> b) -> K1 i c a -> K1 i c b #
FunctorWithIndex i (Magma i t b) Source #
Instance details Defined in Control.Lens.Internal.Magma Methods imap :: (i -> a -> b0) -> Magma i t b a -> Magma i t b b0 #
FunctorWithIndex r ((->) r)
Instance details Defined in WithIndex Methods imap :: (r -> a -> b) -> (r -> a) -> r -> b #
FunctorWithIndex [Int] Tree
Instance details Defined in WithIndex Methods imap :: ([Int] -> a -> b) -> Tree a -> Tree b #
FunctorWithIndex i f => FunctorWithIndex [i] (Cofree f)
Instance details Defined in Control.Comonad.Cofree Methods imap :: ([i] -> a -> b) -> Cofree f a -> Cofree f b #
FunctorWithIndex i f => FunctorWithIndex [i] (Free f)
Instance details Defined in Control.Monad.Free Methods imap :: ([i] -> a -> b) -> Free f a -> Free f b #
FunctorWithIndex i m => FunctorWithIndex (e, i) (ReaderT e m)
Instance details Defined in WithIndex Methods imap :: ((e, i) -> a -> b) -> ReaderT e m a -> ReaderT e m b #
FunctorWithIndex i w => FunctorWithIndex (s, i) (TracedT s w)
Instance details Defined in Control.Comonad.Trans.Traced Methods imap :: ((s, i) -> a -> b) -> TracedT s w a -> TracedT s w b #
(FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (Either i j) (Product f g)
Instance details Defined in WithIndex Methods imap :: (Either i j -> a -> b) -> Product f g a -> Product f g b #
(FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (Either i j) (Sum f g)
Instance details Defined in WithIndex Methods imap :: (Either i j -> a -> b) -> Sum f g a -> Sum f g b #
(FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (Either i j) (f :*: g)
Instance details Defined in WithIndex Methods imap :: (Either i j -> a -> b) -> (f :: g) a -> (f :: g) b #
(FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (Either i j) (f :+: g)
Instance details Defined in WithIndex Methods imap :: (Either i j -> a -> b) -> (f :+: g) a -> (f :+: g) b #
(FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (i, j) (Compose f g)
Instance details Defined in WithIndex Methods imap :: ((i, j) -> a -> b) -> Compose f g a -> Compose f g b #
(FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (i, j) (f :.: g)
Instance details Defined in WithIndex Methods imap :: ((i, j) -> a -> b) -> (f :.: g) a -> (f :.: g) b #

data Sequenced a m Source #

Used internally by mapM_ and the like.

The argument a of the result should not be used!

See 4.16 Changelog entry for the explanation of "why not Apply f =>"?

Instances

Instances details

Monad m => Monoid (Sequenced a m) Source #
Instance details Defined in Control.Lens.Internal.Fold Methods mempty :: Sequenced a m # mappend :: Sequenced a m -> Sequenced a m -> Sequenced a m # mconcat :: [Sequenced a m] -> Sequenced a m #
Monad m => Semigroup (Sequenced a m) Source #
Instance details Defined in Control.Lens.Internal.Fold Methods (<>) :: Sequenced a m -> Sequenced a m -> Sequenced a m # sconcat :: NonEmpty (Sequenced a m) -> Sequenced a m # stimes :: Integral b => b -> Sequenced a m -> Sequenced a m #

data Traversed a f Source #

Used internally by traverseOf_ and the like.

The argument a of the result should not be used!

Instances

Instances details

Applicative f => Monoid (Traversed a f) Source #
Instance details Defined in Control.Lens.Internal.Fold Methods mempty :: Traversed a f # mappend :: Traversed a f -> Traversed a f -> Traversed a f # mconcat :: [Traversed a f] -> Traversed a f #
Applicative f => Semigroup (Traversed a f) Source #
Instance details Defined in Control.Lens.Internal.Fold Methods (<>) :: Traversed a f -> Traversed a f -> Traversed a f # sconcat :: NonEmpty (Traversed a f) -> Traversed a f # stimes :: Integral b => b -> Traversed a f -> Traversed a f #

class Profunctor (p :: Type -> Type -> Type) where #

Formally, the class Profunctor represents a profunctor from Hask -> Hask.

Intuitively it is a bifunctor where the first argument is contravariant and the second argument is covariant.

You can define a Profunctor by either defining dimap or by defining both lmap and rmap.

If you supply dimap, you should ensure that:

dimap id id ≡ id

If you supply lmap and rmap, ensure:

lmap id ≡ id
rmap id ≡ id

If you supply both, you should also ensure:

dimap f g ≡ lmap f . rmap g

These ensure by parametricity:

dimap (f . g) (h . i) ≡ dimap g h . dimap f i
lmap (f . g) ≡ lmap g . lmap f
rmap (f . g) ≡ rmap f . rmap g

Minimal complete definition

dimap | lmap, rmap

Methods

dimap :: (a -> b) -> (c -> d) -> p b c -> p a d #

Map over both arguments at the same time.

dimap f g ≡ lmap f . rmap g

lmap :: (a -> b) -> p b c -> p a c #

Map the first argument contravariantly.

lmap f ≡ dimap f id

rmap :: (b -> c) -> p a b -> p a c #

Map the second argument covariantly.

rmap ≡ dimap id

Instances

Instances details

Profunctor ReifiedFold Source #
Instance details Defined in Control.Lens.Reified Methods dimap :: (a -> b) -> (c -> d) -> ReifiedFold b c -> ReifiedFold a d # lmap :: (a -> b) -> ReifiedFold b c -> ReifiedFold a c # rmap :: (b -> c) -> ReifiedFold a b -> ReifiedFold a c # (#.) :: forall a b c q. Coercible c b => q b c -> ReifiedFold a b -> ReifiedFold a c # (.#) :: forall a b c q. Coercible b a => ReifiedFold b c -> q a b -> ReifiedFold a c #
Profunctor ReifiedGetter Source #
Instance details Defined in Control.Lens.Reified Methods dimap :: (a -> b) -> (c -> d) -> ReifiedGetter b c -> ReifiedGetter a d # lmap :: (a -> b) -> ReifiedGetter b c -> ReifiedGetter a c # rmap :: (b -> c) -> ReifiedGetter a b -> ReifiedGetter a c # (#.) :: forall a b c q. Coercible c b => q b c -> ReifiedGetter a b -> ReifiedGetter a c # (.#) :: forall a b c q. Coercible b a => ReifiedGetter b c -> q a b -> ReifiedGetter a c #
Monad m => Profunctor (Kleisli m)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Kleisli m b c -> Kleisli m a d # lmap :: (a -> b) -> Kleisli m b c -> Kleisli m a c # rmap :: (b -> c) -> Kleisli m a b -> Kleisli m a c # (#.) :: forall a b c q. Coercible c b => q b c -> Kleisli m a b -> Kleisli m a c # (.#) :: forall a b c q. Coercible b a => Kleisli m b c -> q a b -> Kleisli m a c #
Profunctor (Indexed i) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods dimap :: (a -> b) -> (c -> d) -> Indexed i b c -> Indexed i a d # lmap :: (a -> b) -> Indexed i b c -> Indexed i a c # rmap :: (b -> c) -> Indexed i a b -> Indexed i a c # (#.) :: forall a b c q. Coercible c b => q b c -> Indexed i a b -> Indexed i a c # (.#) :: forall a b c q. Coercible b a => Indexed i b c -> q a b -> Indexed i a c #
Profunctor (ReifiedIndexedFold i) Source #
Instance details Defined in Control.Lens.Reified Methods dimap :: (a -> b) -> (c -> d) -> ReifiedIndexedFold i b c -> ReifiedIndexedFold i a d # lmap :: (a -> b) -> ReifiedIndexedFold i b c -> ReifiedIndexedFold i a c # rmap :: (b -> c) -> ReifiedIndexedFold i a b -> ReifiedIndexedFold i a c # (#.) :: forall a b c q. Coercible c b => q b c -> ReifiedIndexedFold i a b -> ReifiedIndexedFold i a c # (.#) :: forall a b c q. Coercible b a => ReifiedIndexedFold i b c -> q a b -> ReifiedIndexedFold i a c #
Profunctor (ReifiedIndexedGetter i) Source #
Instance details Defined in Control.Lens.Reified Methods dimap :: (a -> b) -> (c -> d) -> ReifiedIndexedGetter i b c -> ReifiedIndexedGetter i a d # lmap :: (a -> b) -> ReifiedIndexedGetter i b c -> ReifiedIndexedGetter i a c # rmap :: (b -> c) -> ReifiedIndexedGetter i a b -> ReifiedIndexedGetter i a c # (#.) :: forall a b c q. Coercible c b => q b c -> ReifiedIndexedGetter i a b -> ReifiedIndexedGetter i a c # (.#) :: forall a b c q. Coercible b a => ReifiedIndexedGetter i b c -> q a b -> ReifiedIndexedGetter i a c #
Profunctor (CopastroSum p)
Instance details Defined in Data.Profunctor.Choice Methods dimap :: (a -> b) -> (c -> d) -> CopastroSum p b c -> CopastroSum p a d # lmap :: (a -> b) -> CopastroSum p b c -> CopastroSum p a c # rmap :: (b -> c) -> CopastroSum p a b -> CopastroSum p a c # (#.) :: forall a b c q. Coercible c b => q b c -> CopastroSum p a b -> CopastroSum p a c # (.#) :: forall a b c q. Coercible b a => CopastroSum p b c -> q a b -> CopastroSum p a c #
Profunctor (CotambaraSum p)
Instance details Defined in Data.Profunctor.Choice Methods dimap :: (a -> b) -> (c -> d) -> CotambaraSum p b c -> CotambaraSum p a d # lmap :: (a -> b) -> CotambaraSum p b c -> CotambaraSum p a c # rmap :: (b -> c) -> CotambaraSum p a b -> CotambaraSum p a c # (#.) :: forall a b c q. Coercible c b => q b c -> CotambaraSum p a b -> CotambaraSum p a c # (.#) :: forall a b c q. Coercible b a => CotambaraSum p b c -> q a b -> CotambaraSum p a c #
Profunctor (PastroSum p)
Instance details Defined in Data.Profunctor.Choice Methods dimap :: (a -> b) -> (c -> d) -> PastroSum p b c -> PastroSum p a d # lmap :: (a -> b) -> PastroSum p b c -> PastroSum p a c # rmap :: (b -> c) -> PastroSum p a b -> PastroSum p a c # (#.) :: forall a b c q. Coercible c b => q b c -> PastroSum p a b -> PastroSum p a c # (.#) :: forall a b c q. Coercible b a => PastroSum p b c -> q a b -> PastroSum p a c #
Profunctor p => Profunctor (TambaraSum p)
Instance details Defined in Data.Profunctor.Choice Methods dimap :: (a -> b) -> (c -> d) -> TambaraSum p b c -> TambaraSum p a d # lmap :: (a -> b) -> TambaraSum p b c -> TambaraSum p a c # rmap :: (b -> c) -> TambaraSum p a b -> TambaraSum p a c # (#.) :: forall a b c q. Coercible c b => q b c -> TambaraSum p a b -> TambaraSum p a c # (.#) :: forall a b c q. Coercible b a => TambaraSum p b c -> q a b -> TambaraSum p a c #
Profunctor p => Profunctor (Closure p)
Instance details Defined in Data.Profunctor.Closed Methods dimap :: (a -> b) -> (c -> d) -> Closure p b c -> Closure p a d # lmap :: (a -> b) -> Closure p b c -> Closure p a c # rmap :: (b -> c) -> Closure p a b -> Closure p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Closure p a b -> Closure p a c # (.#) :: forall a b c q. Coercible b a => Closure p b c -> q a b -> Closure p a c #
Profunctor (Environment p)
Instance details Defined in Data.Profunctor.Closed Methods dimap :: (a -> b) -> (c -> d) -> Environment p b c -> Environment p a d # lmap :: (a -> b) -> Environment p b c -> Environment p a c # rmap :: (b -> c) -> Environment p a b -> Environment p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Environment p a b -> Environment p a c # (.#) :: forall a b c q. Coercible b a => Environment p b c -> q a b -> Environment p a c #
Profunctor p => Profunctor (CofreeMapping p)
Instance details Defined in Data.Profunctor.Mapping Methods dimap :: (a -> b) -> (c -> d) -> CofreeMapping p b c -> CofreeMapping p a d # lmap :: (a -> b) -> CofreeMapping p b c -> CofreeMapping p a c # rmap :: (b -> c) -> CofreeMapping p a b -> CofreeMapping p a c # (#.) :: forall a b c q. Coercible c b => q b c -> CofreeMapping p a b -> CofreeMapping p a c # (.#) :: forall a b c q. Coercible b a => CofreeMapping p b c -> q a b -> CofreeMapping p a c #
Profunctor (FreeMapping p)
Instance details Defined in Data.Profunctor.Mapping Methods dimap :: (a -> b) -> (c -> d) -> FreeMapping p b c -> FreeMapping p a d # lmap :: (a -> b) -> FreeMapping p b c -> FreeMapping p a c # rmap :: (b -> c) -> FreeMapping p a b -> FreeMapping p a c # (#.) :: forall a b c q. Coercible c b => q b c -> FreeMapping p a b -> FreeMapping p a c # (.#) :: forall a b c q. Coercible b a => FreeMapping p b c -> q a b -> FreeMapping p a c #
Profunctor (Copastro p)
Instance details Defined in Data.Profunctor.Strong Methods dimap :: (a -> b) -> (c -> d) -> Copastro p b c -> Copastro p a d # lmap :: (a -> b) -> Copastro p b c -> Copastro p a c # rmap :: (b -> c) -> Copastro p a b -> Copastro p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Copastro p a b -> Copastro p a c # (.#) :: forall a b c q. Coercible b a => Copastro p b c -> q a b -> Copastro p a c #
Profunctor (Cotambara p)
Instance details Defined in Data.Profunctor.Strong Methods dimap :: (a -> b) -> (c -> d) -> Cotambara p b c -> Cotambara p a d # lmap :: (a -> b) -> Cotambara p b c -> Cotambara p a c # rmap :: (b -> c) -> Cotambara p a b -> Cotambara p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Cotambara p a b -> Cotambara p a c # (.#) :: forall a b c q. Coercible b a => Cotambara p b c -> q a b -> Cotambara p a c #
Profunctor (Pastro p)
Instance details Defined in Data.Profunctor.Strong Methods dimap :: (a -> b) -> (c -> d) -> Pastro p b c -> Pastro p a d # lmap :: (a -> b) -> Pastro p b c -> Pastro p a c # rmap :: (b -> c) -> Pastro p a b -> Pastro p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Pastro p a b -> Pastro p a c # (.#) :: forall a b c q. Coercible b a => Pastro p b c -> q a b -> Pastro p a c #
Profunctor p => Profunctor (Tambara p)
Instance details Defined in Data.Profunctor.Strong Methods dimap :: (a -> b) -> (c -> d) -> Tambara p b c -> Tambara p a d # lmap :: (a -> b) -> Tambara p b c -> Tambara p a c # rmap :: (b -> c) -> Tambara p a b -> Tambara p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Tambara p a b -> Tambara p a c # (.#) :: forall a b c q. Coercible b a => Tambara p b c -> q a b -> Tambara p a c #
Profunctor (Baz t)
Instance details Defined in Data.Profunctor.Traversing Methods dimap :: (a -> b) -> (c -> d) -> Baz t b c -> Baz t a d # lmap :: (a -> b) -> Baz t b c -> Baz t a c # rmap :: (b -> c) -> Baz t a b -> Baz t a c # (#.) :: forall a b c q. Coercible c b => q b c -> Baz t a b -> Baz t a c # (.#) :: forall a b c q. Coercible b a => Baz t b c -> q a b -> Baz t a c #
Profunctor (Bazaar a)
Instance details Defined in Data.Profunctor.Traversing Methods dimap :: (a0 -> b) -> (c -> d) -> Bazaar a b c -> Bazaar a a0 d # lmap :: (a0 -> b) -> Bazaar a b c -> Bazaar a a0 c # rmap :: (b -> c) -> Bazaar a a0 b -> Bazaar a a0 c # (#.) :: forall a0 b c q. Coercible c b => q b c -> Bazaar a a0 b -> Bazaar a a0 c # (.#) :: forall a0 b c q. Coercible b a0 => Bazaar a b c -> q a0 b -> Bazaar a a0 c #
Profunctor p => Profunctor (CofreeTraversing p)
Instance details Defined in Data.Profunctor.Traversing Methods dimap :: (a -> b) -> (c -> d) -> CofreeTraversing p b c -> CofreeTraversing p a d # lmap :: (a -> b) -> CofreeTraversing p b c -> CofreeTraversing p a c # rmap :: (b -> c) -> CofreeTraversing p a b -> CofreeTraversing p a c # (#.) :: forall a b c q. Coercible c b => q b c -> CofreeTraversing p a b -> CofreeTraversing p a c # (.#) :: forall a b c q. Coercible b a => CofreeTraversing p b c -> q a b -> CofreeTraversing p a c #
Profunctor (FreeTraversing p)
Instance details Defined in Data.Profunctor.Traversing Methods dimap :: (a -> b) -> (c -> d) -> FreeTraversing p b c -> FreeTraversing p a d # lmap :: (a -> b) -> FreeTraversing p b c -> FreeTraversing p a c # rmap :: (b -> c) -> FreeTraversing p a b -> FreeTraversing p a c # (#.) :: forall a b c q. Coercible c b => q b c -> FreeTraversing p a b -> FreeTraversing p a c # (.#) :: forall a b c q. Coercible b a => FreeTraversing p b c -> q a b -> FreeTraversing p a c #
Profunctor (Tagged :: Type -> Type -> Type)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Tagged b c -> Tagged a d # lmap :: (a -> b) -> Tagged b c -> Tagged a c # rmap :: (b -> c) -> Tagged a b -> Tagged a c # (#.) :: forall a b c q. Coercible c b => q b c -> Tagged a b -> Tagged a c # (.#) :: forall a b c q. Coercible b a => Tagged b c -> q a b -> Tagged a c #
Functor w => Profunctor (Cokleisli w)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Cokleisli w b c -> Cokleisli w a d # lmap :: (a -> b) -> Cokleisli w b c -> Cokleisli w a c # rmap :: (b -> c) -> Cokleisli w a b -> Cokleisli w a c # (#.) :: forall a b c q. Coercible c b => q b c -> Cokleisli w a b -> Cokleisli w a c # (.#) :: forall a b c q. Coercible b a => Cokleisli w b c -> q a b -> Cokleisli w a c #
Profunctor (Exchange a b) Source #
Instance details Defined in Control.Lens.Internal.Iso Methods dimap :: (a0 -> b0) -> (c -> d) -> Exchange a b b0 c -> Exchange a b a0 d # lmap :: (a0 -> b0) -> Exchange a b b0 c -> Exchange a b a0 c # rmap :: (b0 -> c) -> Exchange a b a0 b0 -> Exchange a b a0 c # (#.) :: forall a0 b0 c q. Coercible c b0 => q b0 c -> Exchange a b a0 b0 -> Exchange a b a0 c # (.#) :: forall a0 b0 c q. Coercible b0 a0 => Exchange a b b0 c -> q a0 b0 -> Exchange a b a0 c #
Profunctor (Market a b) Source #
Instance details Defined in Control.Lens.Internal.Prism Methods dimap :: (a0 -> b0) -> (c -> d) -> Market a b b0 c -> Market a b a0 d # lmap :: (a0 -> b0) -> Market a b b0 c -> Market a b a0 c # rmap :: (b0 -> c) -> Market a b a0 b0 -> Market a b a0 c # (#.) :: forall a0 b0 c q. Coercible c b0 => q b0 c -> Market a b a0 b0 -> Market a b a0 c # (.#) :: forall a0 b0 c q. Coercible b0 a0 => Market a b b0 c -> q a0 b0 -> Market a b a0 c #
(Functor f, Profunctor p) => Profunctor (WrappedPafb f p) Source #
Instance details Defined in Control.Lens.Internal.Profunctor Methods dimap :: (a -> b) -> (c -> d) -> WrappedPafb f p b c -> WrappedPafb f p a d # lmap :: (a -> b) -> WrappedPafb f p b c -> WrappedPafb f p a c # rmap :: (b -> c) -> WrappedPafb f p a b -> WrappedPafb f p a c # (#.) :: forall a b c q. Coercible c b => q b c -> WrappedPafb f p a b -> WrappedPafb f p a c # (.#) :: forall a b c q. Coercible b a => WrappedPafb f p b c -> q a b -> WrappedPafb f p a c #
Functor f => Profunctor (Costar f)
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> Costar f b c -> Costar f a d # lmap :: (a -> b) -> Costar f b c -> Costar f a c # rmap :: (b -> c) -> Costar f a b -> Costar f a c # (#.) :: forall a b c q. Coercible c b => q b c -> Costar f a b -> Costar f a c # (.#) :: forall a b c q. Coercible b a => Costar f b c -> q a b -> Costar f a c #
Profunctor (Forget r :: Type -> Type -> Type)
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> Forget r b c -> Forget r a d # lmap :: (a -> b) -> Forget r b c -> Forget r a c # rmap :: (b -> c) -> Forget r a b -> Forget r a c # (#.) :: forall a b c q. Coercible c b => q b c -> Forget r a b -> Forget r a c # (.#) :: forall a b c q. Coercible b a => Forget r b c -> q a b -> Forget r a c #
Functor f => Profunctor (Star f)
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> Star f b c -> Star f a d # lmap :: (a -> b) -> Star f b c -> Star f a c # rmap :: (b -> c) -> Star f a b -> Star f a c # (#.) :: forall a b c q. Coercible c b => q b c -> Star f a b -> Star f a c # (.#) :: forall a b c q. Coercible b a => Star f b c -> q a b -> Star f a c #
Profunctor (->)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> (b -> c) -> a -> d # lmap :: (a -> b) -> (b -> c) -> a -> c # rmap :: (b -> c) -> (a -> b) -> a -> c # (#.) :: forall a b c q. Coercible c b => q b c -> (a -> b) -> a -> c # (.#) :: forall a b c q. Coercible b a => (b -> c) -> q a b -> a -> c #
Contravariant f => Profunctor (Clown f :: Type -> Type -> Type)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Clown f b c -> Clown f a d # lmap :: (a -> b) -> Clown f b c -> Clown f a c # rmap :: (b -> c) -> Clown f a b -> Clown f a c # (#.) :: forall a b c q. Coercible c b => q b c -> Clown f a b -> Clown f a c # (.#) :: forall a b c q. Coercible b a => Clown f b c -> q a b -> Clown f a c #
Functor f => Profunctor (Joker f :: Type -> Type -> Type)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Joker f b c -> Joker f a d # lmap :: (a -> b) -> Joker f b c -> Joker f a c # rmap :: (b -> c) -> Joker f a b -> Joker f a c # (#.) :: forall a b c q. Coercible c b => q b c -> Joker f a b -> Joker f a c # (.#) :: forall a b c q. Coercible b a => Joker f b c -> q a b -> Joker f a c #
Arrow p => Profunctor (WrappedArrow p)
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> WrappedArrow p b c -> WrappedArrow p a d # lmap :: (a -> b) -> WrappedArrow p b c -> WrappedArrow p a c # rmap :: (b -> c) -> WrappedArrow p a b -> WrappedArrow p a c # (#.) :: forall a b c q. Coercible c b => q b c -> WrappedArrow p a b -> WrappedArrow p a c # (.#) :: forall a b c q. Coercible b a => WrappedArrow p b c -> q a b -> WrappedArrow p a c #
(Profunctor p, Profunctor q) => Profunctor (Product p q)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Product p q b c -> Product p q a d # lmap :: (a -> b) -> Product p q b c -> Product p q a c # rmap :: (b -> c) -> Product p q a b -> Product p q a c # (#.) :: forall a b c q0. Coercible c b => q0 b c -> Product p q a b -> Product p q a c # (.#) :: forall a b c q0. Coercible b a => Product p q b c -> q0 a b -> Product p q a c #
(Profunctor p, Profunctor q) => Profunctor (Sum p q)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Sum p q b c -> Sum p q a d # lmap :: (a -> b) -> Sum p q b c -> Sum p q a c # rmap :: (b -> c) -> Sum p q a b -> Sum p q a c # (#.) :: forall a b c q0. Coercible c b => q0 b c -> Sum p q a b -> Sum p q a c # (.#) :: forall a b c q0. Coercible b a => Sum p q b c -> q0 a b -> Sum p q a c #
(Functor f, Profunctor p) => Profunctor (Tannen f p)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Tannen f p b c -> Tannen f p a d # lmap :: (a -> b) -> Tannen f p b c -> Tannen f p a c # rmap :: (b -> c) -> Tannen f p a b -> Tannen f p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Tannen f p a b -> Tannen f p a c # (.#) :: forall a b c q. Coercible b a => Tannen f p b c -> q a b -> Tannen f p a c #
(Functor f, Profunctor p) => Profunctor (Cayley f p)
Instance details Defined in Data.Profunctor.Cayley Methods dimap :: (a -> b) -> (c -> d) -> Cayley f p b c -> Cayley f p a d # lmap :: (a -> b) -> Cayley f p b c -> Cayley f p a c # rmap :: (b -> c) -> Cayley f p a b -> Cayley f p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Cayley f p a b -> Cayley f p a c # (.#) :: forall a b c q. Coercible b a => Cayley f p b c -> q a b -> Cayley f p a c #
(Profunctor p, Profunctor q) => Profunctor (Procompose p q)
Instance details Defined in Data.Profunctor.Composition Methods dimap :: (a -> b) -> (c -> d) -> Procompose p q b c -> Procompose p q a d # lmap :: (a -> b) -> Procompose p q b c -> Procompose p q a c # rmap :: (b -> c) -> Procompose p q a b -> Procompose p q a c # (#.) :: forall a b c q0. Coercible c b => q0 b c -> Procompose p q a b -> Procompose p q a c # (.#) :: forall a b c q0. Coercible b a => Procompose p q b c -> q0 a b -> Procompose p q a c #
(Profunctor p, Profunctor q) => Profunctor (Rift p q)
Instance details Defined in Data.Profunctor.Composition Methods dimap :: (a -> b) -> (c -> d) -> Rift p q b c -> Rift p q a d # lmap :: (a -> b) -> Rift p q b c -> Rift p q a c # rmap :: (b -> c) -> Rift p q a b -> Rift p q a c # (#.) :: forall a b c q0. Coercible c b => q0 b c -> Rift p q a b -> Rift p q a c # (.#) :: forall a b c q0. Coercible b a => Rift p q b c -> q0 a b -> Rift p q a c #
(Profunctor p, Functor f, Functor g) => Profunctor (Biff p f g)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Biff p f g b c -> Biff p f g a d # lmap :: (a -> b) -> Biff p f g b c -> Biff p f g a c # rmap :: (b -> c) -> Biff p f g a b -> Biff p f g a c # (#.) :: forall a b c q. Coercible c b => q b c -> Biff p f g a b -> Biff p f g a c # (.#) :: forall a b c q. Coercible b a => Biff p f g b c -> q a b -> Biff p f g a c #

class Profunctor p => Choice (p :: Type -> Type -> Type) where #

The generalization of Costar of Functor that is strong with respect to Either.

Note: This is also a notion of strength, except with regards to another monoidal structure that we can choose to equip Hask with: the cocartesian coproduct.

Minimal complete definition

left' | right'

Methods

left' :: p a b -> p (Either a c) (Either b c) #

Laws:

left' ≡ dimap swapE swapE . right' where
  swapE :: Either a b -> Either b a
  swapE = either Right Left
rmap Left ≡ lmap Left . left'
lmap (right f) . left' ≡ rmap (right f) . left'
left' . left' ≡ dimap assocE unassocE . left' where
  assocE :: Either (Either a b) c -> Either a (Either b c)
  assocE (Left (Left a)) = Left a
  assocE (Left (Right b)) = Right (Left b)
  assocE (Right c) = Right (Right c)
  unassocE :: Either a (Either b c) -> Either (Either a b) c
  unassocE (Left a) = Left (Left a)
  unassocE (Right (Left b)) = Left (Right b)
  unassocE (Right (Right c)) = Right c

right' :: p a b -> p (Either c a) (Either c b) #

Laws:

right' ≡ dimap swapE swapE . left' where
  swapE :: Either a b -> Either b a
  swapE = either Right Left
rmap Right ≡ lmap Right . right'
lmap (left f) . right' ≡ rmap (left f) . right'
right' . right' ≡ dimap unassocE assocE . right' where
  assocE :: Either (Either a b) c -> Either a (Either b c)
  assocE (Left (Left a)) = Left a
  assocE (Left (Right b)) = Right (Left b)
  assocE (Right c) = Right (Right c)
  unassocE :: Either a (Either b c) -> Either (Either a b) c
  unassocE (Left a) = Left (Left a)
  unassocE (Right (Left b)) = Left (Right b)
  unassocE (Right (Right c)) = Right c

Instances

Instances details

Choice ReifiedFold Source #
Instance details Defined in Control.Lens.Reified Methods left' :: ReifiedFold a b -> ReifiedFold (Either a c) (Either b c) # right' :: ReifiedFold a b -> ReifiedFold (Either c a) (Either c b) #
Choice ReifiedGetter Source #
Instance details Defined in Control.Lens.Reified Methods left' :: ReifiedGetter a b -> ReifiedGetter (Either a c) (Either b c) # right' :: ReifiedGetter a b -> ReifiedGetter (Either c a) (Either c b) #
Monad m => Choice (Kleisli m)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Kleisli m a b -> Kleisli m (Either a c) (Either b c) # right' :: Kleisli m a b -> Kleisli m (Either c a) (Either c b) #
Choice (Indexed i) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods left' :: Indexed i a b -> Indexed i (Either a c) (Either b c) # right' :: Indexed i a b -> Indexed i (Either c a) (Either c b) #
Choice (PastroSum p)
Instance details Defined in Data.Profunctor.Choice Methods left' :: PastroSum p a b -> PastroSum p (Either a c) (Either b c) # right' :: PastroSum p a b -> PastroSum p (Either c a) (Either c b) #
Profunctor p => Choice (TambaraSum p)
Instance details Defined in Data.Profunctor.Choice Methods left' :: TambaraSum p a b -> TambaraSum p (Either a c) (Either b c) # right' :: TambaraSum p a b -> TambaraSum p (Either c a) (Either c b) #
Profunctor p => Choice (CofreeMapping p)
Instance details Defined in Data.Profunctor.Mapping Methods left' :: CofreeMapping p a b -> CofreeMapping p (Either a c) (Either b c) # right' :: CofreeMapping p a b -> CofreeMapping p (Either c a) (Either c b) #
Choice (FreeMapping p)
Instance details Defined in Data.Profunctor.Mapping Methods left' :: FreeMapping p a b -> FreeMapping p (Either a c) (Either b c) # right' :: FreeMapping p a b -> FreeMapping p (Either c a) (Either c b) #
Choice p => Choice (Tambara p)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Tambara p a b -> Tambara p (Either a c) (Either b c) # right' :: Tambara p a b -> Tambara p (Either c a) (Either c b) #
Profunctor p => Choice (CofreeTraversing p)
Instance details Defined in Data.Profunctor.Traversing Methods left' :: CofreeTraversing p a b -> CofreeTraversing p (Either a c) (Either b c) # right' :: CofreeTraversing p a b -> CofreeTraversing p (Either c a) (Either c b) #
Choice (FreeTraversing p)
Instance details Defined in Data.Profunctor.Traversing Methods left' :: FreeTraversing p a b -> FreeTraversing p (Either a c) (Either b c) # right' :: FreeTraversing p a b -> FreeTraversing p (Either c a) (Either c b) #
Choice (Tagged :: Type -> Type -> Type)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Tagged a b -> Tagged (Either a c) (Either b c) # right' :: Tagged a b -> Tagged (Either c a) (Either c b) #
Comonad w => Choice (Cokleisli w)	`extract` approximates `costrength`
Instance details Defined in Data.Profunctor.Choice Methods left' :: Cokleisli w a b -> Cokleisli w (Either a c) (Either b c) # right' :: Cokleisli w a b -> Cokleisli w (Either c a) (Either c b) #
Choice (Market a b) Source #
Instance details Defined in Control.Lens.Internal.Prism Methods left' :: Market a b a0 b0 -> Market a b (Either a0 c) (Either b0 c) # right' :: Market a b a0 b0 -> Market a b (Either c a0) (Either c b0) #
(Applicative f, Choice p) => Choice (WrappedPafb f p) Source #
Instance details Defined in Control.Lens.Internal.Profunctor Methods left' :: WrappedPafb f p a b -> WrappedPafb f p (Either a c) (Either b c) # right' :: WrappedPafb f p a b -> WrappedPafb f p (Either c a) (Either c b) #
Monoid r => Choice (Forget r :: Type -> Type -> Type)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Forget r a b -> Forget r (Either a c) (Either b c) # right' :: Forget r a b -> Forget r (Either c a) (Either c b) #
Applicative f => Choice (Star f)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Star f a b -> Star f (Either a c) (Either b c) # right' :: Star f a b -> Star f (Either c a) (Either c b) #
Choice (->)
Instance details Defined in Data.Profunctor.Choice Methods left' :: (a -> b) -> Either a c -> Either b c # right' :: (a -> b) -> Either c a -> Either c b #
Functor f => Choice (Joker f :: Type -> Type -> Type)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Joker f a b -> Joker f (Either a c) (Either b c) # right' :: Joker f a b -> Joker f (Either c a) (Either c b) #
ArrowChoice p => Choice (WrappedArrow p)
Instance details Defined in Data.Profunctor.Choice Methods left' :: WrappedArrow p a b -> WrappedArrow p (Either a c) (Either b c) # right' :: WrappedArrow p a b -> WrappedArrow p (Either c a) (Either c b) #
(Choice p, Choice q) => Choice (Product p q)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Product p q a b -> Product p q (Either a c) (Either b c) # right' :: Product p q a b -> Product p q (Either c a) (Either c b) #
(Choice p, Choice q) => Choice (Sum p q)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Sum p q a b -> Sum p q (Either a c) (Either b c) # right' :: Sum p q a b -> Sum p q (Either c a) (Either c b) #
(Functor f, Choice p) => Choice (Tannen f p)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Tannen f p a b -> Tannen f p (Either a c) (Either b c) # right' :: Tannen f p a b -> Tannen f p (Either c a) (Either c b) #
(Functor f, Choice p) => Choice (Cayley f p)
Instance details Defined in Data.Profunctor.Cayley Methods left' :: Cayley f p a b -> Cayley f p (Either a c) (Either b c) # right' :: Cayley f p a b -> Cayley f p (Either c a) (Either c b) #
(Choice p, Choice q) => Choice (Procompose p q)
Instance details Defined in Data.Profunctor.Composition Methods left' :: Procompose p q a b -> Procompose p q (Either a c) (Either b c) # right' :: Procompose p q a b -> Procompose p q (Either c a) (Either c b) #

type Traversing p f s t a b = Over p (BazaarT p f a b) s t a b Source #

When you see this as an argument to a function, it expects

to be indexed if p is an instance of Indexed i,
to be unindexed if p is (->),
a Traversal if f is Applicative,
a Getter if f is only a Functor and Contravariant,
a Lens if f is only a Functor,
a Fold if f is Applicative and Contravariant.

type Iso s t a b = forall p f. (Profunctor p, Functor f) => p a (f b) -> p s (f t) Source #

Isomorphism families can be composed with another Lens using (.) and id.

Since every Iso is both a valid Lens and a valid Prism, the laws for those types imply the following laws for an Iso f:

f . from f ≡ id
from f . f ≡ id

Note: Composition with an Iso is index- and measure- preserving.

class (Foldable1 t, Traversable t) => Traversable1 (t :: Type -> Type) where #

Minimal complete definition

traverse1 | sequence1

Methods

traverse1 :: Apply f => (a -> f b) -> t a -> f (t b) #

Instances

Instances details

Traversable1 Complex
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Complex a -> f (Complex b) # sequence1 :: Apply f => Complex (f b) -> f (Complex b) #
Traversable1 Identity
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Identity a -> f (Identity b) # sequence1 :: Apply f => Identity (f b) -> f (Identity b) #
Traversable1 First
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> First a -> f (First b) # sequence1 :: Apply f => First (f b) -> f (First b) #
Traversable1 Last
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Last a -> f (Last b) # sequence1 :: Apply f => Last (f b) -> f (Last b) #
Traversable1 Max
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Max a -> f (Max b) # sequence1 :: Apply f => Max (f b) -> f (Max b) #
Traversable1 Min
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Min a -> f (Min b) # sequence1 :: Apply f => Min (f b) -> f (Min b) #
Traversable1 Dual
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Dual a -> f (Dual b) # sequence1 :: Apply f => Dual (f b) -> f (Dual b) #
Traversable1 Product
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Product a -> f (Product b) # sequence1 :: Apply f => Product (f b) -> f (Product b) #
Traversable1 Sum
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Sum a -> f (Sum b) # sequence1 :: Apply f => Sum (f b) -> f (Sum b) #
Traversable1 NonEmpty
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> NonEmpty a -> f (NonEmpty b) # sequence1 :: Apply f => NonEmpty (f b) -> f (NonEmpty b) #
Traversable1 Par1
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Par1 a -> f (Par1 b) # sequence1 :: Apply f => Par1 (f b) -> f (Par1 b) #
Traversable1 Tree
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Tree a -> f (Tree b) # sequence1 :: Apply f => Tree (f b) -> f (Tree b) #
Traversable1 (V1 :: Type -> Type)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> V1 a -> f (V1 b) # sequence1 :: Apply f => V1 (f b) -> f (V1 b) #
Traversable1 f => Traversable1 (Cofree f)
Instance details Defined in Control.Comonad.Cofree Methods traverse1 :: Apply f0 => (a -> f0 b) -> Cofree f a -> f0 (Cofree f b) # sequence1 :: Apply f0 => Cofree f (f0 b) -> f0 (Cofree f b) #
Traversable1 f => Traversable1 (Free f)
Instance details Defined in Control.Monad.Free Methods traverse1 :: Apply f0 => (a -> f0 b) -> Free f a -> f0 (Free f b) # sequence1 :: Apply f0 => Free f (f0 b) -> f0 (Free f b) #
Traversable1 f => Traversable1 (F f)
Instance details Defined in Control.Monad.Free.Church Methods traverse1 :: Apply f0 => (a -> f0 b) -> F f a -> f0 (F f b) # sequence1 :: Apply f0 => F f (f0 b) -> f0 (F f b) #
(Monad m, Traversable1 m) => Traversable1 (IterT m)
Instance details Defined in Control.Monad.Trans.Iter Methods traverse1 :: Apply f => (a -> f b) -> IterT m a -> f (IterT m b) # sequence1 :: Apply f => IterT m (f b) -> f (IterT m b) #
Traversable1 f => Traversable1 (Yoneda f)
Instance details Defined in Data.Functor.Yoneda Methods traverse1 :: Apply f0 => (a -> f0 b) -> Yoneda f a -> f0 (Yoneda f b) # sequence1 :: Apply f0 => Yoneda f (f0 b) -> f0 (Yoneda f b) #
Traversable1 f => Traversable1 (Lift f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Lift f a -> f0 (Lift f b) # sequence1 :: Apply f0 => Lift f (f0 b) -> f0 (Lift f b) #
Traversable1 ((,) a)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a0 -> f b) -> (a, a0) -> f (a, b) # sequence1 :: Apply f => (a, f b) -> f (a, b) #
Traversable1 f => Traversable1 (Alt f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Alt f a -> f0 (Alt f b) # sequence1 :: Apply f0 => Alt f (f0 b) -> f0 (Alt f b) #
Traversable1 f => Traversable1 (Rec1 f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Rec1 f a -> f0 (Rec1 f b) # sequence1 :: Apply f0 => Rec1 f (f0 b) -> f0 (Rec1 f b) #
Bitraversable1 p => Traversable1 (Join p)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Join p a -> f (Join p b) # sequence1 :: Apply f => Join p (f b) -> f (Join p b) #
Traversable1 f => Traversable1 (AlongsideLeft f b) Source #
Instance details Defined in Control.Lens.Internal.Getter Methods traverse1 :: Apply f0 => (a -> f0 b0) -> AlongsideLeft f b a -> f0 (AlongsideLeft f b b0) # sequence1 :: Apply f0 => AlongsideLeft f b (f0 b0) -> f0 (AlongsideLeft f b b0) #
Traversable1 f => Traversable1 (AlongsideRight f a) Source #
Instance details Defined in Control.Lens.Internal.Getter Methods traverse1 :: Apply f0 => (a0 -> f0 b) -> AlongsideRight f a a0 -> f0 (AlongsideRight f a b) # sequence1 :: Apply f0 => AlongsideRight f a (f0 b) -> f0 (AlongsideRight f a b) #
Traversable1 (Tagged a)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a0 -> f b) -> Tagged a a0 -> f (Tagged a b) # sequence1 :: Apply f => Tagged a (f b) -> f (Tagged a b) #
Traversable1 f => Traversable1 (Backwards f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Backwards f a -> f0 (Backwards f b) # sequence1 :: Apply f0 => Backwards f (f0 b) -> f0 (Backwards f b) #
Traversable1 f => Traversable1 (IdentityT f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> IdentityT f a -> f0 (IdentityT f b) # sequence1 :: Apply f0 => IdentityT f (f0 b) -> f0 (IdentityT f b) #
Traversable1 f => Traversable1 (Reverse f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Reverse f a -> f0 (Reverse f b) # sequence1 :: Apply f0 => Reverse f (f0 b) -> f0 (Reverse f b) #
(Traversable1 f, Traversable1 g) => Traversable1 (Product f g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Product f g a -> f0 (Product f g b) # sequence1 :: Apply f0 => Product f g (f0 b) -> f0 (Product f g b) #
(Traversable1 f, Traversable1 g) => Traversable1 (Sum f g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Sum f g a -> f0 (Sum f g b) # sequence1 :: Apply f0 => Sum f g (f0 b) -> f0 (Sum f g b) #
(Traversable1 f, Traversable1 g) => Traversable1 (f :*: g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> (f :: g) a -> f0 ((f :: g) b) # sequence1 :: Apply f0 => (f :: g) (f0 b) -> f0 ((f :: g) b) #
(Traversable1 f, Traversable1 g) => Traversable1 (f :+: g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b) # sequence1 :: Apply f0 => (f :+: g) (f0 b) -> f0 ((f :+: g) b) #
(Traversable1 f, Traversable1 g) => Traversable1 (Compose f g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Compose f g a -> f0 (Compose f g b) # sequence1 :: Apply f0 => Compose f g (f0 b) -> f0 (Compose f g b) #
(Traversable1 f, Traversable1 g) => Traversable1 (f :.: g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b) # sequence1 :: Apply f0 => (f :.: g) (f0 b) -> f0 ((f :.: g) b) #
Traversable1 f => Traversable1 (M1 i c f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> M1 i c f a -> f0 (M1 i c f b) # sequence1 :: Apply f0 => M1 i c f (f0 b) -> f0 (M1 i c f b) #
Traversable1 g => Traversable1 (Joker g a)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a0 -> f b) -> Joker g a a0 -> f (Joker g a b) # sequence1 :: Apply f => Joker g a (f b) -> f (Joker g a b) #

type As a = Equality' a a Source #

Composable asTypeOf. Useful for constraining excess polymorphism, foo . (id :: As Int) . bar.

type Lens s t a b = forall f. Functor f => (a -> f b) -> s -> f t Source #

A Lens is actually a lens family as described in http://comonad.com/reader/2012/mirrored-lenses/.

With great power comes great responsibility and a Lens is subject to the three common sense Lens laws:

1) You get back what you put in:

view l (set l v s)  ≡ v

2) Putting back what you got doesn't change anything:

set l (view l s) s  ≡ s

3) Setting twice is the same as setting once:

set l v' (set l v s) ≡ set l v' s

These laws are strong enough that the 4 type parameters of a Lens cannot vary fully independently. For more on how they interact, read the "Why is it a Lens Family?" section of http://comonad.com/reader/2012/mirrored-lenses/.

There are some emergent properties of these laws:

1) set l s must be injective for every s This is a consequence of law #1

2) set l must be surjective, because of law #2, which indicates that it is possible to obtain any v from some s such that set s v = s

3) Given just the first two laws you can prove a weaker form of law #3 where the values v that you are setting match:

set l v (set l v s) ≡ set l v s

Every Lens can be used directly as a Setter or Traversal.

You can also use a Lens for Getting as if it were a Fold or Getter.

Since every Lens is a valid Traversal, the Traversal laws are required of any Lens you create:

l pure ≡ pure
fmap (l f) . l g ≡ getCompose . l (Compose . fmap f . g)

type Lens s t a b = forall f. Functor f => LensLike f s t a b

class Ixed m => At m where Source #

At provides a Lens that can be used to read, write or delete the value associated with a key in a Map-like container on an ad hoc basis.

An instance of At should satisfy:

ix k ≡ at k . traverse

Methods

at :: Index m -> Lens' m (Maybe (IxValue m)) Source #

>>> Map.fromList [(1,"world")] ^.at 1
Just "world"

>>> at 1 ?~ "hello" $ Map.empty
fromList [(1,"hello")]

Note: Map-like containers form a reasonable instance, but not Array-like ones, where you cannot satisfy the Lens laws.

Instances

Instances details

At IntSet Source #
Instance details Defined in Control.Lens.At Methods at :: Index IntSet -> Lens' IntSet (Maybe (IxValue IntSet)) Source #
At (IntMap a) Source #
Instance details Defined in Control.Lens.At Methods at :: Index (IntMap a) -> Lens' (IntMap a) (Maybe (IxValue (IntMap a))) Source #
Ord k => At (Set k) Source #
Instance details Defined in Control.Lens.At Methods at :: Index (Set k) -> Lens' (Set k) (Maybe (IxValue (Set k))) Source #
(Eq k, Hashable k) => At (HashSet k) Source #
Instance details Defined in Control.Lens.At Methods at :: Index (HashSet k) -> Lens' (HashSet k) (Maybe (IxValue (HashSet k))) Source #
At (Maybe a) Source #
Instance details Defined in Control.Lens.At Methods at :: Index (Maybe a) -> Lens' (Maybe a) (Maybe (IxValue (Maybe a))) Source #
Ord k => At (Map k a) Source #
Instance details Defined in Control.Lens.At Methods at :: Index (Map k a) -> Lens' (Map k a) (Maybe (IxValue (Map k a))) Source #
(Eq k, Hashable k) => At (HashMap k a) Source #
Instance details Defined in Control.Lens.At Methods at :: Index (HashMap k a) -> Lens' (HashMap k a) (Maybe (IxValue (HashMap k a))) Source #

class Cons s t a b | s -> a, t -> b, s b -> t, t a -> s where Source #

This class provides a way to attach or detach elements on the left side of a structure in a flexible manner.

Methods

_Cons :: Prism s t (a, s) (b, t) Source #

_Cons :: Prism [a] [b] (a, [a]) (b, [b])
_Cons :: Prism (Seq a) (Seq b) (a, Seq a) (b, Seq b)
_Cons :: Prism (Vector a) (Vector b) (a, Vector a) (b, Vector b)
_Cons :: Prism' String (Char, String)
_Cons :: Prism' Text (Char, Text)
_Cons :: Prism' ByteString (Word8, ByteString)

Instances

Instances details

Cons ByteString ByteString Word8 Word8 Source #
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism ByteString ByteString (Word8, ByteString) (Word8, ByteString) Source #
Cons ByteString ByteString Word8 Word8 Source #
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism ByteString ByteString (Word8, ByteString) (Word8, ByteString) Source #
Cons Text Text Char Char Source #
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism Text Text (Char, Text) (Char, Text) Source #
Cons Text Text Char Char Source #
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism Text Text (Char, Text) (Char, Text) Source #
Cons (ZipList a) (ZipList b) a b Source #
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism (ZipList a) (ZipList b) (a, ZipList a) (b, ZipList b) Source #
Cons (Seq a) (Seq b) a b Source #
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism (Seq a) (Seq b) (a, Seq a) (b, Seq b) Source #
Cons (Deque a) (Deque b) a b Source #
Instance details Defined in Control.Lens.Internal.Deque Methods _Cons :: Prism (Deque a) (Deque b) (a, Deque a) (b, Deque b) Source #
Cons (Vector a) (Vector b) a b Source #
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism (Vector a) (Vector b) (a, Vector a) (b, Vector b) Source #
(Prim a, Prim b) => Cons (Vector a) (Vector b) a b Source #
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism (Vector a) (Vector b) (a, Vector a) (b, Vector b) Source #
(Storable a, Storable b) => Cons (Vector a) (Vector b) a b Source #
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism (Vector a) (Vector b) (a, Vector a) (b, Vector b) Source #
(Unbox a, Unbox b) => Cons (Vector a) (Vector b) a b Source #
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism (Vector a) (Vector b) (a, Vector a) (b, Vector b) Source #
Cons [a] [b] a b Source #
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism [a] [b] (a, [a]) (b, [b]) Source #

class Each s t a b | s -> a, t -> b, s b -> t, t a -> s where Source #

Extract each element of a (potentially monomorphic) container.

Notably, when applied to a tuple, this generalizes both to arbitrary homogeneous tuples.

>>> (1,2,3) & each *~ 10
(10,20,30)

It can also be used on monomorphic containers like Text or ByteString.

>>> over each Char.toUpper ("hello"^.Text.packed)
"HELLO"

>>> ("hello","world") & each.each %~ Char.toUpper
("HELLO","WORLD")

Minimal complete definition

Nothing

Methods

each :: Traversal s t a b Source #

default each :: (Traversable g, s ~ g a, t ~ g b) => Traversal s t a b Source #

Instances

Instances details

(a ~ Word8, b ~ Word8) => Each ByteString ByteString a b Source #	`each` :: `Traversal` `ByteString` `ByteString` `Word8` `Word8`
Instance details Defined in Control.Lens.Each Methods each :: Traversal ByteString ByteString a b Source #
(a ~ Word8, b ~ Word8) => Each ByteString ByteString a b Source #	`each` :: `Traversal` `ByteString` `ByteString` `Word8` `Word8`
Instance details Defined in Control.Lens.Each Methods each :: Traversal ByteString ByteString a b Source #
(a ~ Char, b ~ Char) => Each Text Text a b Source #	`each` :: `Traversal` `Text` `Text` `Char` `Char`
Instance details Defined in Control.Lens.Each Methods each :: Traversal Text Text a b Source #
(a ~ Char, b ~ Char) => Each Text Text a b Source #	`each` :: `Traversal` `Text` `Text` `Char` `Char`
Instance details Defined in Control.Lens.Each Methods each :: Traversal Text Text a b Source #
Each (Complex a) (Complex b) a b Source #	`each` :: (`RealFloat` a, `RealFloat` b) => `Traversal` (`Complex` a) (`Complex` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Complex a) (Complex b) a b Source #
Each (Identity a) (Identity b) a b Source #	`each` :: `Traversal` (`Identity` a) (`Identity` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Identity a) (Identity b) a b Source #
Each (NonEmpty a) (NonEmpty b) a b Source #	`each` :: `Traversal` (NonEmpty a) (NonEmpty b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (NonEmpty a) (NonEmpty b) a b Source #
Each (IntMap a) (IntMap b) a b Source #	`each` :: `Traversal` (`Map` c a) (`Map` c b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (IntMap a) (IntMap b) a b Source #
Each (Seq a) (Seq b) a b Source #	`each` :: `Traversal` (`Seq` a) (`Seq` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Seq a) (Seq b) a b Source #
Each (Tree a) (Tree b) a b Source #	`each` :: `Traversal` (`Tree` a) (`Tree` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Tree a) (Tree b) a b Source #
Each (Maybe a) (Maybe b) a b Source #	Since: 4.20
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Maybe a) (Maybe b) a b Source #
Each (Vector a) (Vector b) a b Source #	`each` :: `Traversal` (`Vector` a) (`Vector` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Vector a) (Vector b) a b Source #
(Prim a, Prim b) => Each (Vector a) (Vector b) a b Source #	`each` :: (`Prim` a, `Prim` b) => `Traversal` (`Vector` a) (`Vector` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Vector a) (Vector b) a b Source #
(Storable a, Storable b) => Each (Vector a) (Vector b) a b Source #	`each` :: (`Storable` a, `Storable` b) => `Traversal` (`Vector` a) (`Vector` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Vector a) (Vector b) a b Source #
(Unbox a, Unbox b) => Each (Vector a) (Vector b) a b Source #	`each` :: (`Unbox` a, `Unbox` b) => `Traversal` (`Vector` a) (`Vector` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Vector a) (Vector b) a b Source #
Each (Maybe a) (Maybe b) a b Source #	`each` :: `Traversal` (`Maybe` a) (`Maybe` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Maybe a) (Maybe b) a b Source #
Each [a] [b] a b Source #	`each` :: `Traversal` [a] [b] a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal [a] [b] a b Source #
(Ix i, IArray UArray a, IArray UArray b, i ~ j) => Each (UArray i a) (UArray j b) a b Source #	`each` :: (`Ix` i, `IArray` `UArray` a, `IArray` `UArray` b) => `Traversal` (`Array` i a) (`Array` i b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (UArray i a) (UArray j b) a b Source #
(a ~ a', b ~ b') => Each (Either a a') (Either b b') a b Source #	`each` :: `Traversal` (`Either` a a) (`Either` b b) a b Since: 4.18
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Either a a') (Either b b') a b Source #
(Ix i, i ~ j) => Each (Array i a) (Array j b) a b Source #	`each` :: `Ix` i => `Traversal` (`Array` i a) (`Array` i b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Array i a) (Array j b) a b Source #
c ~ d => Each (Map c a) (Map d b) a b Source #	`each` :: `Traversal` (`Map` c a) (`Map` c b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Map c a) (Map d b) a b Source #
(a ~ a', b ~ b') => Each (Either a a') (Either b b') a b Source #	Since: 4.20
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Either a a') (Either b b') a b Source #
(a ~ a', b ~ b') => Each (These a a') (These b b') a b Source #	Since: 4.20
Instance details Defined in Control.Lens.Each Methods each :: Traversal (These a a') (These b b') a b Source #
(a ~ a', b ~ b') => Each (Pair a a') (Pair b b') a b Source #	Since: 4.20
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Pair a a') (Pair b b') a b Source #
(a ~ a', b ~ b') => Each (These a a') (These b b') a b Source #	Since: 4.20
Instance details Defined in Control.Lens.Each Methods each :: Traversal (These a a') (These b b') a b Source #
c ~ d => Each (HashMap c a) (HashMap d b) a b Source #	`each` :: `Traversal` (`HashMap` c a) (`HashMap` c b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (HashMap c a) (HashMap d b) a b Source #
(a ~ a', b ~ b') => Each (a, a') (b, b') a b Source #	`each` :: `Traversal` (a,a) (b,b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (a, a') (b, b') a b Source #
(a ~ a2, a ~ a3, b ~ b2, b ~ b3) => Each (a, a2, a3) (b, b2, b3) a b Source #	`each` :: `Traversal` (a,a,a) (b,b,b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (a, a2, a3) (b, b2, b3) a b Source #
(a ~ a2, a ~ a3, a ~ a4, b ~ b2, b ~ b3, b ~ b4) => Each (a, a2, a3, a4) (b, b2, b3, b4) a b Source #	`each` :: `Traversal` (a,a,a,a) (b,b,b,b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (a, a2, a3, a4) (b, b2, b3, b4) a b Source #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, b ~ b2, b ~ b3, b ~ b4, b ~ b5) => Each (a, a2, a3, a4, a5) (b, b2, b3, b4, b5) a b Source #	`each` :: `Traversal` (a,a,a,a,a) (b,b,b,b,b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (a, a2, a3, a4, a5) (b, b2, b3, b4, b5) a b Source #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6, b ~ b2, b ~ b3, b ~ b4, b ~ b5, b ~ b6) => Each (a, a2, a3, a4, a5, a6) (b, b2, b3, b4, b5, b6) a b Source #	`each` :: `Traversal` (a,a,a,a,a,a) (b,b,b,b,b,b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (a, a2, a3, a4, a5, a6) (b, b2, b3, b4, b5, b6) a b Source #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6, a ~ a7, b ~ b2, b ~ b3, b ~ b4, b ~ b5, b ~ b6, b ~ b7) => Each (a, a2, a3, a4, a5, a6, a7) (b, b2, b3, b4, b5, b6, b7) a b Source #	`each` :: `Traversal` (a,a,a,a,a,a,a) (b,b,b,b,b,b,b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (a, a2, a3, a4, a5, a6, a7) (b, b2, b3, b4, b5, b6, b7) a b Source #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6, a ~ a7, a ~ a8, b ~ b2, b ~ b3, b ~ b4, b ~ b5, b ~ b6, b ~ b7, b ~ b8) => Each (a, a2, a3, a4, a5, a6, a7, a8) (b, b2, b3, b4, b5, b6, b7, b8) a b Source #	`each` :: `Traversal` (a,a,a,a,a,a,a,a) (b,b,b,b,b,b,b,b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (a, a2, a3, a4, a5, a6, a7, a8) (b, b2, b3, b4, b5, b6, b7, b8) a b Source #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6, a ~ a7, a ~ a8, a ~ a9, b ~ b2, b ~ b3, b ~ b4, b ~ b5, b ~ b6, b ~ b7, b ~ b8, b ~ b9) => Each (a, a2, a3, a4, a5, a6, a7, a8, a9) (b, b2, b3, b4, b5, b6, b7, b8, b9) a b Source #	`each` :: `Traversal` (a,a,a,a,a,a,a,a,a) (b,b,b,b,b,b,b,b,b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (a, a2, a3, a4, a5, a6, a7, a8, a9) (b, b2, b3, b4, b5, b6, b7, b8, b9) a b Source #

type Equality (s :: k1) (t :: k2) (a :: k1) (b :: k2) = forall k3 (p :: k1 -> k3 -> Type) (f :: k2 -> k3). p a (f b) -> p s (f t) Source #

A witness that (a ~ s, b ~ t).

Note: Composition with an Equality is index-preserving.

type Fold s a = forall f. (Contravariant f, Applicative f) => (a -> f a) -> s -> f s Source #

A Fold describes how to retrieve multiple values in a way that can be composed with other LensLike constructions.

A Fold s a provides a structure with operations very similar to those of the Foldable typeclass, see foldMapOf and the other Fold combinators.

By convention, if there exists a foo method that expects a Foldable (f a), then there should be a fooOf method that takes a Fold s a and a value of type s.

A Getter is a legal Fold that just ignores the supplied Monoid.

Unlike a Traversal a Fold is read-only. Since a Fold cannot be used to write back there are no Lens laws that apply.

type Getter s a = forall f. (Contravariant f, Functor f) => (a -> f a) -> s -> f s Source #

A Getter describes how to retrieve a single value in a way that can be composed with other LensLike constructions.

Unlike a Lens a Getter is read-only. Since a Getter cannot be used to write back there are no Lens laws that can be applied to it. In fact, it is isomorphic to an arbitrary function from (s -> a).

Moreover, a Getter can be used directly as a Fold, since it just ignores the Applicative.

newtype Indexed i a b Source #

A function with access to a index. This constructor may be useful when you need to store an Indexable in a container to avoid ImpredicativeTypes.

index :: Indexed i a b -> i -> a -> b

Constructors

Indexed
Fields runIndexed :: i -> a -> b

Instances

Instances details

Category (Indexed i :: Type -> Type -> Type) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods id :: forall (a :: k). Indexed i a a # (.) :: forall (b :: k) (c :: k) (a :: k). Indexed i b c -> Indexed i a b -> Indexed i a c #
i ~ j => Indexable i (Indexed j) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods indexed :: Indexed j a b -> i -> a -> b Source #
Arrow (Indexed i) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods arr :: (b -> c) -> Indexed i b c # first :: Indexed i b c -> Indexed i (b, d) (c, d) # second :: Indexed i b c -> Indexed i (d, b) (d, c) # (***) :: Indexed i b c -> Indexed i b' c' -> Indexed i (b, b') (c, c') # (&&&) :: Indexed i b c -> Indexed i b c' -> Indexed i b (c, c') #
ArrowApply (Indexed i) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods app :: Indexed i (Indexed i b c, b) c #
ArrowChoice (Indexed i) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods left :: Indexed i b c -> Indexed i (Either b d) (Either c d) # right :: Indexed i b c -> Indexed i (Either d b) (Either d c) # (+++) :: Indexed i b c -> Indexed i b' c' -> Indexed i (Either b b') (Either c c') # (\|\|\|) :: Indexed i b d -> Indexed i c d -> Indexed i (Either b c) d #
ArrowLoop (Indexed i) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods loop :: Indexed i (b, d) (c, d) -> Indexed i b c #
Conjoined (Indexed i) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods distrib :: Functor f => Indexed i a b -> Indexed i (f a) (f b) Source # conjoined :: (Indexed i ~ (->) => q (a -> b) r) -> q (Indexed i a b) r -> q (Indexed i a b) r Source #
Choice (Indexed i) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods left' :: Indexed i a b -> Indexed i (Either a c) (Either b c) # right' :: Indexed i a b -> Indexed i (Either c a) (Either c b) #
Closed (Indexed i) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods closed :: Indexed i a b -> Indexed i (x -> a) (x -> b) #
Corepresentable (Indexed i) Source #
Instance details Defined in Control.Lens.Internal.Indexed Associated Types type Corep (Indexed i) :: Type -> Type # Methods cotabulate :: (Corep (Indexed i) d -> c) -> Indexed i d c #
Representable (Indexed i) Source #
Instance details Defined in Control.Lens.Internal.Indexed Associated Types type Rep (Indexed i) :: Type -> Type # Methods tabulate :: (d -> Rep (Indexed i) c) -> Indexed i d c #
Costrong (Indexed i) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods unfirst :: Indexed i (a, d) (b, d) -> Indexed i a b # unsecond :: Indexed i (d, a) (d, b) -> Indexed i a b #
Strong (Indexed i) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods first' :: Indexed i a b -> Indexed i (a, c) (b, c) # second' :: Indexed i a b -> Indexed i (c, a) (c, b) #
Profunctor (Indexed i) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods dimap :: (a -> b) -> (c -> d) -> Indexed i b c -> Indexed i a d # lmap :: (a -> b) -> Indexed i b c -> Indexed i a c # rmap :: (b -> c) -> Indexed i a b -> Indexed i a c # (#.) :: forall a b c q. Coercible c b => q b c -> Indexed i a b -> Indexed i a c # (.#) :: forall a b c q. Coercible b a => Indexed i b c -> q a b -> Indexed i a c #
Bizarre (Indexed Int) Mafic Source #
Instance details Defined in Control.Lens.Internal.Magma Methods bazaar :: Applicative f => Indexed Int a (f b) -> Mafic a b t -> f t Source #
Bizarre (Indexed i) (Molten i) Source #
Instance details Defined in Control.Lens.Internal.Magma Methods bazaar :: Applicative f => Indexed i a (f b) -> Molten i a b t -> f t Source #
Sellable (Indexed i) (Molten i) Source #
Instance details Defined in Control.Lens.Internal.Magma Methods sell :: Indexed i a (Molten i a b b) Source #
Cosieve (Indexed i) ((,) i) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods cosieve :: Indexed i a b -> (i, a) -> b #
Sieve (Indexed i) ((->) i) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods sieve :: Indexed i a b -> a -> i -> b #
MonadFix (Indexed i a) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods mfix :: (a0 -> Indexed i a a0) -> Indexed i a a0 #
Applicative (Indexed i a) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods pure :: a0 -> Indexed i a a0 # (<>) :: Indexed i a (a0 -> b) -> Indexed i a a0 -> Indexed i a b # liftA2 :: (a0 -> b -> c) -> Indexed i a a0 -> Indexed i a b -> Indexed i a c # (>) :: Indexed i a a0 -> Indexed i a b -> Indexed i a b # (<*) :: Indexed i a a0 -> Indexed i a b -> Indexed i a a0 #
Functor (Indexed i a) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods fmap :: (a0 -> b) -> Indexed i a a0 -> Indexed i a b # (<$) :: a0 -> Indexed i a b -> Indexed i a a0 #
Monad (Indexed i a) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods (>>=) :: Indexed i a a0 -> (a0 -> Indexed i a b) -> Indexed i a b # (>>) :: Indexed i a a0 -> Indexed i a b -> Indexed i a b # return :: a0 -> Indexed i a a0 #
Apply (Indexed i a) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods (<.>) :: Indexed i a (a0 -> b) -> Indexed i a a0 -> Indexed i a b # (.>) :: Indexed i a a0 -> Indexed i a b -> Indexed i a b # (<.) :: Indexed i a a0 -> Indexed i a b -> Indexed i a a0 # liftF2 :: (a0 -> b -> c) -> Indexed i a a0 -> Indexed i a b -> Indexed i a c #
Bind (Indexed i a) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods (>>-) :: Indexed i a a0 -> (a0 -> Indexed i a b) -> Indexed i a b # join :: Indexed i a (Indexed i a a0) -> Indexed i a a0 #
type Corep (Indexed i) Source #
Instance details Defined in Control.Lens.Internal.Indexed type Corep (Indexed i) = (,) i
type Rep (Indexed i) Source #
Instance details Defined in Control.Lens.Internal.Indexed type Rep (Indexed i) = (->) i

data Level i a Source #

This data type represents a path-compressed copy of one level of a source data structure. We can safely use path-compression because we know the depth of the tree.

Path compression is performed by viewing a Level as a PATRICIA trie of the paths into the structure to leaves at a given depth, similar in many ways to a IntMap, but unlike a regular PATRICIA trie we do not need to store the mask bits merely the depth of the fork.

One invariant of this structure is that underneath a Two node you will not find any Zero nodes, so Zero can only occur at the root.

Instances

Instances details

FoldableWithIndex i (Level i) Source #
Instance details Defined in Control.Lens.Internal.Level Methods ifoldMap :: Monoid m => (i -> a -> m) -> Level i a -> m # ifoldMap' :: Monoid m => (i -> a -> m) -> Level i a -> m # ifoldr :: (i -> a -> b -> b) -> b -> Level i a -> b # ifoldl :: (i -> b -> a -> b) -> b -> Level i a -> b # ifoldr' :: (i -> a -> b -> b) -> b -> Level i a -> b # ifoldl' :: (i -> b -> a -> b) -> b -> Level i a -> b #
FunctorWithIndex i (Level i) Source #
Instance details Defined in Control.Lens.Internal.Level Methods imap :: (i -> a -> b) -> Level i a -> Level i b #
TraversableWithIndex i (Level i) Source #
Instance details Defined in Control.Lens.Internal.Level Methods itraverse :: Applicative f => (i -> a -> f b) -> Level i a -> f (Level i b) #
Foldable (Level i) Source #
Instance details Defined in Control.Lens.Internal.Level Methods fold :: Monoid m => Level i m -> m # foldMap :: Monoid m => (a -> m) -> Level i a -> m # foldMap' :: Monoid m => (a -> m) -> Level i a -> m # foldr :: (a -> b -> b) -> b -> Level i a -> b # foldr' :: (a -> b -> b) -> b -> Level i a -> b # foldl :: (b -> a -> b) -> b -> Level i a -> b # foldl' :: (b -> a -> b) -> b -> Level i a -> b # foldr1 :: (a -> a -> a) -> Level i a -> a # foldl1 :: (a -> a -> a) -> Level i a -> a # toList :: Level i a -> [a] # null :: Level i a -> Bool # length :: Level i a -> Int # elem :: Eq a => a -> Level i a -> Bool # maximum :: Ord a => Level i a -> a # minimum :: Ord a => Level i a -> a # sum :: Num a => Level i a -> a # product :: Num a => Level i a -> a #
Traversable (Level i) Source #
Instance details Defined in Control.Lens.Internal.Level Methods traverse :: Applicative f => (a -> f b) -> Level i a -> f (Level i b) # sequenceA :: Applicative f => Level i (f a) -> f (Level i a) # mapM :: Monad m => (a -> m b) -> Level i a -> m (Level i b) # sequence :: Monad m => Level i (m a) -> m (Level i a) #
Functor (Level i) Source #
Instance details Defined in Control.Lens.Internal.Level Methods fmap :: (a -> b) -> Level i a -> Level i b # (<$) :: a -> Level i b -> Level i a #
(Read i, Read a) => Read (Level i a) Source #
Instance details Defined in Control.Lens.Internal.Level Methods readsPrec :: Int -> ReadS (Level i a) # readList :: ReadS [Level i a] # readPrec :: ReadPrec (Level i a) # readListPrec :: ReadPrec [Level i a] #
(Show i, Show a) => Show (Level i a) Source #
Instance details Defined in Control.Lens.Internal.Level Methods showsPrec :: Int -> Level i a -> ShowS # show :: Level i a -> String # showList :: [Level i a] -> ShowS #
(Eq i, Eq a) => Eq (Level i a) Source #
Instance details Defined in Control.Lens.Internal.Level Methods (==) :: Level i a -> Level i a -> Bool # (/=) :: Level i a -> Level i a -> Bool #
(Ord i, Ord a) => Ord (Level i a) Source #
Instance details Defined in Control.Lens.Internal.Level Methods compare :: Level i a -> Level i a -> Ordering # (<) :: Level i a -> Level i a -> Bool # (<=) :: Level i a -> Level i a -> Bool # (>) :: Level i a -> Level i a -> Bool # (>=) :: Level i a -> Level i a -> Bool # max :: Level i a -> Level i a -> Level i a # min :: Level i a -> Level i a -> Level i a #

class Plated a where Source #

A Plated type is one where we know how to extract its immediate self-similar children.

Example 1:

import Control.Applicative
import Control.Lens
import Control.Lens.Plated
import Data.Data
import Data.Data.Lens (uniplate)

data Expr
  = Val Int
  | Neg Expr
  | Add Expr Expr
  deriving (Eq,Ord,Show,Read,Data)

instance Plated Expr where
  plate f (Neg e) = Neg <$> f e
  plate f (Add a b) = Add <$> f a <*> f b
  plate _ a = pure a

or

instance Plated Expr where
  plate = uniplate

Example 2:

import Control.Applicative
import Control.Lens
import Control.Lens.Plated
import Data.Data
import Data.Data.Lens (uniplate)

data Tree a
  = Bin (Tree a) (Tree a)
  | Tip a
  deriving (Eq,Ord,Show,Read,Data)

instance Plated (Tree a) where
  plate f (Bin l r) = Bin <$> f l <*> f r
  plate _ t = pure t

or

instance Data a => Plated (Tree a) where
  plate = uniplate

Note the big distinction between these two implementations.

The former will only treat children directly in this tree as descendents, the latter will treat trees contained in the values under the tips also as descendants!

When in doubt, pick a Traversal and just use the various ...Of combinators rather than pollute Plated with orphan instances!

If you want to find something unplated and non-recursive with biplate use the ...OnOf variant with ignored, though those usecases are much better served in most cases by using the existing Lens combinators! e.g.

toListOf biplate ≡ universeOnOf biplate ignored

This same ability to explicitly pass the Traversal in question is why there is no analogue to uniplate's Biplate.

Moreover, since we can allow custom traversals, we implement reasonable defaults for polymorphic data types, that only traverse into themselves, and not their polymorphic arguments.

Minimal complete definition

Nothing

Methods

plate :: Traversal' a a Source #

Traversal of the immediate children of this structure.

If you're using GHC 7.2 or newer and your type has a Data instance, plate will default to uniplate and you can choose to not override it with your own definition.

default plate :: Data a => Traversal' a a Source #

Instances

Instances details

Plated Con Source #
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' Con Con Source #
Plated Dec Source #
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' Dec Dec Source #
Plated Exp Source #
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' Exp Exp Source #
Plated Pat Source #
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' Pat Pat Source #
Plated Stmt Source #
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' Stmt Stmt Source #
Plated Type Source #
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' Type Type Source #
Plated (Tree a) Source #
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' (Tree a) (Tree a) Source #
Plated [a] Source #
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' [a] [a] Source #
Traversable f => Plated (Cofree f a) Source #
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' (Cofree f a) (Cofree f a) Source #
Traversable f => Plated (Free f a) Source #
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' (Free f a) (Free f a) Source #
Traversable f => Plated (F f a) Source #
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' (F f a) (F f a) Source #
(Traversable f, Traversable w) => Plated (CofreeT f w a) Source #
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' (CofreeT f w a) (CofreeT f w a) Source #
(Traversable f, Traversable m) => Plated (FreeT f m a) Source #
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' (FreeT f m a) (FreeT f m a) Source #

type Prism s t a b = forall p f. (Choice p, Applicative f) => p a (f b) -> p s (f t) Source #

A Prism l is a Traversal that can also be turned around with re to obtain a Getter in the opposite direction.

There are three laws that a Prism should satisfy:

First, if I re or review a value with a Prism and then preview or use (^?), I will get it back:

preview l (review l b) ≡ Just b

Second, if you can extract a value a using a Prism l from a value s, then the value s is completely described by l and a:

preview l s ≡ Just a ⟹ review l a ≡ s

Third, if you get non-match t, you can convert it result back to s:

matching l s ≡ Left t ⟹ matching l t ≡ Left s

The first two laws imply that the Traversal laws hold for every Prism and that we traverse at most 1 element:

lengthOf l x <= 1

It may help to think of this as an Iso that can be partial in one direction.

Every Prism is a valid Traversal.

Every Iso is a valid Prism.

For example, you might have a Prism' Integer Natural allows you to always go from a Natural to an Integer, and provide you with tools to check if an Integer is a Natural and/or to edit one if it is.

nat :: Prism' Integer Natural
nat = prism toInteger $ \ i ->
   if i < 0
   then Left i
   else Right (fromInteger i)

Now we can ask if an Integer is a Natural.

>>> 5^?nat
Just 5

>>> (-5)^?nat
Nothing

We can update the ones that are:

>>> (-3,4) & both.nat *~ 2
(-3,8)

And we can then convert from a Natural to an Integer.

>>> 5 ^. re nat -- :: Natural
5

Similarly we can use a Prism to traverse the Left half of an Either:

>>> Left "hello" & _Left %~ length
Left 5

or to construct an Either:

>>> 5^.re _Left
Left 5

such that if you query it with the Prism, you will get your original input back.

>>> 5^.re _Left ^? _Left
Just 5

Another interesting way to think of a Prism is as the categorical dual of a Lens -- a co-Lens, so to speak. This is what permits the construction of outside.

Note: Composition with a Prism is index-preserving.

type Review t b = forall p f. (Choice p, Bifunctor p, Settable f) => Optic' p f t b Source #

This is a limited form of a Prism that can only be used for re operations.

Like with a Getter, there are no laws to state for a Review.

You can generate a Review by using unto. You can also use any Prism or Iso directly as a Review.

type Setter s t a b = forall f. Settable f => (a -> f b) -> s -> f t Source #

The only LensLike law that can apply to a Setter l is that

set l y (set l x a) ≡ set l y a

You can't view a Setter in general, so the other two laws are irrelevant.

However, two Functor laws apply to a Setter:

over l id ≡ id
over l f . over l g ≡ over l (f . g)

These can be stated more directly:

l pure ≡ pure
l f . untainted . l g ≡ l (f . untainted . g)

You can compose a Setter with a Lens or a Traversal using (.) from the Prelude and the result is always only a Setter and nothing more.

>>> over traverse f [a,b,c,d]
[f a,f b,f c,f d]

>>> over _1 f (a,b)
(f a,b)

>>> over (traverse._1) f [(a,b),(c,d)]
[(f a,b),(f c,d)]

>>> over both f (a,b)
(f a,f b)

>>> over (traverse.both) f [(a,b),(c,d)]
[(f a,f b),(f c,f d)]

type Traversal s t a b = forall f. Applicative f => (a -> f b) -> s -> f t Source #

A Traversal can be used directly as a Setter or a Fold (but not as a Lens) and provides the ability to both read and update multiple fields, subject to some relatively weak Traversal laws.

These have also been known as multilenses, but they have the signature and spirit of

traverse :: Traversable f => Traversal (f a) (f b) a b

and the more evocative name suggests their application.

Most of the time the Traversal you will want to use is just traverse, but you can also pass any Lens or Iso as a Traversal, and composition of a Traversal (or Lens or Iso) with a Traversal (or Lens or Iso) using (.) forms a valid Traversal.

The laws for a Traversal t follow from the laws for Traversable as stated in "The Essence of the Iterator Pattern".

t pure ≡ pure
fmap (t f) . t g ≡ getCompose . t (Compose . fmap f . g)

One consequence of this requirement is that a Traversal needs to leave the same number of elements as a candidate for subsequent Traversal that it started with. Another testament to the strength of these laws is that the caveat expressed in section 5.5 of the "Essence of the Iterator Pattern" about exotic Traversable instances that traverse the same entry multiple times was actually already ruled out by the second law in that same paper!

class Wrapped s where Source #

Wrapped provides isomorphisms to wrap and unwrap newtypes or data types with one constructor.

Minimal complete definition

Nothing

Associated Types

type Unwrapped s :: Type Source #

type Unwrapped s = GUnwrapped (Rep s)

Methods

_Wrapped' :: Iso' s (Unwrapped s) Source #

An isomorphism between s and a.

If your type has a Generic instance, _Wrapped' will default to _GWrapped', and you can choose to not override it with your own definition.

default _Wrapped' :: (Generic s, D1 d (C1 c (S1 s' (Rec0 a))) ~ Rep s, Unwrapped s ~ GUnwrapped (Rep s)) => Iso' s (Unwrapped s) Source #

Instances

Instances details

Wrapped NoMethodError Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped NoMethodError Source # Methods _Wrapped' :: Iso' NoMethodError (Unwrapped NoMethodError) Source #
Wrapped PatternMatchFail Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped PatternMatchFail Source # Methods _Wrapped' :: Iso' PatternMatchFail (Unwrapped PatternMatchFail) Source #
Wrapped RecConError Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped RecConError Source # Methods _Wrapped' :: Iso' RecConError (Unwrapped RecConError) Source #
Wrapped RecSelError Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped RecSelError Source # Methods _Wrapped' :: Iso' RecSelError (Unwrapped RecSelError) Source #
Wrapped RecUpdError Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped RecUpdError Source # Methods _Wrapped' :: Iso' RecUpdError (Unwrapped RecUpdError) Source #
Wrapped TypeError Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped TypeError Source # Methods _Wrapped' :: Iso' TypeError (Unwrapped TypeError) Source #
Wrapped All Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped All Source # Methods _Wrapped' :: Iso' All (Unwrapped All) Source #
Wrapped Any Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped Any Source # Methods _Wrapped' :: Iso' Any (Unwrapped Any) Source #
Wrapped Errno Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped Errno Source # Methods _Wrapped' :: Iso' Errno (Unwrapped Errno) Source #
Wrapped CBool Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CBool Source # Methods _Wrapped' :: Iso' CBool (Unwrapped CBool) Source #
Wrapped CChar Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CChar Source # Methods _Wrapped' :: Iso' CChar (Unwrapped CChar) Source #
Wrapped CClock Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CClock Source # Methods _Wrapped' :: Iso' CClock (Unwrapped CClock) Source #
Wrapped CDouble Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CDouble Source # Methods _Wrapped' :: Iso' CDouble (Unwrapped CDouble) Source #
Wrapped CFloat Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CFloat Source # Methods _Wrapped' :: Iso' CFloat (Unwrapped CFloat) Source #
Wrapped CInt Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CInt Source # Methods _Wrapped' :: Iso' CInt (Unwrapped CInt) Source #
Wrapped CIntMax Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CIntMax Source # Methods _Wrapped' :: Iso' CIntMax (Unwrapped CIntMax) Source #
Wrapped CIntPtr Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CIntPtr Source # Methods _Wrapped' :: Iso' CIntPtr (Unwrapped CIntPtr) Source #
Wrapped CLLong Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CLLong Source # Methods _Wrapped' :: Iso' CLLong (Unwrapped CLLong) Source #
Wrapped CLong Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CLong Source # Methods _Wrapped' :: Iso' CLong (Unwrapped CLong) Source #
Wrapped CPtrdiff Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CPtrdiff Source # Methods _Wrapped' :: Iso' CPtrdiff (Unwrapped CPtrdiff) Source #
Wrapped CSChar Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CSChar Source # Methods _Wrapped' :: Iso' CSChar (Unwrapped CSChar) Source #
Wrapped CSUSeconds Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CSUSeconds Source # Methods _Wrapped' :: Iso' CSUSeconds (Unwrapped CSUSeconds) Source #
Wrapped CShort Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CShort Source # Methods _Wrapped' :: Iso' CShort (Unwrapped CShort) Source #
Wrapped CSigAtomic Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CSigAtomic Source # Methods _Wrapped' :: Iso' CSigAtomic (Unwrapped CSigAtomic) Source #
Wrapped CSize Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CSize Source # Methods _Wrapped' :: Iso' CSize (Unwrapped CSize) Source #
Wrapped CTime Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CTime Source # Methods _Wrapped' :: Iso' CTime (Unwrapped CTime) Source #
Wrapped CUChar Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CUChar Source # Methods _Wrapped' :: Iso' CUChar (Unwrapped CUChar) Source #
Wrapped CUInt Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CUInt Source # Methods _Wrapped' :: Iso' CUInt (Unwrapped CUInt) Source #
Wrapped CUIntMax Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CUIntMax Source # Methods _Wrapped' :: Iso' CUIntMax (Unwrapped CUIntMax) Source #
Wrapped CUIntPtr Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CUIntPtr Source # Methods _Wrapped' :: Iso' CUIntPtr (Unwrapped CUIntPtr) Source #
Wrapped CULLong Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CULLong Source # Methods _Wrapped' :: Iso' CULLong (Unwrapped CULLong) Source #
Wrapped CULong Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CULong Source # Methods _Wrapped' :: Iso' CULong (Unwrapped CULong) Source #
Wrapped CUSeconds Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CUSeconds Source # Methods _Wrapped' :: Iso' CUSeconds (Unwrapped CUSeconds) Source #
Wrapped CUShort Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CUShort Source # Methods _Wrapped' :: Iso' CUShort (Unwrapped CUShort) Source #
Wrapped CWchar Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CWchar Source # Methods _Wrapped' :: Iso' CWchar (Unwrapped CWchar) Source #
Wrapped ErrorCall Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped ErrorCall Source # Methods _Wrapped' :: Iso' ErrorCall (Unwrapped ErrorCall) Source #
Wrapped AssertionFailed Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped AssertionFailed Source # Methods _Wrapped' :: Iso' AssertionFailed (Unwrapped AssertionFailed) Source #
Wrapped CompactionFailed Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CompactionFailed Source # Methods _Wrapped' :: Iso' CompactionFailed (Unwrapped CompactionFailed) Source #
Wrapped CBlkCnt Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CBlkCnt Source # Methods _Wrapped' :: Iso' CBlkCnt (Unwrapped CBlkCnt) Source #
Wrapped CBlkSize Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CBlkSize Source # Methods _Wrapped' :: Iso' CBlkSize (Unwrapped CBlkSize) Source #
Wrapped CCc Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CCc Source # Methods _Wrapped' :: Iso' CCc (Unwrapped CCc) Source #
Wrapped CClockId Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CClockId Source # Methods _Wrapped' :: Iso' CClockId (Unwrapped CClockId) Source #
Wrapped CDev Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CDev Source # Methods _Wrapped' :: Iso' CDev (Unwrapped CDev) Source #
Wrapped CFsBlkCnt Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CFsBlkCnt Source # Methods _Wrapped' :: Iso' CFsBlkCnt (Unwrapped CFsBlkCnt) Source #
Wrapped CFsFilCnt Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CFsFilCnt Source # Methods _Wrapped' :: Iso' CFsFilCnt (Unwrapped CFsFilCnt) Source #
Wrapped CGid Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CGid Source # Methods _Wrapped' :: Iso' CGid (Unwrapped CGid) Source #
Wrapped CId Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CId Source # Methods _Wrapped' :: Iso' CId (Unwrapped CId) Source #
Wrapped CIno Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CIno Source # Methods _Wrapped' :: Iso' CIno (Unwrapped CIno) Source #
Wrapped CKey Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CKey Source # Methods _Wrapped' :: Iso' CKey (Unwrapped CKey) Source #
Wrapped CMode Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CMode Source # Methods _Wrapped' :: Iso' CMode (Unwrapped CMode) Source #
Wrapped CNlink Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CNlink Source # Methods _Wrapped' :: Iso' CNlink (Unwrapped CNlink) Source #
Wrapped COff Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped COff Source # Methods _Wrapped' :: Iso' COff (Unwrapped COff) Source #
Wrapped CPid Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CPid Source # Methods _Wrapped' :: Iso' CPid (Unwrapped CPid) Source #
Wrapped CRLim Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CRLim Source # Methods _Wrapped' :: Iso' CRLim (Unwrapped CRLim) Source #
Wrapped CSpeed Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CSpeed Source # Methods _Wrapped' :: Iso' CSpeed (Unwrapped CSpeed) Source #
Wrapped CSsize Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CSsize Source # Methods _Wrapped' :: Iso' CSsize (Unwrapped CSsize) Source #
Wrapped CTcflag Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CTcflag Source # Methods _Wrapped' :: Iso' CTcflag (Unwrapped CTcflag) Source #
Wrapped CTimer Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CTimer Source # Methods _Wrapped' :: Iso' CTimer (Unwrapped CTimer) Source #
Wrapped CUid Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CUid Source # Methods _Wrapped' :: Iso' CUid (Unwrapped CUid) Source #
Wrapped Fd Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped Fd Source # Methods _Wrapped' :: Iso' Fd (Unwrapped Fd) Source #
Wrapped IntSet Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped IntSet Source # Methods _Wrapped' :: Iso' IntSet (Unwrapped IntSet) Source #
Wrapped (ZipList a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ZipList a) Source # Methods _Wrapped' :: Iso' (ZipList a) (Unwrapped (ZipList a)) Source #
Wrapped (Comparison a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Comparison a) Source # Methods _Wrapped' :: Iso' (Comparison a) (Unwrapped (Comparison a)) Source #
Wrapped (Equivalence a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Equivalence a) Source # Methods _Wrapped' :: Iso' (Equivalence a) (Unwrapped (Equivalence a)) Source #
Wrapped (Predicate a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Predicate a) Source # Methods _Wrapped' :: Iso' (Predicate a) (Unwrapped (Predicate a)) Source #
Wrapped (Identity a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Identity a) Source # Methods _Wrapped' :: Iso' (Identity a) (Unwrapped (Identity a)) Source #
Wrapped (First a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (First a) Source # Methods _Wrapped' :: Iso' (First a) (Unwrapped (First a)) Source #
Wrapped (Last a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Last a) Source # Methods _Wrapped' :: Iso' (Last a) (Unwrapped (Last a)) Source #
Wrapped (Down a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Down a) Source # Methods _Wrapped' :: Iso' (Down a) (Unwrapped (Down a)) Source #
Wrapped (First a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (First a) Source # Methods _Wrapped' :: Iso' (First a) (Unwrapped (First a)) Source #
Wrapped (Last a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Last a) Source # Methods _Wrapped' :: Iso' (Last a) (Unwrapped (Last a)) Source #
Wrapped (Max a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Max a) Source # Methods _Wrapped' :: Iso' (Max a) (Unwrapped (Max a)) Source #
Wrapped (Min a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Min a) Source # Methods _Wrapped' :: Iso' (Min a) (Unwrapped (Min a)) Source #
Wrapped (WrappedMonoid a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WrappedMonoid a) Source # Methods _Wrapped' :: Iso' (WrappedMonoid a) (Unwrapped (WrappedMonoid a)) Source #
Wrapped (Dual a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Dual a) Source # Methods _Wrapped' :: Iso' (Dual a) (Unwrapped (Dual a)) Source #
Wrapped (Endo a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Endo a) Source # Methods _Wrapped' :: Iso' (Endo a) (Unwrapped (Endo a)) Source #
Wrapped (Product a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Product a) Source # Methods _Wrapped' :: Iso' (Product a) (Unwrapped (Product a)) Source #
Wrapped (Sum a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Sum a) Source # Methods _Wrapped' :: Iso' (Sum a) (Unwrapped (Sum a)) Source #
Wrapped (NonEmpty a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (NonEmpty a) Source # Methods _Wrapped' :: Iso' (NonEmpty a) (Unwrapped (NonEmpty a)) Source #
Wrapped (Par1 p) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Par1 p) Source # Methods _Wrapped' :: Iso' (Par1 p) (Unwrapped (Par1 p)) Source #
Wrapped (IntMap a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (IntMap a) Source # Methods _Wrapped' :: Iso' (IntMap a) (Unwrapped (IntMap a)) Source #
Wrapped (Seq a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Seq a) Source # Methods _Wrapped' :: Iso' (Seq a) (Unwrapped (Seq a)) Source #
Ord a => Wrapped (Set a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Set a) Source # Methods _Wrapped' :: Iso' (Set a) (Unwrapped (Set a)) Source #
(Hashable a, Eq a) => Wrapped (HashSet a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (HashSet a) Source # Methods _Wrapped' :: Iso' (HashSet a) (Unwrapped (HashSet a)) Source #
Wrapped (Vector a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Vector a) Source # Methods _Wrapped' :: Iso' (Vector a) (Unwrapped (Vector a)) Source #
Prim a => Wrapped (Vector a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Vector a) Source # Methods _Wrapped' :: Iso' (Vector a) (Unwrapped (Vector a)) Source #
Storable a => Wrapped (Vector a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Vector a) Source # Methods _Wrapped' :: Iso' (Vector a) (Unwrapped (Vector a)) Source #
Unbox a => Wrapped (Vector a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Vector a) Source # Methods _Wrapped' :: Iso' (Vector a) (Unwrapped (Vector a)) Source #
Wrapped (WrappedMonad m a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WrappedMonad m a) Source # Methods _Wrapped' :: Iso' (WrappedMonad m a) (Unwrapped (WrappedMonad m a)) Source #
Wrapped (ArrowMonad m a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ArrowMonad m a) Source # Methods _Wrapped' :: Iso' (ArrowMonad m a) (Unwrapped (ArrowMonad m a)) Source #
Wrapped (Op a b) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Op a b) Source # Methods _Wrapped' :: Iso' (Op a b) (Unwrapped (Op a b)) Source #
Ord k => Wrapped (Map k a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Map k a) Source # Methods _Wrapped' :: Iso' (Map k a) (Unwrapped (Map k a)) Source #
Wrapped (CatchT m a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (CatchT m a) Source # Methods _Wrapped' :: Iso' (CatchT m a) (Unwrapped (CatchT m a)) Source #
Wrapped (Alt f a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Alt f a) Source # Methods _Wrapped' :: Iso' (Alt f a) (Unwrapped (Alt f a)) Source #
Wrapped (CoiterT w a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (CoiterT w a) Source # Methods _Wrapped' :: Iso' (CoiterT w a) (Unwrapped (CoiterT w a)) Source #
Wrapped (IterT m a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (IterT m a) Source # Methods _Wrapped' :: Iso' (IterT m a) (Unwrapped (IterT m a)) Source #
Wrapped (MaybeApply f a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (MaybeApply f a) Source # Methods _Wrapped' :: Iso' (MaybeApply f a) (Unwrapped (MaybeApply f a)) Source #
Wrapped (WrappedApplicative f a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WrappedApplicative f a) Source # Methods _Wrapped' :: Iso' (WrappedApplicative f a) (Unwrapped (WrappedApplicative f a)) Source #
Wrapped (MaybeT m a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (MaybeT m a) Source # Methods _Wrapped' :: Iso' (MaybeT m a) (Unwrapped (MaybeT m a)) Source #
(Hashable k, Eq k) => Wrapped (HashMap k a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (HashMap k a) Source # Methods _Wrapped' :: Iso' (HashMap k a) (Unwrapped (HashMap k a)) Source #
Wrapped (WrappedArrow a b c) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WrappedArrow a b c) Source # Methods _Wrapped' :: Iso' (WrappedArrow a b c) (Unwrapped (WrappedArrow a b c)) Source #
Wrapped (Kleisli m a b) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Kleisli m a b) Source # Methods _Wrapped' :: Iso' (Kleisli m a b) (Unwrapped (Kleisli m a b)) Source #
Wrapped (Const a x) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Const a x) Source # Methods _Wrapped' :: Iso' (Const a x) (Unwrapped (Const a x)) Source #
Wrapped (Ap f a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Ap f a) Source # Methods _Wrapped' :: Iso' (Ap f a) (Unwrapped (Ap f a)) Source #
Wrapped (Alt f a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Alt f a) Source # Methods _Wrapped' :: Iso' (Alt f a) (Unwrapped (Alt f a)) Source #
Wrapped (Rec1 f p) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Rec1 f p) Source # Methods _Wrapped' :: Iso' (Rec1 f p) (Unwrapped (Rec1 f p)) Source #
Wrapped (Fix p a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Fix p a) Source # Methods _Wrapped' :: Iso' (Fix p a) (Unwrapped (Fix p a)) Source #
Wrapped (Join p a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Join p a) Source # Methods _Wrapped' :: Iso' (Join p a) (Unwrapped (Join p a)) Source #
Wrapped (TracedT m w a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (TracedT m w a) Source # Methods _Wrapped' :: Iso' (TracedT m w a) (Unwrapped (TracedT m w a)) Source #
Wrapped (Compose f g a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Compose f g a) Source # Methods _Wrapped' :: Iso' (Compose f g a) (Unwrapped (Compose f g a)) Source #
Wrapped (ComposeCF f g a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ComposeCF f g a) Source # Methods _Wrapped' :: Iso' (ComposeCF f g a) (Unwrapped (ComposeCF f g a)) Source #
Wrapped (ComposeFC f g a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ComposeFC f g a) Source # Methods _Wrapped' :: Iso' (ComposeFC f g a) (Unwrapped (ComposeFC f g a)) Source #
Wrapped (ApT f g a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ApT f g a) Source # Methods _Wrapped' :: Iso' (ApT f g a) (Unwrapped (ApT f g a)) Source #
Wrapped (CofreeT f w a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (CofreeT f w a) Source # Methods _Wrapped' :: Iso' (CofreeT f w a) (Unwrapped (CofreeT f w a)) Source #
Wrapped (FreeT f m a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (FreeT f m a) Source # Methods _Wrapped' :: Iso' (FreeT f m a) (Unwrapped (FreeT f m a)) Source #
Wrapped (Static f a b) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Static f a b) Source # Methods _Wrapped' :: Iso' (Static f a b) (Unwrapped (Static f a b)) Source #
Wrapped (Tagged s a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Tagged s a) Source # Methods _Wrapped' :: Iso' (Tagged s a) (Unwrapped (Tagged s a)) Source #
Wrapped (Backwards f a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Backwards f a) Source # Methods _Wrapped' :: Iso' (Backwards f a) (Unwrapped (Backwards f a)) Source #
Wrapped (ExceptT e m a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ExceptT e m a) Source # Methods _Wrapped' :: Iso' (ExceptT e m a) (Unwrapped (ExceptT e m a)) Source #
Wrapped (IdentityT m a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (IdentityT m a) Source # Methods _Wrapped' :: Iso' (IdentityT m a) (Unwrapped (IdentityT m a)) Source #
Wrapped (ReaderT r m a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ReaderT r m a) Source # Methods _Wrapped' :: Iso' (ReaderT r m a) (Unwrapped (ReaderT r m a)) Source #
Wrapped (StateT s m a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (StateT s m a) Source # Methods _Wrapped' :: Iso' (StateT s m a) (Unwrapped (StateT s m a)) Source #
Wrapped (StateT s m a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (StateT s m a) Source # Methods _Wrapped' :: Iso' (StateT s m a) (Unwrapped (StateT s m a)) Source #
Wrapped (WriterT w m a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WriterT w m a) Source # Methods _Wrapped' :: Iso' (WriterT w m a) (Unwrapped (WriterT w m a)) Source #
Wrapped (WriterT w m a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WriterT w m a) Source # Methods _Wrapped' :: Iso' (WriterT w m a) (Unwrapped (WriterT w m a)) Source #
Wrapped (Constant a b) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Constant a b) Source # Methods _Wrapped' :: Iso' (Constant a b) (Unwrapped (Constant a b)) Source #
Wrapped (Reverse f a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Reverse f a) Source # Methods _Wrapped' :: Iso' (Reverse f a) (Unwrapped (Reverse f a)) Source #
Wrapped (K1 i c p) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (K1 i c p) Source # Methods _Wrapped' :: Iso' (K1 i c p) (Unwrapped (K1 i c p)) Source #
Wrapped (Costar f d c) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Costar f d c) Source # Methods _Wrapped' :: Iso' (Costar f d c) (Unwrapped (Costar f d c)) Source #
Wrapped (Forget r a b) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Forget r a b) Source # Methods _Wrapped' :: Iso' (Forget r a b) (Unwrapped (Forget r a b)) Source #
Wrapped (Star f d c) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Star f d c) Source # Methods _Wrapped' :: Iso' (Star f d c) (Unwrapped (Star f d c)) Source #
Wrapped (ContT r m a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ContT r m a) Source # Methods _Wrapped' :: Iso' (ContT r m a) (Unwrapped (ContT r m a)) Source #
Wrapped (Compose f g a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Compose f g a) Source # Methods _Wrapped' :: Iso' (Compose f g a) (Unwrapped (Compose f g a)) Source #
Wrapped ((f :.: g) p) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped ((f :.: g) p) Source # Methods _Wrapped' :: Iso' ((f :.: g) p) (Unwrapped ((f :.: g) p)) Source #
Wrapped (M1 i c f p) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (M1 i c f p) Source # Methods _Wrapped' :: Iso' (M1 i c f p) (Unwrapped (M1 i c f p)) Source #
Wrapped (Clown f a b) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Clown f a b) Source # Methods _Wrapped' :: Iso' (Clown f a b) (Unwrapped (Clown f a b)) Source #
Wrapped (Flip p a b) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Flip p a b) Source # Methods _Wrapped' :: Iso' (Flip p a b) (Unwrapped (Flip p a b)) Source #
Wrapped (Joker g a b) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Joker g a b) Source # Methods _Wrapped' :: Iso' (Joker g a b) (Unwrapped (Joker g a b)) Source #
Wrapped (WrappedBifunctor p a b) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WrappedBifunctor p a b) Source # Methods _Wrapped' :: Iso' (WrappedBifunctor p a b) (Unwrapped (WrappedBifunctor p a b)) Source #
Wrapped (WrappedArrow p a b) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WrappedArrow p a b) Source # Methods _Wrapped' :: Iso' (WrappedArrow p a b) (Unwrapped (WrappedArrow p a b)) Source #
Wrapped (Semi m a b) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Semi m a b) Source # Methods _Wrapped' :: Iso' (Semi m a b) (Unwrapped (Semi m a b)) Source #
Wrapped (WrappedCategory k3 a b) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WrappedCategory k3 a b) Source # Methods _Wrapped' :: Iso' (WrappedCategory k3 a b) (Unwrapped (WrappedCategory k3 a b)) Source #
Wrapped (Dual k3 a b) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Dual k3 a b) Source # Methods _Wrapped' :: Iso' (Dual k3 a b) (Unwrapped (Dual k3 a b)) Source #
Wrapped (RWST r w s m a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (RWST r w s m a) Source # Methods _Wrapped' :: Iso' (RWST r w s m a) (Unwrapped (RWST r w s m a)) Source #
Wrapped (RWST r w s m a) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (RWST r w s m a) Source # Methods _Wrapped' :: Iso' (RWST r w s m a) (Unwrapped (RWST r w s m a)) Source #
Wrapped (Tannen f p a b) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Tannen f p a b) Source # Methods _Wrapped' :: Iso' (Tannen f p a b) (Unwrapped (Tannen f p a b)) Source #
Wrapped (Cayley f p a b) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Cayley f p a b) Source # Methods _Wrapped' :: Iso' (Cayley f p a b) (Unwrapped (Cayley f p a b)) Source #
Wrapped (Biff p f g a b) Source #
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Biff p f g a b) Source # Methods _Wrapped' :: Iso' (Biff p f g a b) (Unwrapped (Biff p f g a b)) Source #

class (MonadState s m, MonadState t n) => Zoom m n s t | m -> s, n -> t, m t -> n, n s -> m where Source #

This class allows us to use zoom in, changing the State supplied by many different Monad transformers, potentially quite deep in a Monad transformer stack.

Methods

zoom :: LensLike' (Zoomed m c) t s -> m c -> n c infixr 2 Source #

Run a monadic action in a larger State than it was defined in, using a Lens' or Traversal'.

This is commonly used to lift actions in a simpler State Monad into a State Monad with a larger State type.

When applied to a Traversal' over multiple values, the actions for each target are executed sequentially and the results are aggregated.

This can be used to edit pretty much any Monad transformer stack with a State in it!

>>> flip State.evalState (a,b) $ zoom _1 $ use id
a

>>> flip State.execState (a,b) $ zoom _1 $ id .= c
(c,b)

>>> flip State.execState [(a,b),(c,d)] $ zoom traverse $ _2 %= f
[(a,f b),(c,f d)]

>>> flip State.runState [(a,b),(c,d)] $ zoom traverse $ _2 <%= f
(f b <> f d <> mempty,[(a,f b),(c,f d)])

>>> flip State.evalState (a,b) $ zoom both (use id)
a <> b

zoom :: Monad m             => Lens' s t      -> StateT t m a -> StateT s m a
zoom :: (Monad m, Monoid c) => Traversal' s t -> StateT t m c -> StateT s m c
zoom :: (Monad m, Monoid w)             => Lens' s t      -> RWST r w t m c -> RWST r w s m c
zoom :: (Monad m, Monoid w, Monoid c) => Traversal' s t -> RWST r w t m c -> RWST r w s m c
zoom :: (Monad m, Monoid w, Error e)  => Lens' s t      -> ErrorT e (RWST r w t m) c -> ErrorT e (RWST r w s m) c
zoom :: (Monad m, Monoid w, Monoid c, Error e) => Traversal' s t -> ErrorT e (RWST r w t m) c -> ErrorT e (RWST r w s m) c
...

Instances

Instances details

Zoom m n s t => Zoom (MaybeT m) (MaybeT n) s t Source #
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (MaybeT m) c) t s -> MaybeT m c -> MaybeT n c Source #
(Functor f, Zoom m n s t) => Zoom (FreeT f m) (FreeT f n) s t Source #
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (FreeT f m) c) t s -> FreeT f m c -> FreeT f n c Source #
Zoom m n s t => Zoom (ExceptT e m) (ExceptT e n) s t Source #
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (ExceptT e m) c) t s -> ExceptT e m c -> ExceptT e n c Source #
Zoom m n s t => Zoom (IdentityT m) (IdentityT n) s t Source #
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (IdentityT m) c) t s -> IdentityT m c -> IdentityT n c Source #
Zoom m n s t => Zoom (ReaderT e m) (ReaderT e n) s t Source #
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (ReaderT e m) c) t s -> ReaderT e m c -> ReaderT e n c Source #
Monad z => Zoom (StateT s z) (StateT t z) s t Source #
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (StateT s z) c) t s -> StateT s z c -> StateT t z c Source #
Monad z => Zoom (StateT s z) (StateT t z) s t Source #
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (StateT s z) c) t s -> StateT s z c -> StateT t z c Source #
(Monoid w, Zoom m n s t) => Zoom (WriterT w m) (WriterT w n) s t Source #
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (WriterT w m) c) t s -> WriterT w m c -> WriterT w n c Source #
(Monoid w, Zoom m n s t) => Zoom (WriterT w m) (WriterT w n) s t Source #
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (WriterT w m) c) t s -> WriterT w m c -> WriterT w n c Source #
(Monoid w, Monad z) => Zoom (RWST r w s z) (RWST r w t z) s t Source #
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (RWST r w s z) c) t s -> RWST r w s z c -> RWST r w t z c Source #
(Monoid w, Monad z) => Zoom (RWST r w s z) (RWST r w t z) s t Source #
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (RWST r w s z) c) t s -> RWST r w s z c -> RWST r w t z c Source #

type family Index (s :: Type) :: Type Source #

Instances

Instances details

type Index ByteString Source #
Instance details Defined in Control.Lens.At type Index ByteString = Int
type Index ByteString Source #
Instance details Defined in Control.Lens.At type Index ByteString = Int64
type Index IntSet Source #
Instance details Defined in Control.Lens.At type Index IntSet = Int
type Index Text Source #
Instance details Defined in Control.Lens.At type Index Text = Int
type Index Text Source #
Instance details Defined in Control.Lens.At type Index Text = Int64
type Index (Complex a) Source #
Instance details Defined in Control.Lens.At type Index (Complex a) = Int
type Index (Identity a) Source #
Instance details Defined in Control.Lens.At type Index (Identity a) = ()
type Index (NonEmpty a) Source #
Instance details Defined in Control.Lens.At type Index (NonEmpty a) = Int
type Index (IntMap a) Source #
Instance details Defined in Control.Lens.At type Index (IntMap a) = Int
type Index (Seq a) Source #
Instance details Defined in Control.Lens.At type Index (Seq a) = Int
type Index (Set a) Source #
Instance details Defined in Control.Lens.At type Index (Set a) = a
type Index (Tree a) Source #
Instance details Defined in Control.Lens.At type Index (Tree a) = [Int]
type Index (HashSet a) Source #
Instance details Defined in Control.Lens.At type Index (HashSet a) = a
type Index (Vector a) Source #
Instance details Defined in Control.Lens.At type Index (Vector a) = Int
type Index (Vector a) Source #
Instance details Defined in Control.Lens.At type Index (Vector a) = Int
type Index (Vector a) Source #
Instance details Defined in Control.Lens.At type Index (Vector a) = Int
type Index (Vector a) Source #
Instance details Defined in Control.Lens.At type Index (Vector a) = Int
type Index (Maybe a) Source #
Instance details Defined in Control.Lens.At type Index (Maybe a) = ()
type Index [a] Source #
Instance details Defined in Control.Lens.At type Index [a] = Int
type Index (UArray i e) Source #
Instance details Defined in Control.Lens.At type Index (UArray i e) = i
type Index (Array i e) Source #
Instance details Defined in Control.Lens.At type Index (Array i e) = i
type Index (Map k a) Source #
Instance details Defined in Control.Lens.At type Index (Map k a) = k
type Index (HashMap k a) Source #
Instance details Defined in Control.Lens.At type Index (HashMap k a) = k
type Index (a, b) Source #
Instance details Defined in Control.Lens.At type Index (a, b) = Int
type Index (e -> a) Source #
Instance details Defined in Control.Lens.At type Index (e -> a) = e
type Index (a, b, c) Source #
Instance details Defined in Control.Lens.At type Index (a, b, c) = Int
type Index (a, b, c, d) Source #
Instance details Defined in Control.Lens.At type Index (a, b, c, d) = Int
type Index (a, b, c, d, e) Source #
Instance details Defined in Control.Lens.At type Index (a, b, c, d, e) = Int
type Index (a, b, c, d, e, f) Source #
Instance details Defined in Control.Lens.At type Index (a, b, c, d, e, f) = Int
type Index (a, b, c, d, e, f, g) Source #
Instance details Defined in Control.Lens.At type Index (a, b, c, d, e, f, g) = Int
type Index (a, b, c, d, e, f, g, h) Source #
Instance details Defined in Control.Lens.At type Index (a, b, c, d, e, f, g, h) = Int
type Index (a, b, c, d, e, f, g, h, i) Source #
Instance details Defined in Control.Lens.At type Index (a, b, c, d, e, f, g, h, i) = Int

type family IxValue (m :: Type) :: Type Source #

This provides a common notion of a value at an index that is shared by both Ixed and At.

Instances

Instances details

type IxValue ByteString Source #
Instance details Defined in Control.Lens.At type IxValue ByteString = Word8
type IxValue ByteString Source #
Instance details Defined in Control.Lens.At type IxValue ByteString = Word8
type IxValue IntSet Source #
Instance details Defined in Control.Lens.At type IxValue IntSet = ()
type IxValue Text Source #
Instance details Defined in Control.Lens.At type IxValue Text = Char
type IxValue Text Source #
Instance details Defined in Control.Lens.At type IxValue Text = Char
type IxValue (Identity a) Source #
Instance details Defined in Control.Lens.At type IxValue (Identity a) = a
type IxValue (NonEmpty a) Source #
Instance details Defined in Control.Lens.At type IxValue (NonEmpty a) = a
type IxValue (IntMap a) Source #
Instance details Defined in Control.Lens.At type IxValue (IntMap a) = a
type IxValue (Seq a) Source #
Instance details Defined in Control.Lens.At type IxValue (Seq a) = a
type IxValue (Set k) Source #
Instance details Defined in Control.Lens.At type IxValue (Set k) = ()
type IxValue (Tree a) Source #
Instance details Defined in Control.Lens.At type IxValue (Tree a) = a
type IxValue (HashSet k) Source #
Instance details Defined in Control.Lens.At type IxValue (HashSet k) = ()
type IxValue (Vector a) Source #
Instance details Defined in Control.Lens.At type IxValue (Vector a) = a
type IxValue (Vector a) Source #
Instance details Defined in Control.Lens.At type IxValue (Vector a) = a
type IxValue (Vector a) Source #
Instance details Defined in Control.Lens.At type IxValue (Vector a) = a
type IxValue (Vector a) Source #
Instance details Defined in Control.Lens.At type IxValue (Vector a) = a
type IxValue (Maybe a) Source #
Instance details Defined in Control.Lens.At type IxValue (Maybe a) = a
type IxValue [a] Source #
Instance details Defined in Control.Lens.At type IxValue [a] = a
type IxValue (UArray i e) Source #
Instance details Defined in Control.Lens.At type IxValue (UArray i e) = e
type IxValue (Array i e) Source #
Instance details Defined in Control.Lens.At type IxValue (Array i e) = e
type IxValue (Map k a) Source #
Instance details Defined in Control.Lens.At type IxValue (Map k a) = a
type IxValue (HashMap k a) Source #
Instance details Defined in Control.Lens.At type IxValue (HashMap k a) = a
type IxValue (a, a2) Source #	`ix` :: `Int` -> `Traversal'` (a,a) a
Instance details Defined in Control.Lens.At type IxValue (a, a2) = a
type IxValue (e -> a) Source #
Instance details Defined in Control.Lens.At type IxValue (e -> a) = a
type IxValue (a, a2, a3) Source #	`ix` :: `Int` -> `Traversal'` (a,a,a) a
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3) = a
type IxValue (a, a2, a3, a4) Source #	`ix` :: `Int` -> `Traversal'` (a,a,a,a) a
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3, a4) = a
type IxValue (a, a2, a3, a4, a5) Source #	`ix` :: `Int` -> `Traversal'` (a,a,a,a,a) a
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3, a4, a5) = a
type IxValue (a, a2, a3, a4, a5, a6) Source #	`ix` :: `Int` -> `Traversal'` (a,a,a,a,a,a) a
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3, a4, a5, a6) = a
type IxValue (a, a2, a3, a4, a5, a6, a7) Source #	`ix` :: `Int` -> `Traversal'` (a,a,a,a,a,a,a) a
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3, a4, a5, a6, a7) = a
type IxValue (a, a2, a3, a4, a5, a6, a7, a8) Source #	`ix` :: `Int` -> `Traversal'` (a,a,a,a,a,a,a,a) a
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3, a4, a5, a6, a7, a8) = a
type IxValue (a, a2, a3, a4, a5, a6, a7, a8, a9) Source #	`ix` :: `Int` -> `Traversal'` (a,a,a,a,a,a,a,a,a) a
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3, a4, a5, a6, a7, a8, a9) = a

class Ixed m where Source #

Provides a simple Traversal lets you traverse the value at a given key in a Map or element at an ordinal position in a list or Seq.

Minimal complete definition

Nothing

Methods

ix :: Index m -> Traversal' m (IxValue m) Source #

NB: Setting the value of this Traversal will only set the value in at if it is already present.

If you want to be able to insert missing values, you want at.

>>> Seq.fromList [a,b,c,d] & ix 2 %~ f
fromList [a,b,f c,d]

>>> Seq.fromList [a,b,c,d] & ix 2 .~ e
fromList [a,b,e,d]

>>> Seq.fromList [a,b,c,d] ^? ix 2
Just c

>>> Seq.fromList [] ^? ix 2
Nothing

default ix :: At m => Index m -> Traversal' m (IxValue m) Source #

Instances

Instances details

Ixed ByteString Source #
Instance details Defined in Control.Lens.At Methods ix :: Index ByteString -> Traversal' ByteString (IxValue ByteString) Source #
Ixed ByteString Source #
Instance details Defined in Control.Lens.At Methods ix :: Index ByteString -> Traversal' ByteString (IxValue ByteString) Source #
Ixed IntSet Source #
Instance details Defined in Control.Lens.At Methods ix :: Index IntSet -> Traversal' IntSet (IxValue IntSet) Source #
Ixed Text Source #
Instance details Defined in Control.Lens.At Methods ix :: Index Text -> Traversal' Text (IxValue Text) Source #
Ixed Text Source #
Instance details Defined in Control.Lens.At Methods ix :: Index Text -> Traversal' Text (IxValue Text) Source #
Ixed (Identity a) Source #
Instance details Defined in Control.Lens.At Methods ix :: Index (Identity a) -> Traversal' (Identity a) (IxValue (Identity a)) Source #
Ixed (NonEmpty a) Source #
Instance details Defined in Control.Lens.At Methods ix :: Index (NonEmpty a) -> Traversal' (NonEmpty a) (IxValue (NonEmpty a)) Source #
Ixed (IntMap a) Source #
Instance details Defined in Control.Lens.At Methods ix :: Index (IntMap a) -> Traversal' (IntMap a) (IxValue (IntMap a)) Source #
Ixed (Seq a) Source #
Instance details Defined in Control.Lens.At Methods ix :: Index (Seq a) -> Traversal' (Seq a) (IxValue (Seq a)) Source #
Ord k => Ixed (Set k) Source #
Instance details Defined in Control.Lens.At Methods ix :: Index (Set k) -> Traversal' (Set k) (IxValue (Set k)) Source #
Ixed (Tree a) Source #
Instance details Defined in Control.Lens.At Methods ix :: Index (Tree a) -> Traversal' (Tree a) (IxValue (Tree a)) Source #
(Eq k, Hashable k) => Ixed (HashSet k) Source #
Instance details Defined in Control.Lens.At Methods ix :: Index (HashSet k) -> Traversal' (HashSet k) (IxValue (HashSet k)) Source #
Ixed (Vector a) Source #
Instance details Defined in Control.Lens.At Methods ix :: Index (Vector a) -> Traversal' (Vector a) (IxValue (Vector a)) Source #
Prim a => Ixed (Vector a) Source #
Instance details Defined in Control.Lens.At Methods ix :: Index (Vector a) -> Traversal' (Vector a) (IxValue (Vector a)) Source #
Storable a => Ixed (Vector a) Source #
Instance details Defined in Control.Lens.At Methods ix :: Index (Vector a) -> Traversal' (Vector a) (IxValue (Vector a)) Source #
Unbox a => Ixed (Vector a) Source #
Instance details Defined in Control.Lens.At Methods ix :: Index (Vector a) -> Traversal' (Vector a) (IxValue (Vector a)) Source #
Ixed (Maybe a) Source #
Instance details Defined in Control.Lens.At Methods ix :: Index (Maybe a) -> Traversal' (Maybe a) (IxValue (Maybe a)) Source #
Ixed [a] Source #
Instance details Defined in Control.Lens.At Methods ix :: Index [a] -> Traversal' [a] (IxValue [a]) Source #
(IArray UArray e, Ix i) => Ixed (UArray i e) Source #	arr `!` i ≡ arr `^.` `ix` i arr `//` [(i,e)] ≡ `ix` i `.~` e `$` arr
Instance details Defined in Control.Lens.At Methods ix :: Index (UArray i e) -> Traversal' (UArray i e) (IxValue (UArray i e)) Source #
Ix i => Ixed (Array i e) Source #	arr `!` i ≡ arr `^.` `ix` i arr `//` [(i,e)] ≡ `ix` i `.~` e `$` arr
Instance details Defined in Control.Lens.At Methods ix :: Index (Array i e) -> Traversal' (Array i e) (IxValue (Array i e)) Source #
Ord k => Ixed (Map k a) Source #
Instance details Defined in Control.Lens.At Methods ix :: Index (Map k a) -> Traversal' (Map k a) (IxValue (Map k a)) Source #
(Eq k, Hashable k) => Ixed (HashMap k a) Source #
Instance details Defined in Control.Lens.At Methods ix :: Index (HashMap k a) -> Traversal' (HashMap k a) (IxValue (HashMap k a)) Source #
a ~ a2 => Ixed (a, a2) Source #
Instance details Defined in Control.Lens.At Methods ix :: Index (a, a2) -> Traversal' (a, a2) (IxValue (a, a2)) Source #
Eq e => Ixed (e -> a) Source #
Instance details Defined in Control.Lens.At Methods ix :: Index (e -> a) -> Traversal' (e -> a) (IxValue (e -> a)) Source #
(a ~ a2, a ~ a3) => Ixed (a, a2, a3) Source #
Instance details Defined in Control.Lens.At Methods ix :: Index (a, a2, a3) -> Traversal' (a, a2, a3) (IxValue (a, a2, a3)) Source #
(a ~ a2, a ~ a3, a ~ a4) => Ixed (a, a2, a3, a4) Source #
Instance details Defined in Control.Lens.At Methods ix :: Index (a, a2, a3, a4) -> Traversal' (a, a2, a3, a4) (IxValue (a, a2, a3, a4)) Source #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5) => Ixed (a, a2, a3, a4, a5) Source #
Instance details Defined in Control.Lens.At Methods ix :: Index (a, a2, a3, a4, a5) -> Traversal' (a, a2, a3, a4, a5) (IxValue (a, a2, a3, a4, a5)) Source #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6) => Ixed (a, a2, a3, a4, a5, a6) Source #
Instance details Defined in Control.Lens.At Methods ix :: Index (a, a2, a3, a4, a5, a6) -> Traversal' (a, a2, a3, a4, a5, a6) (IxValue (a, a2, a3, a4, a5, a6)) Source #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6, a ~ a7) => Ixed (a, a2, a3, a4, a5, a6, a7) Source #
Instance details Defined in Control.Lens.At Methods ix :: Index (a, a2, a3, a4, a5, a6, a7) -> Traversal' (a, a2, a3, a4, a5, a6, a7) (IxValue (a, a2, a3, a4, a5, a6, a7)) Source #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6, a ~ a7, a ~ a8) => Ixed (a, a2, a3, a4, a5, a6, a7, a8) Source #
Instance details Defined in Control.Lens.At Methods ix :: Index (a, a2, a3, a4, a5, a6, a7, a8) -> Traversal' (a, a2, a3, a4, a5, a6, a7, a8) (IxValue (a, a2, a3, a4, a5, a6, a7, a8)) Source #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6, a ~ a7, a ~ a8, a ~ a9) => Ixed (a, a2, a3, a4, a5, a6, a7, a8, a9) Source #
Instance details Defined in Control.Lens.At Methods ix :: Index (a, a2, a3, a4, a5, a6, a7, a8, a9) -> Traversal' (a, a2, a3, a4, a5, a6, a7, a8, a9) (IxValue (a, a2, a3, a4, a5, a6, a7, a8, a9)) Source #

class Contains m where Source #

This class provides a simple Lens that lets you view (and modify) information about whether or not a container contains a given Index.

Methods

contains :: Index m -> Lens' m Bool Source #

>>> IntSet.fromList [1,2,3,4] ^. contains 3
True

>>> IntSet.fromList [1,2,3,4] ^. contains 5
False

>>> IntSet.fromList [1,2,3,4] & contains 3 .~ False
fromList [1,2,4]

Instances

Instances details

Contains IntSet Source #
Instance details Defined in Control.Lens.At Methods contains :: Index IntSet -> Lens' IntSet Bool Source #
Ord a => Contains (Set a) Source #
Instance details Defined in Control.Lens.At Methods contains :: Index (Set a) -> Lens' (Set a) Bool Source #
(Eq a, Hashable a) => Contains (HashSet a) Source #
Instance details Defined in Control.Lens.At Methods contains :: Index (HashSet a) -> Lens' (HashSet a) Bool Source #

class Snoc s t a b | s -> a, t -> b, s b -> t, t a -> s where Source #

This class provides a way to attach or detach elements on the right side of a structure in a flexible manner.

Methods

_Snoc :: Prism s t (s, a) (t, b) Source #

_Snoc :: Prism [a] [b] ([a], a) ([b], b)
_Snoc :: Prism (Seq a) (Seq b) (Seq a, a) (Seq b, b)
_Snoc :: Prism (Vector a) (Vector b) (Vector a, a) (Vector b, b)
_Snoc :: Prism' String (String, Char)
_Snoc :: Prism' Text (Text, Char)
_Snoc :: Prism' ByteString (ByteString, Word8)

Instances

Instances details

Snoc ByteString ByteString Word8 Word8 Source #
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism ByteString ByteString (ByteString, Word8) (ByteString, Word8) Source #
Snoc ByteString ByteString Word8 Word8 Source #
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism ByteString ByteString (ByteString, Word8) (ByteString, Word8) Source #
Snoc Text Text Char Char Source #
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism Text Text (Text, Char) (Text, Char) Source #
Snoc Text Text Char Char Source #
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism Text Text (Text, Char) (Text, Char) Source #
Snoc (ZipList a) (ZipList b) a b Source #
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism (ZipList a) (ZipList b) (ZipList a, a) (ZipList b, b) Source #
Snoc (Seq a) (Seq b) a b Source #
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism (Seq a) (Seq b) (Seq a, a) (Seq b, b) Source #
Snoc (Deque a) (Deque b) a b Source #
Instance details Defined in Control.Lens.Internal.Deque Methods _Snoc :: Prism (Deque a) (Deque b) (Deque a, a) (Deque b, b) Source #
Snoc (Vector a) (Vector b) a b Source #
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism (Vector a) (Vector b) (Vector a, a) (Vector b, b) Source #
(Prim a, Prim b) => Snoc (Vector a) (Vector b) a b Source #
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism (Vector a) (Vector b) (Vector a, a) (Vector b, b) Source #
(Storable a, Storable b) => Snoc (Vector a) (Vector b) a b Source #
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism (Vector a) (Vector b) (Vector a, a) (Vector b, b) Source #
(Unbox a, Unbox b) => Snoc (Vector a) (Vector b) a b Source #
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism (Vector a) (Vector b) (Vector a, a) (Vector b, b) Source #
Snoc [a] [b] a b Source #
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism [a] [b] ([a], a) ([b], b) Source #

class AsEmpty a where Source #

Minimal complete definition

Nothing

Methods

_Empty :: Prism' a () Source #

>>> isn't _Empty [1,2,3]
True

default _Empty :: (Monoid a, Eq a) => Prism' a () Source #

Instances

Instances details

AsEmpty All Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' All () Source #
AsEmpty Any Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' Any () Source #
AsEmpty Event Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' Event () Source #
AsEmpty ByteString Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' ByteString () Source #
AsEmpty ByteString Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' ByteString () Source #
AsEmpty IntSet Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' IntSet () Source #
AsEmpty Ordering Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' Ordering () Source #
AsEmpty Text Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' Text () Source #
AsEmpty Text Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' Text () Source #
AsEmpty () Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' () () Source #
AsEmpty (ZipList a) Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (ZipList a) () Source #
AsEmpty (First a) Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (First a) () Source #
AsEmpty (Last a) Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Last a) () Source #
AsEmpty a => AsEmpty (Dual a) Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Dual a) () Source #
(Eq a, Num a) => AsEmpty (Product a) Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Product a) () Source #
(Eq a, Num a) => AsEmpty (Sum a) Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Sum a) () Source #
AsEmpty (IntMap a) Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (IntMap a) () Source #
AsEmpty (Seq a) Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Seq a) () Source #
AsEmpty (Set a) Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Set a) () Source #
AsEmpty (HashSet a) Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (HashSet a) () Source #
AsEmpty (Vector a) Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Vector a) () Source #
Storable a => AsEmpty (Vector a) Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Vector a) () Source #
Unbox a => AsEmpty (Vector a) Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Vector a) () Source #
AsEmpty (Maybe a) Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Maybe a) () Source #
AsEmpty [a] Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' [a] () Source #
AsEmpty (Map k a) Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Map k a) () Source #
AsEmpty (HashMap k a) Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (HashMap k a) () Source #
(AsEmpty a, AsEmpty b) => AsEmpty (a, b) Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (a, b) () Source #
(AsEmpty a, AsEmpty b, AsEmpty c) => AsEmpty (a, b, c) Source #
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (a, b, c) () Source #

type Equality' s a = Equality s s a a Source #

A Simple Equality.

type AnEquality s t a b = Identical a (Proxy b) a (Proxy b) -> Identical a (Proxy b) s (Proxy t) Source #

When you see this as an argument to a function, it expects an Equality.

type AnEquality' s a = AnEquality s s a a Source #

A Simple AnEquality.

data Identical a b s t where Source #

Provides witness that (s ~ a, b ~ t) holds.

Constructors

Identical :: Identical a b a b

type IndexedFold i s a = forall p f. (Indexable i p, Contravariant f, Applicative f) => p a (f a) -> s -> f s Source #

Every IndexedFold is a valid Fold and can be used for Getting.

data Leftmost a Source #

Used for firstOf.

Instances

Instances details

Monoid (Leftmost a) Source #
Instance details Defined in Control.Lens.Internal.Fold Methods mempty :: Leftmost a # mappend :: Leftmost a -> Leftmost a -> Leftmost a # mconcat :: [Leftmost a] -> Leftmost a #
Semigroup (Leftmost a) Source #
Instance details Defined in Control.Lens.Internal.Fold Methods (<>) :: Leftmost a -> Leftmost a -> Leftmost a # sconcat :: NonEmpty (Leftmost a) -> Leftmost a # stimes :: Integral b => b -> Leftmost a -> Leftmost a #

data Rightmost a Source #

Used for lastOf.

Instances

Instances details

Monoid (Rightmost a) Source #
Instance details Defined in Control.Lens.Internal.Fold Methods mempty :: Rightmost a # mappend :: Rightmost a -> Rightmost a -> Rightmost a # mconcat :: [Rightmost a] -> Rightmost a #
Semigroup (Rightmost a) Source #
Instance details Defined in Control.Lens.Internal.Fold Methods (<>) :: Rightmost a -> Rightmost a -> Rightmost a # sconcat :: NonEmpty (Rightmost a) -> Rightmost a # stimes :: Integral b => b -> Rightmost a -> Rightmost a #

data Magma i t b a Source #

This provides a way to peek at the internal structure of a Traversal or IndexedTraversal

Instances

Instances details

FoldableWithIndex i (Magma i t b) Source #
Instance details Defined in Control.Lens.Internal.Magma Methods ifoldMap :: Monoid m => (i -> a -> m) -> Magma i t b a -> m # ifoldMap' :: Monoid m => (i -> a -> m) -> Magma i t b a -> m # ifoldr :: (i -> a -> b0 -> b0) -> b0 -> Magma i t b a -> b0 # ifoldl :: (i -> b0 -> a -> b0) -> b0 -> Magma i t b a -> b0 # ifoldr' :: (i -> a -> b0 -> b0) -> b0 -> Magma i t b a -> b0 # ifoldl' :: (i -> b0 -> a -> b0) -> b0 -> Magma i t b a -> b0 #
FunctorWithIndex i (Magma i t b) Source #
Instance details Defined in Control.Lens.Internal.Magma Methods imap :: (i -> a -> b0) -> Magma i t b a -> Magma i t b b0 #
TraversableWithIndex i (Magma i t b) Source #
Instance details Defined in Control.Lens.Internal.Magma Methods itraverse :: Applicative f => (i -> a -> f b0) -> Magma i t b a -> f (Magma i t b b0) #
Foldable (Magma i t b) Source #
Instance details Defined in Control.Lens.Internal.Magma Methods fold :: Monoid m => Magma i t b m -> m # foldMap :: Monoid m => (a -> m) -> Magma i t b a -> m # foldMap' :: Monoid m => (a -> m) -> Magma i t b a -> m # foldr :: (a -> b0 -> b0) -> b0 -> Magma i t b a -> b0 # foldr' :: (a -> b0 -> b0) -> b0 -> Magma i t b a -> b0 # foldl :: (b0 -> a -> b0) -> b0 -> Magma i t b a -> b0 # foldl' :: (b0 -> a -> b0) -> b0 -> Magma i t b a -> b0 # foldr1 :: (a -> a -> a) -> Magma i t b a -> a # foldl1 :: (a -> a -> a) -> Magma i t b a -> a # toList :: Magma i t b a -> [a] # null :: Magma i t b a -> Bool # length :: Magma i t b a -> Int # elem :: Eq a => a -> Magma i t b a -> Bool # maximum :: Ord a => Magma i t b a -> a # minimum :: Ord a => Magma i t b a -> a # sum :: Num a => Magma i t b a -> a # product :: Num a => Magma i t b a -> a #
Traversable (Magma i t b) Source #
Instance details Defined in Control.Lens.Internal.Magma Methods traverse :: Applicative f => (a -> f b0) -> Magma i t b a -> f (Magma i t b b0) # sequenceA :: Applicative f => Magma i t b (f a) -> f (Magma i t b a) # mapM :: Monad m => (a -> m b0) -> Magma i t b a -> m (Magma i t b b0) # sequence :: Monad m => Magma i t b (m a) -> m (Magma i t b a) #
Functor (Magma i t b) Source #
Instance details Defined in Control.Lens.Internal.Magma Methods fmap :: (a -> b0) -> Magma i t b a -> Magma i t b b0 # (<$) :: a -> Magma i t b b0 -> Magma i t b a #
(Show i, Show a) => Show (Magma i t b a) Source #
Instance details Defined in Control.Lens.Internal.Magma Methods showsPrec :: Int -> Magma i t b a -> ShowS # show :: Magma i t b a -> String # showList :: [Magma i t b a] -> ShowS #

type IndexedGetter i s a = forall p f. (Indexable i p, Contravariant f, Functor f) => p a (f a) -> s -> f s Source #

Every IndexedGetter is a valid IndexedFold and can be used for Getting like a Getter.

type Getting r s a = (a -> Const r a) -> s -> Const r s Source #

When you see this in a type signature it indicates that you can pass the function a Lens, Getter, Traversal, Fold, Prism, Iso, or one of the indexed variants, and it will just "do the right thing".

Most Getter combinators are able to be used with both a Getter or a Fold in limited situations, to do so, they need to be monomorphic in what we are going to extract with Const. To be compatible with Lens, Traversal and Iso we also restricted choices of the irrelevant t and b parameters.

If a function accepts a Getting r s a, then when r is a Monoid, then you can pass a Fold (or Traversal), otherwise you can only pass this a Getter or Lens.

type IndexedGetting i m s a = Indexed i a (Const m a) -> s -> Const m s Source #

Used to consume an IndexedFold.

type Accessing p m s a = p a (Const m a) -> s -> Const m s Source #

This is a convenient alias used when consuming (indexed) getters and (indexed) folds in a highly general fashion.

class Conjoined p => Indexable i p where Source #

This class permits overloading of function application for things that also admit a notion of a key or index.

Methods

indexed :: p a b -> i -> a -> b Source #

Build a function from an indexed function.

Instances

Instances details

i ~ j => Indexable i (Indexed j) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods indexed :: Indexed j a b -> i -> a -> b Source #
Indexable i (->) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods indexed :: (a -> b) -> i -> a -> b Source #

class (Choice p, Corepresentable p, Comonad (Corep p), Traversable (Corep p), Strong p, Representable p, Monad (Rep p), MonadFix (Rep p), Distributive (Rep p), Costrong p, ArrowLoop p, ArrowApply p, ArrowChoice p, Closed p) => Conjoined p where Source #

This is a Profunctor that is both Corepresentable by f and Representable by g such that f is left adjoint to g. From this you can derive a lot of structure due to the preservation of limits and colimits.

Minimal complete definition

Nothing

Methods

distrib :: Functor f => p a b -> p (f a) (f b) Source #

Conjoined is strong enough to let us distribute every Conjoined Profunctor over every Haskell Functor. This is effectively a generalization of fmap.

conjoined :: (p ~ (->) => q (a -> b) r) -> q (p a b) r -> q (p a b) r Source #

This permits us to make a decision at an outermost point about whether or not we use an index.

Ideally any use of this function should be done in such a way so that you compute the same answer, but this cannot be enforced at the type level.

Instances

Instances details

Conjoined ReifiedGetter Source #
Instance details Defined in Control.Lens.Reified Methods distrib :: Functor f => ReifiedGetter a b -> ReifiedGetter (f a) (f b) Source # conjoined :: (ReifiedGetter ~ (->) => q (a -> b) r) -> q (ReifiedGetter a b) r -> q (ReifiedGetter a b) r Source #
Conjoined (Indexed i) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods distrib :: Functor f => Indexed i a b -> Indexed i (f a) (f b) Source # conjoined :: (Indexed i ~ (->) => q (a -> b) r) -> q (Indexed i a b) r -> q (Indexed i a b) r Source #
Conjoined (->) Source #
Instance details Defined in Control.Lens.Internal.Indexed Methods distrib :: Functor f => (a -> b) -> f a -> f b Source # conjoined :: ((->) ~ (->) => q (a -> b) r) -> q (a -> b) r -> q (a -> b) r Source #

newtype Bazaar p a b t Source #

This is used to characterize a Traversal.

a.k.a. indexed Cartesian store comonad, indexed Kleene store comonad, or an indexed FunList.

http://twanvl.nl/blog/haskell/non-regular1

A Bazaar is like a Traversal that has already been applied to some structure.

Where a Context a b t holds an a and a function from b to t, a Bazaar a b t holds N as and a function from N bs to t, (where N might be infinite).

Mnemonically, a Bazaar holds many stores and you can easily add more.

This is a final encoding of Bazaar.

Constructors

Bazaar
Fields runBazaar :: forall f. Applicative f => p a (f b) -> f t

Instances

Instances details

Profunctor p => Bizarre p (Bazaar p) Source #
Instance details Defined in Control.Lens.Internal.Bazaar Methods bazaar :: Applicative f => p a (f b) -> Bazaar p a b t -> f t Source #
Corepresentable p => Sellable p (Bazaar p) Source #
Instance details Defined in Control.Lens.Internal.Bazaar Methods sell :: p a (Bazaar p a b b) Source #
Conjoined p => IndexedComonad (Bazaar p) Source #
Instance details Defined in Control.Lens.Internal.Bazaar Methods iextract :: Bazaar p a a t -> t Source # iduplicate :: Bazaar p a c t -> Bazaar p a b (Bazaar p b c t) Source # iextend :: (Bazaar p b c t -> r) -> Bazaar p a c t -> Bazaar p a b r Source #
IndexedFunctor (Bazaar p) Source #
Instance details Defined in Control.Lens.Internal.Bazaar Methods ifmap :: (s -> t) -> Bazaar p a b s -> Bazaar p a b t Source #
Applicative (Bazaar p a b) Source #
Instance details Defined in Control.Lens.Internal.Bazaar Methods pure :: a0 -> Bazaar p a b a0 # (<>) :: Bazaar p a b (a0 -> b0) -> Bazaar p a b a0 -> Bazaar p a b b0 # liftA2 :: (a0 -> b0 -> c) -> Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b c # (>) :: Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b b0 # (<*) :: Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b a0 #
Functor (Bazaar p a b) Source #
Instance details Defined in Control.Lens.Internal.Bazaar Methods fmap :: (a0 -> b0) -> Bazaar p a b a0 -> Bazaar p a b b0 # (<$) :: a0 -> Bazaar p a b b0 -> Bazaar p a b a0 #
(a ~ b, Conjoined p) => Comonad (Bazaar p a b) Source #
Instance details Defined in Control.Lens.Internal.Bazaar Methods extract :: Bazaar p a b a0 -> a0 # duplicate :: Bazaar p a b a0 -> Bazaar p a b (Bazaar p a b a0) # extend :: (Bazaar p a b a0 -> b0) -> Bazaar p a b a0 -> Bazaar p a b b0 #
(a ~ b, Conjoined p) => ComonadApply (Bazaar p a b) Source #
Instance details Defined in Control.Lens.Internal.Bazaar Methods (<@>) :: Bazaar p a b (a0 -> b0) -> Bazaar p a b a0 -> Bazaar p a b b0 # (@>) :: Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b b0 # (<@) :: Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b a0 #
Apply (Bazaar p a b) Source #
Instance details Defined in Control.Lens.Internal.Bazaar Methods (<.>) :: Bazaar p a b (a0 -> b0) -> Bazaar p a b a0 -> Bazaar p a b b0 # (.>) :: Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b b0 # (<.) :: Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b a0 # liftF2 :: (a0 -> b0 -> c) -> Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b c #

data Context a b t Source #

The indexed store can be used to characterize a Lens and is used by cloneLens.

Context a b t is isomorphic to newtype Context a b t = Context { runContext :: forall f. Functor f => (a -> f b) -> f t }, and to exists s. (s, Lens s t a b).

A Context is like a Lens that has already been applied to a some structure.

Constructors

Context (b -> t) a

Instances

Instances details

IndexedComonad Context Source #
Instance details Defined in Control.Lens.Internal.Context Methods iextract :: Context a a t -> t Source # iduplicate :: Context a c t -> Context a b (Context b c t) Source # iextend :: (Context b c t -> r) -> Context a c t -> Context a b r Source #
IndexedComonadStore Context Source #
Instance details Defined in Control.Lens.Internal.Context Methods ipos :: Context a c t -> a Source # ipeek :: c -> Context a c t -> t Source # ipeeks :: (a -> c) -> Context a c t -> t Source # iseek :: b -> Context a c t -> Context b c t Source # iseeks :: (a -> b) -> Context a c t -> Context b c t Source # iexperiment :: Functor f => (b -> f c) -> Context b c t -> f t Source # context :: Context a b t -> Context a b t Source #
IndexedFunctor Context Source #
Instance details Defined in Control.Lens.Internal.Context Methods ifmap :: (s -> t) -> Context a b s -> Context a b t Source #
a ~ b => ComonadStore a (Context a b) Source #
Instance details Defined in Control.Lens.Internal.Context Methods pos :: Context a b a0 -> a # peek :: a -> Context a b a0 -> a0 # peeks :: (a -> a) -> Context a b a0 -> a0 # seek :: a -> Context a b a0 -> Context a b a0 # seeks :: (a -> a) -> Context a b a0 -> Context a b a0 # experiment :: Functor f => (a -> f a) -> Context a b a0 -> f a0 #
Functor (Context a b) Source #
Instance details Defined in Control.Lens.Internal.Context Methods fmap :: (a0 -> b0) -> Context a b a0 -> Context a b b0 # (<$) :: a0 -> Context a b b0 -> Context a b a0 #
a ~ b => Comonad (Context a b) Source #
Instance details Defined in Control.Lens.Internal.Context Methods extract :: Context a b a0 -> a0 # duplicate :: Context a b a0 -> Context a b (Context a b a0) # extend :: (Context a b a0 -> b0) -> Context a b a0 -> Context a b b0 #
Sellable (->) Context Source #
Instance details Defined in Control.Lens.Internal.Context Methods sell :: a -> Context a b b Source #

type Bazaar' p a = Bazaar p a a Source #

This alias is helpful when it comes to reducing repetition in type signatures.

type Bazaar' p a t = Bazaar p a a t

newtype Bazaar1 p a b t Source #

This is used to characterize a Traversal.

a.k.a. indexed Cartesian store comonad, indexed Kleene store comonad, or an indexed FunList.

http://twanvl.nl/blog/haskell/non-regular1

A Bazaar1 is like a Traversal that has already been applied to some structure.

Where a Context a b t holds an a and a function from b to t, a Bazaar1 a b t holds N as and a function from N bs to t, (where N might be infinite).

Mnemonically, a Bazaar1 holds many stores and you can easily add more.

This is a final encoding of Bazaar1.

Constructors

Bazaar1
Fields runBazaar1 :: forall f. Apply f => p a (f b) -> f t

Instances

Instances details

Profunctor p => Bizarre1 p (Bazaar1 p) Source #
Instance details Defined in Control.Lens.Internal.Bazaar Methods bazaar1 :: Apply f => p a (f b) -> Bazaar1 p a b t -> f t Source #
Corepresentable p => Sellable p (Bazaar1 p) Source #
Instance details Defined in Control.Lens.Internal.Bazaar Methods sell :: p a (Bazaar1 p a b b) Source #
Conjoined p => IndexedComonad (Bazaar1 p) Source #
Instance details Defined in Control.Lens.Internal.Bazaar Methods iextract :: Bazaar1 p a a t -> t Source # iduplicate :: Bazaar1 p a c t -> Bazaar1 p a b (Bazaar1 p b c t) Source # iextend :: (Bazaar1 p b c t -> r) -> Bazaar1 p a c t -> Bazaar1 p a b r Source #
IndexedFunctor (Bazaar1 p) Source #
Instance details Defined in Control.Lens.Internal.Bazaar Methods ifmap :: (s -> t) -> Bazaar1 p a b s -> Bazaar1 p a b t Source #
Functor (Bazaar1 p a b) Source #
Instance details Defined in Control.Lens.Internal.Bazaar Methods fmap :: (a0 -> b0) -> Bazaar1 p a b a0 -> Bazaar1 p a b b0 # (<$) :: a0 -> Bazaar1 p a b b0 -> Bazaar1 p a b a0 #
(a ~ b, Conjoined p) => Comonad (Bazaar1 p a b) Source #
Instance details Defined in Control.Lens.Internal.Bazaar Methods extract :: Bazaar1 p a b a0 -> a0 # duplicate :: Bazaar1 p a b a0 -> Bazaar1 p a b (Bazaar1 p a b a0) # extend :: (Bazaar1 p a b a0 -> b0) -> Bazaar1 p a b a0 -> Bazaar1 p a b b0 #
(a ~ b, Conjoined p) => ComonadApply (Bazaar1 p a b) Source #
Instance details Defined in Control.Lens.Internal.Bazaar Methods (<@>) :: Bazaar1 p a b (a0 -> b0) -> Bazaar1 p a b a0 -> Bazaar1 p a b b0 # (@>) :: Bazaar1 p a b a0 -> Bazaar1 p a b b0 -> Bazaar1 p a b b0 # (<@) :: Bazaar1 p a b a0 -> Bazaar1 p a b b0 -> Bazaar1 p a b a0 #
Apply (Bazaar1 p a b) Source #
Instance details Defined in Control.Lens.Internal.Bazaar Methods (<.>) :: Bazaar1 p a b (a0 -> b0) -> Bazaar1 p a b a0 -> Bazaar1 p a b b0 # (.>) :: Bazaar1 p a b a0 -> Bazaar1 p a b b0 -> Bazaar1 p a b b0 # (<.) :: Bazaar1 p a b a0 -> Bazaar1 p a b b0 -> Bazaar1 p a b a0 # liftF2 :: (a0 -> b0 -> c) -> Bazaar1 p a b a0 -> Bazaar1 p a b b0 -> Bazaar1 p a b c #

type Bazaar1' p a = Bazaar1 p a a Source #

This alias is helpful when it comes to reducing repetition in type signatures.

type Bazaar1' p a t = Bazaar1 p a a t

type Context' a = Context a a Source #

type Context' a s = Context a a s

data LensRules Source #

Rules to construct lenses for data fields.

type FieldNamer Source #

Arguments

= Name	Name of the data type that lenses are being generated for.
-> [Name]	Names of all fields (including the field being named) in the data type.
-> Name	Name of the field being named.
-> [DefName]	Name(s) of the lens functions. If empty, no lens is created for that field.

The rule to create function names of lenses for data fields.

Although it's sometimes useful, you won't need the first two arguments most of the time.

data DefName Source #

Name to give to generated field optics.

Constructors

TopName Name	Simple top-level definition name
MethodName Name Name	makeFields-style class name and method name

Instances

Instances details

Show DefName Source #
Instance details Defined in Control.Lens.Internal.FieldTH Methods showsPrec :: Int -> DefName -> ShowS # show :: DefName -> String # showList :: [DefName] -> ShowS #
Eq DefName Source #
Instance details Defined in Control.Lens.Internal.FieldTH Methods (==) :: DefName -> DefName -> Bool # (/=) :: DefName -> DefName -> Bool #
Ord DefName Source #
Instance details Defined in Control.Lens.Internal.FieldTH Methods compare :: DefName -> DefName -> Ordering # (<) :: DefName -> DefName -> Bool # (<=) :: DefName -> DefName -> Bool # (>) :: DefName -> DefName -> Bool # (>=) :: DefName -> DefName -> Bool # max :: DefName -> DefName -> DefName # min :: DefName -> DefName -> DefName #

type ClassyNamer Source #

Arguments

= Name	Name of the data type that lenses are being generated for.
-> Maybe (Name, Name)	Names of the class and the main method it generates, respectively.

The optional rule to create a class and method around a monomorphic data type. If this naming convention is provided, it generates a "classy" lens.

class Reversing t where Source #

This class provides a generalized notion of list reversal extended to other containers.

Methods

reversing :: t -> t Source #

Instances

Instances details

Reversing ByteString Source #
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: ByteString -> ByteString Source #
Reversing ByteString Source #
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: ByteString -> ByteString Source #
Reversing Text Source #
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: Text -> Text Source #
Reversing Text Source #
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: Text -> Text Source #
Reversing (NonEmpty a) Source #
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: NonEmpty a -> NonEmpty a Source #
Reversing (Seq a) Source #
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: Seq a -> Seq a Source #
Reversing (Deque a) Source #
Instance details Defined in Control.Lens.Internal.Deque Methods reversing :: Deque a -> Deque a Source #
Reversing (Vector a) Source #
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: Vector a -> Vector a Source #
Prim a => Reversing (Vector a) Source #
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: Vector a -> Vector a Source #
Storable a => Reversing (Vector a) Source #
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: Vector a -> Vector a Source #
Unbox a => Reversing (Vector a) Source #
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: Vector a -> Vector a Source #
Reversing [a] Source #
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: [a] -> [a] Source #

class (Profunctor p, Bifunctor p) => Reviewable p Source #

This class is provided mostly for backwards compatibility with lens 3.8, but it can also shorten type signatures.

Instances

Instances details

(Profunctor p, Bifunctor p) => Reviewable p Source #
Instance details Defined in Control.Lens.Internal.Review

class (Applicative f, Distributive f, Traversable f) => Settable f Source #

Anything Settable must be isomorphic to the Identity Functor.

Minimal complete definition

untainted

Instances

Instances details

Settable Identity Source #	So you can pass our `Setter` into combinators from other lens libraries.
Instance details Defined in Control.Lens.Internal.Setter Methods untainted :: Identity a -> a Source # untaintedDot :: Profunctor p => p a (Identity b) -> p a b Source # taintedDot :: Profunctor p => p a b -> p a (Identity b) Source #
Settable f => Settable (Backwards f) Source #	`backwards`
Instance details Defined in Control.Lens.Internal.Setter Methods untainted :: Backwards f a -> a Source # untaintedDot :: Profunctor p => p a (Backwards f b) -> p a b Source # taintedDot :: Profunctor p => p a b -> p a (Backwards f b) Source #
(Settable f, Settable g) => Settable (Compose f g) Source #
Instance details Defined in Control.Lens.Internal.Setter Methods untainted :: Compose f g a -> a Source # untaintedDot :: Profunctor p => p a (Compose f g b) -> p a b Source # taintedDot :: Profunctor p => p a b -> p a (Compose f g b) Source #

type Iso' s a = Iso s s a a Source #

type Iso' = Simple Iso

type AnIso s t a b = Exchange a b a (Identity b) -> Exchange a b s (Identity t) Source #

When you see this as an argument to a function, it expects an Iso.

type AnIso' s a = AnIso s s a a Source #

A Simple AnIso.

type Lens' s a = Lens s s a a Source #

type Lens' = Simple Lens

type IndexedLens i s t a b = forall f p. (Indexable i p, Functor f) => p a (f b) -> s -> f t Source #

Every IndexedLens is a valid Lens and a valid IndexedTraversal.

type IndexedLens' i s a = IndexedLens i s s a a Source #

type IndexedLens' i = Simple (IndexedLens i)

type ALens s t a b = LensLike (Pretext (->) a b) s t a b Source #

When you see this as an argument to a function, it expects a Lens.

This type can also be used when you need to store a Lens in a container, since it is rank-1. You can turn them back into a Lens with cloneLens, or use it directly with combinators like storing and (^#).

type ALens' s a = ALens s s a a Source #

type ALens' = Simple ALens

type AnIndexedLens i s t a b = Optical (Indexed i) (->) (Pretext (Indexed i) a b) s t a b Source #

When you see this as an argument to a function, it expects an IndexedLens

type AnIndexedLens' i s a = AnIndexedLens i s s a a Source #

type AnIndexedLens' = Simple (AnIndexedLens i)

class GPlated a g Source #

Minimal complete definition

gplate'

Instances

Instances details

GPlated a (U1 :: k -> Type) Source #
Instance details Defined in Control.Lens.Plated Methods gplate' :: forall (p :: k0). Traversal' (U1 p) a
GPlated a (V1 :: k -> Type) Source #
Instance details Defined in Control.Lens.Plated Methods gplate' :: forall (p :: k0). Traversal' (V1 p) a
GPlated a (URec b :: k -> Type) Source #
Instance details Defined in Control.Lens.Plated Methods gplate' :: forall (p :: k0). Traversal' (URec b p) a
(GPlated a f, GPlated a g) => GPlated a (f :*: g :: k -> Type) Source #
Instance details Defined in Control.Lens.Plated Methods gplate' :: forall (p :: k0). Traversal' ((f :*: g) p) a
(GPlated a f, GPlated a g) => GPlated a (f :+: g :: k -> Type) Source #
Instance details Defined in Control.Lens.Plated Methods gplate' :: forall (p :: k0). Traversal' ((f :+: g) p) a
GPlated a (K1 i a :: k -> Type) Source #
Instance details Defined in Control.Lens.Plated Methods gplate' :: forall (p :: k0). Traversal' (K1 i a p) a
GPlated a (K1 i b :: k -> Type) Source #
Instance details Defined in Control.Lens.Plated Methods gplate' :: forall (p :: k0). Traversal' (K1 i b p) a
GPlated a f => GPlated a (M1 i c f :: k -> Type) Source #
Instance details Defined in Control.Lens.Plated Methods gplate' :: forall (p :: k0). Traversal' (M1 i c f p) a

class GPlated1 f g Source #

Minimal complete definition

gplate1'

Instances

Instances details

GPlated1 (f :: Type -> Type) Par1 Source #	ignored
Instance details Defined in Control.Lens.Plated Methods gplate1' :: forall (a :: k). Traversal' (Par1 a) (f a)
GPlated1 (f :: k -> Type) (U1 :: k -> Type) Source #	ignored
Instance details Defined in Control.Lens.Plated Methods gplate1' :: forall (a :: k0). Traversal' (U1 a) (f a)
GPlated1 (f :: k -> Type) (V1 :: k -> Type) Source #	ignored
Instance details Defined in Control.Lens.Plated Methods gplate1' :: forall (a :: k0). Traversal' (V1 a) (f a)
GPlated1 (f :: k -> Type) (Rec1 f :: k -> Type) Source #	match
Instance details Defined in Control.Lens.Plated Methods gplate1' :: forall (a :: k0). Traversal' (Rec1 f a) (f a)
GPlated1 (f :: k -> Type) (Rec1 g :: k -> Type) Source #	ignored
Instance details Defined in Control.Lens.Plated Methods gplate1' :: forall (a :: k0). Traversal' (Rec1 g a) (f a)
GPlated1 (f :: k -> Type) (URec a :: k -> Type) Source #	ignored
Instance details Defined in Control.Lens.Plated Methods gplate1' :: forall (a0 :: k0). Traversal' (URec a a0) (f a0)
(GPlated1 f g, GPlated1 f h) => GPlated1 (f :: k -> Type) (g :*: h :: k -> Type) Source #	recursive match
Instance details Defined in Control.Lens.Plated Methods gplate1' :: forall (a :: k0). Traversal' ((g :*: h) a) (f a)
(GPlated1 f g, GPlated1 f h) => GPlated1 (f :: k -> Type) (g :+: h :: k -> Type) Source #	recursive match
Instance details Defined in Control.Lens.Plated Methods gplate1' :: forall (a :: k0). Traversal' ((g :+: h) a) (f a)
GPlated1 (f :: k -> Type) (K1 i a :: k -> Type) Source #	ignored
Instance details Defined in Control.Lens.Plated Methods gplate1' :: forall (a0 :: k0). Traversal' (K1 i a a0) (f a0)
GPlated1 f g => GPlated1 (f :: k -> Type) (M1 i c g :: k -> Type) Source #	recursive match
Instance details Defined in Control.Lens.Plated Methods gplate1' :: forall (a :: k0). Traversal' (M1 i c g a) (f a)
(Traversable t, GPlated1 f g) => GPlated1 (f :: k1 -> Type) (t :.: g :: k1 -> Type) Source #	recursive match under outer `Traversable` instance
Instance details Defined in Control.Lens.Plated Methods gplate1' :: forall (a :: k). Traversal' ((t :.: g) a) (f a)

type Prism' s a = Prism s s a a Source #

A Simple Prism.

type APrism s t a b = Market a b a (Identity b) -> Market a b s (Identity t) Source #

If you see this in a signature for a function, the function is expecting a Prism.

type APrism' s a = APrism s s a a Source #

type APrism' = Simple APrism

class Prefixed t where Source #

Methods

prefixed :: t -> Prism' t t Source #

A Prism stripping a prefix from a sequence when used as a Traversal, or prepending that prefix when run backwards:

>>> "preview" ^? prefixed "pre"
Just "view"

>>> "review" ^? prefixed "pre"
Nothing

>>> prefixed "pre" # "amble"
"preamble"

Instances

Instances details

Prefixed ByteString Source #
Instance details Defined in Control.Lens.Prism Methods prefixed :: ByteString -> Prism' ByteString ByteString Source #
Prefixed ByteString Source #
Instance details Defined in Control.Lens.Prism Methods prefixed :: ByteString -> Prism' ByteString ByteString Source #
Prefixed Text Source #
Instance details Defined in Control.Lens.Prism Methods prefixed :: Text -> Prism' Text Text Source #
Prefixed Text Source #
Instance details Defined in Control.Lens.Prism Methods prefixed :: Text -> Prism' Text Text Source #
Eq a => Prefixed [a] Source #
Instance details Defined in Control.Lens.Prism Methods prefixed :: [a] -> Prism' [a] [a] Source #

class Suffixed t where Source #

Methods

suffixed :: t -> Prism' t t Source #

A Prism stripping a suffix from a sequence when used as a Traversal, or appending that suffix when run backwards:

>>> "review" ^? suffixed "view"
Just "re"

>>> "review" ^? suffixed "tire"
Nothing

>>> suffixed ".o" # "hello"
"hello.o"

Instances

Instances details

Suffixed ByteString Source #
Instance details Defined in Control.Lens.Prism Methods suffixed :: ByteString -> Prism' ByteString ByteString Source #
Suffixed ByteString Source #
Instance details Defined in Control.Lens.Prism Methods suffixed :: ByteString -> Prism' ByteString ByteString Source #
Suffixed Text Source #
Instance details Defined in Control.Lens.Prism Methods suffixed :: Text -> Prism' Text Text Source #
Suffixed Text Source #
Instance details Defined in Control.Lens.Prism Methods suffixed :: Text -> Prism' Text Text Source #
Eq a => Suffixed [a] Source #
Instance details Defined in Control.Lens.Prism Methods suffixed :: [a] -> Prism' [a] [a] Source #

type Optic p f s t a b = p a (f b) -> p s (f t) Source #

A valid Optic l should satisfy the laws:

l pure ≡ pure
l (Procompose f g) = Procompose (l f) (l g)

This gives rise to the laws for Equality, Iso, Prism, Lens, Traversal, Traversal1, Setter, Fold, Fold1, and Getter as well along with their index-preserving variants.

type LensLike f s t a b = Optic (->) f s t a b

type LensLike f s t a b = (a -> f b) -> s -> f t Source #

Many combinators that accept a Lens can also accept a Traversal in limited situations.

They do so by specializing the type of Functor that they require of the caller.

If a function accepts a LensLike f s t a b for some Functor f, then they may be passed a Lens.

Further, if f is an Applicative, they may also be passed a Traversal.

type ASetter s t a b = (a -> Identity b) -> s -> Identity t Source #

Running a Setter instantiates it to a concrete type.

When consuming a setter directly to perform a mapping, you can use this type, but most user code will not need to use this type.

type ATraversal s t a b = LensLike (Bazaar (->) a b) s t a b Source #

When you see this as an argument to a function, it expects a Traversal.

newtype ReifiedLens s t a b Source #

Reify a Lens so it can be stored safely in a container.

Constructors

Lens
Fields runLens :: Lens s t a b

type AReview t b = Optic' Tagged Identity t b Source #

If you see this in a signature for a function, the function is expecting a Review (in practice, this usually means a Prism).

type Setter' s a = Setter s s a a Source #

A Setter' is just a Setter that doesn't change the types.

These are particularly common when talking about monomorphic containers. e.g.

sets Data.Text.map :: Setter' Text Char

type Setter' = Simple Setter

type IndexedSetter i s t a b = forall f p. (Indexable i p, Settable f) => p a (f b) -> s -> f t Source #

Every IndexedSetter is a valid Setter.

The Setter laws are still required to hold.

type IndexedSetter' i s a = IndexedSetter i s s a a Source #

type IndexedSetter' i = Simple (IndexedSetter i)

type ASetter' s a = ASetter s s a a Source #

This is a useful alias for use when consuming a Setter'.

Most user code will never have to use this type.

type ASetter' = Simple ASetter

type AnIndexedSetter i s t a b = Indexed i a (Identity b) -> s -> Identity t Source #

Running an IndexedSetter instantiates it to a concrete type.

When consuming a setter directly to perform a mapping, you can use this type, but most user code will not need to use this type.

type AnIndexedSetter' i s a = AnIndexedSetter i s s a a Source #

type AnIndexedSetter' i = Simple (AnIndexedSetter i)

type Setting p s t a b = p a (Identity b) -> s -> Identity t Source #

This is a convenient alias when defining highly polymorphic code that takes both ASetter and AnIndexedSetter as appropriate. If a function takes this it is expecting one of those two things based on context.

type Setting' p s a = Setting p s s a a Source #

This is a convenient alias when defining highly polymorphic code that takes both ASetter' and AnIndexedSetter' as appropriate. If a function takes this it is expecting one of those two things based on context.

type Traversal' s a = Traversal s s a a Source #

type Traversal' = Simple Traversal

type Traversal1 s t a b = forall f. Apply f => (a -> f b) -> s -> f t Source #

A Traversal which targets at least one element.

Note that since Apply is not a superclass of Applicative, a Traversal1 cannot always be used in place of a Traversal. In such circumstances cloneTraversal will convert a Traversal1 into a Traversal.

type Traversal1' s a = Traversal1 s s a a Source #

type IndexedTraversal' i s a = IndexedTraversal i s s a a Source #

type IndexedTraversal' i = Simple (IndexedTraversal i)

type IndexedTraversal1 i s t a b = forall p f. (Indexable i p, Apply f) => p a (f b) -> s -> f t Source #

type IndexedTraversal1' i s a = IndexedTraversal1 i s s a a Source #

type ATraversal' s a = ATraversal s s a a Source #

type ATraversal' = Simple ATraversal

type ATraversal1 s t a b = LensLike (Bazaar1 (->) a b) s t a b Source #

When you see this as an argument to a function, it expects a Traversal1.

type ATraversal1' s a = ATraversal1 s s a a Source #

type ATraversal1' = Simple ATraversal1

type AnIndexedTraversal i s t a b = Over (Indexed i) (Bazaar (Indexed i) a b) s t a b Source #

When you see this as an argument to a function, it expects an IndexedTraversal.

type AnIndexedTraversal' i s a = AnIndexedTraversal i s s a a Source #

type AnIndexedTraversal' = Simple (AnIndexedTraversal i)

type AnIndexedTraversal1 i s t a b = Over (Indexed i) (Bazaar1 (Indexed i) a b) s t a b Source #

When you see this as an argument to a function, it expects an IndexedTraversal1.

type AnIndexedTraversal1' i s a = AnIndexedTraversal1 i s s a a Source #

type AnIndexedTraversal1' = Simple (AnIndexedTraversal1 i)

type Traversing' p f s a = Traversing p f s s a a Source #

type Traversing' f = Simple (Traversing f)

type Traversing1 p f s t a b = Over p (BazaarT1 p f a b) s t a b Source #

type Traversing1' p f s a = Traversing1 p f s s a a Source #

class Ord k => TraverseMin k m | m -> k where Source #

Allows IndexedTraversal the value at the smallest index.

Methods

traverseMin :: IndexedTraversal' k (m v) v Source #

IndexedTraversal of the element with the smallest index.

Instances

Instances details

TraverseMin Int IntMap Source #
Instance details Defined in Control.Lens.Traversal Methods traverseMin :: IndexedTraversal' Int (IntMap v) v Source #
Ord k => TraverseMin k (Map k) Source #
Instance details Defined in Control.Lens.Traversal Methods traverseMin :: IndexedTraversal' k (Map k v) v Source #

class Ord k => TraverseMax k m | m -> k where Source #

Allows IndexedTraversal of the value at the largest index.

Methods

traverseMax :: IndexedTraversal' k (m v) v Source #

IndexedTraversal of the element at the largest index.

Instances

Instances details

TraverseMax Int IntMap Source #
Instance details Defined in Control.Lens.Traversal Methods traverseMax :: IndexedTraversal' Int (IntMap v) v Source #
Ord k => TraverseMax k (Map k) Source #
Instance details Defined in Control.Lens.Traversal Methods traverseMax :: IndexedTraversal' k (Map k v) v Source #

class Field1 s t a b | s -> a, t -> b, s b -> t, t a -> s where Source #

Provides access to 1st field of a tuple.

Minimal complete definition

Nothing

Methods

_1 :: Lens s t a b Source #

Access the 1st field of a tuple (and possibly change its type).

>>> (1,2)^._1
1

>>> _1 .~ "hello" $ (1,2)
("hello",2)

>>> (1,2) & _1 .~ "hello"
("hello",2)

>>> _1 putStrLn ("hello","world")
hello
((),"world")

This can also be used on larger tuples as well:

>>> (1,2,3,4,5) & _1 +~ 41
(42,2,3,4,5)

_1 :: Lens (a,b) (a',b) a a'
_1 :: Lens (a,b,c) (a',b,c) a a'
_1 :: Lens (a,b,c,d) (a',b,c,d) a a'
...
_1 :: Lens (a,b,c,d,e,f,g,h,i) (a',b,c,d,e,f,g,h,i) a a'

default _1 :: (Generic s, Generic t, GIxed N0 (Rep s) (Rep t) a b) => Lens s t a b Source #

Instances

Instances details

Field1 (Identity a) (Identity b) a b Source #
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (Identity a) (Identity b) a b Source #
Field1 (Pair a b) (Pair a' b) a a' Source #	Since: 4.20
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (Pair a b) (Pair a' b) a a' Source #
Field1 (a, b) (a', b) a a' Source #	`_1` k ~(a,b) = (\a' -> (a',b)) `<$>` k a
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b) (a', b) a a' Source #
Field1 (a, b, c) (a', b, c) a a' Source #
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c) (a', b, c) a a' Source #
Field1 (a, b, c, d) (a', b, c, d) a a' Source #
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d) (a', b, c, d) a a' Source #
Field1 (Product f g a) (Product f' g a) (f a) (f' a) Source #
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (Product f g a) (Product f' g a) (f a) (f' a) Source #
Field1 ((f :: g) p) ((f' :: g) p) (f p) (f' p) Source #
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens ((f :: g) p) ((f' :: g) p) (f p) (f' p) Source #
Field1 (a, b, c, d, e) (a', b, c, d, e) a a' Source #
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e) (a', b, c, d, e) a a' Source #
Field1 (a, b, c, d, e, f) (a', b, c, d, e, f) a a' Source #
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f) (a', b, c, d, e, f) a a' Source #
Field1 (a, b, c, d, e, f, g) (a', b, c, d, e, f, g) a a' Source #
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g) (a', b, c, d, e, f, g) a a' Source #
Field1 (a, b, c, d, e, f, g, h) (a', b, c, d, e, f, g, h) a a' Source #
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h) (a', b, c, d, e, f, g, h) a a' Source #
Field1 (a, b, c, d, e, f, g, h, i) (a', b, c, d, e, f, g, h, i) a a' Source #
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i) (a', b, c, d, e, f, g, h, i) a a' Source #
Field1 (a, b, c, d, e, f, g, h, i, j) (a', b, c, d, e, f, g, h, i, j) a a' Source #
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j) (a', b, c, d, e, f, g, h, i, j) a a' Source #
Field1 (a, b, c, d, e, f, g, h, i, j, kk) (a', b, c, d, e, f, g, h, i, j, kk) a a' Source #
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a', b, c, d, e, f, g, h, i, j, kk) a a' Source #
Field1 (a, b, c, d, e, f, g, h, i, j, kk, l) (a', b, c, d, e, f, g, h, i, j, kk, l) a a' Source #
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a', b, c, d, e, f, g, h, i, j, kk, l) a a' Source #
Field1 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a', b, c, d, e, f, g, h, i, j, kk, l, m) a a' Source #
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a', b, c, d, e, f, g, h, i, j, kk, l, m) a a' Source #
Field1 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n) a a' Source #
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n) a a' Source #
Field1 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o) a a' Source #
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o) a a' Source #
Field1 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) a a' Source #
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) a a' Source #
Field1 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) a a' Source #
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) a a' Source #
Field1 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) a a' Source #
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) a a' Source #
Field1 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) a a' Source #
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) a a' Source #

class Field2 s t a b | s -> a, t -> b, s b -> t, t a -> s where Source #

Provides access to the 2nd field of a tuple.

Minimal complete definition

Nothing

Methods

_2 :: Lens s t a b Source #

Access the 2nd field of a tuple.

>>> _2 .~ "hello" $ (1,(),3,4)
(1,"hello",3,4)

>>> (1,2,3,4) & _2 *~ 3
(1,6,3,4)

>>> _2 print (1,2)
2
(1,())

anyOf _2 :: (s -> Bool) -> (a, s) -> Bool
traverse . _2 :: (Applicative f, Traversable t) => (a -> f b) -> t (s, a) -> f (t (s, b))
foldMapOf (traverse . _2) :: (Traversable t, Monoid m) => (s -> m) -> t (b, s) -> m

default _2 :: (Generic s, Generic t, GIxed N1 (Rep s) (Rep t) a b) => Lens s t a b Source #

Instances

Instances details

Field2 (Pair a b) (Pair a b') b b' Source #	Since: 4.20
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (Pair a b) (Pair a b') b b' Source #
Field2 (a, b) (a, b') b b' Source #	`_2` k ~(a,b) = (\b' -> (a,b')) `<$>` k b
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b) (a, b') b b' Source #
Field2 (a, b, c) (a, b', c) b b' Source #
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c) (a, b', c) b b' Source #
Field2 (a, b, c, d) (a, b', c, d) b b' Source #
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d) (a, b', c, d) b b' Source #
Field2 (Product f g a) (Product f g' a) (g a) (g' a) Source #
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (Product f g a) (Product f g' a) (g a) (g' a) Source #
Field2 ((f :: g) p) ((f :: g') p) (g p) (g' p) Source #
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens ((f :: g) p) ((f :: g') p) (g p) (g' p) Source #
Field2 (a, b, c, d, e) (a, b', c, d, e) b b' Source #
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e) (a, b', c, d, e) b b' Source #
Field2 (a, b, c, d, e, f) (a, b', c, d, e, f) b b' Source #
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f) (a, b', c, d, e, f) b b' Source #
Field2 (a, b, c, d, e, f, g) (a, b', c, d, e, f, g) b b' Source #
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g) (a, b', c, d, e, f, g) b b' Source #
Field2 (a, b, c, d, e, f, g, h) (a, b', c, d, e, f, g, h) b b' Source #
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h) (a, b', c, d, e, f, g, h) b b' Source #
Field2 (a, b, c, d, e, f, g, h, i) (a, b', c, d, e, f, g, h, i) b b' Source #
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i) (a, b', c, d, e, f, g, h, i) b b' Source #
Field2 (a, b, c, d, e, f, g, h, i, j) (a, b', c, d, e, f, g, h, i, j) b b' Source #
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b', c, d, e, f, g, h, i, j) b b' Source #
Field2 (a, b, c, d, e, f, g, h, i, j, kk) (a, b', c, d, e, f, g, h, i, j, kk) b b' Source #
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b', c, d, e, f, g, h, i, j, kk) b b' Source #
Field2 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b', c, d, e, f, g, h, i, j, kk, l) b b' Source #
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b', c, d, e, f, g, h, i, j, kk, l) b b' Source #
Field2 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b', c, d, e, f, g, h, i, j, kk, l, m) b b' Source #
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b', c, d, e, f, g, h, i, j, kk, l, m) b b' Source #
Field2 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n) b b' Source #
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n) b b' Source #
Field2 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o) b b' Source #
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o) b b' Source #
Field2 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o, p) b b' Source #
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o, p) b b' Source #
Field2 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) b b' Source #
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) b b' Source #
Field2 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) b b' Source #
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) b b' Source #
Field2 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) b b' Source #
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) b b' Source #

class Field3 s t a b | s -> a, t -> b, s b -> t, t a -> s where Source #

Provides access to the 3rd field of a tuple.

Minimal complete definition

Nothing

Methods

_3 :: Lens s t a b Source #

Access the 3rd field of a tuple.

default _3 :: (Generic s, Generic t, GIxed N2 (Rep s) (Rep t) a b) => Lens s t a b Source #

Instances

Instances details

Field3 (a, b, c) (a, b, c') c c' Source #
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c) (a, b, c') c c' Source #
Field3 (a, b, c, d) (a, b, c', d) c c' Source #
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d) (a, b, c', d) c c' Source #
Field3 (a, b, c, d, e) (a, b, c', d, e) c c' Source #
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e) (a, b, c', d, e) c c' Source #
Field3 (a, b, c, d, e, f) (a, b, c', d, e, f) c c' Source #
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f) (a, b, c', d, e, f) c c' Source #
Field3 (a, b, c, d, e, f, g) (a, b, c', d, e, f, g) c c' Source #
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g) (a, b, c', d, e, f, g) c c' Source #
Field3 (a, b, c, d, e, f, g, h) (a, b, c', d, e, f, g, h) c c' Source #
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h) (a, b, c', d, e, f, g, h) c c' Source #
Field3 (a, b, c, d, e, f, g, h, i) (a, b, c', d, e, f, g, h, i) c c' Source #
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i) (a, b, c', d, e, f, g, h, i) c c' Source #
Field3 (a, b, c, d, e, f, g, h, i, j) (a, b, c', d, e, f, g, h, i, j) c c' Source #
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b, c', d, e, f, g, h, i, j) c c' Source #
Field3 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c', d, e, f, g, h, i, j, kk) c c' Source #
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c', d, e, f, g, h, i, j, kk) c c' Source #
Field3 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c', d, e, f, g, h, i, j, kk, l) c c' Source #
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c', d, e, f, g, h, i, j, kk, l) c c' Source #
Field3 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c', d, e, f, g, h, i, j, kk, l, m) c c' Source #
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c', d, e, f, g, h, i, j, kk, l, m) c c' Source #
Field3 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n) c c' Source #
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n) c c' Source #
Field3 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o) c c' Source #
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o) c c' Source #
Field3 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o, p) c c' Source #
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o, p) c c' Source #
Field3 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o, p, q) c c' Source #
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o, p, q) c c' Source #
Field3 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) c c' Source #
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) c c' Source #
Field3 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) c c' Source #
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) c c' Source #

class Field4 s t a b | s -> a, t -> b, s b -> t, t a -> s where Source #

Provide access to the 4th field of a tuple.

Minimal complete definition

Nothing

Methods

_4 :: Lens s t a b Source #

Access the 4th field of a tuple.

default _4 :: (Generic s, Generic t, GIxed N3 (Rep s) (Rep t) a b) => Lens s t a b Source #

Instances

Instances details

Field4 (a, b, c, d) (a, b, c, d') d d' Source #
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d) (a, b, c, d') d d' Source #
Field4 (a, b, c, d, e) (a, b, c, d', e) d d' Source #
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e) (a, b, c, d', e) d d' Source #
Field4 (a, b, c, d, e, f) (a, b, c, d', e, f) d d' Source #
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f) (a, b, c, d', e, f) d d' Source #
Field4 (a, b, c, d, e, f, g) (a, b, c, d', e, f, g) d d' Source #
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g) (a, b, c, d', e, f, g) d d' Source #
Field4 (a, b, c, d, e, f, g, h) (a, b, c, d', e, f, g, h) d d' Source #
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h) (a, b, c, d', e, f, g, h) d d' Source #
Field4 (a, b, c, d, e, f, g, h, i) (a, b, c, d', e, f, g, h, i) d d' Source #
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i) (a, b, c, d', e, f, g, h, i) d d' Source #
Field4 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d', e, f, g, h, i, j) d d' Source #
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b, c, d', e, f, g, h, i, j) d d' Source #
Field4 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d', e, f, g, h, i, j, kk) d d' Source #
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d', e, f, g, h, i, j, kk) d d' Source #
Field4 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d', e, f, g, h, i, j, kk, l) d d' Source #
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d', e, f, g, h, i, j, kk, l) d d' Source #
Field4 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d', e, f, g, h, i, j, kk, l, m) d d' Source #
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d', e, f, g, h, i, j, kk, l, m) d d' Source #
Field4 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n) d d' Source #
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n) d d' Source #
Field4 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o) d d' Source #
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o) d d' Source #
Field4 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o, p) d d' Source #
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o, p) d d' Source #
Field4 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o, p, q) d d' Source #
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o, p, q) d d' Source #
Field4 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o, p, q, r) d d' Source #
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o, p, q, r) d d' Source #
Field4 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) d d' Source #
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) d d' Source #

class Field5 s t a b | s -> a, t -> b, s b -> t, t a -> s where Source #

Provides access to the 5th field of a tuple.

Minimal complete definition

Nothing

Methods

_5 :: Lens s t a b Source #

Access the 5th field of a tuple.

default _5 :: (Generic s, Generic t, GIxed N4 (Rep s) (Rep t) a b) => Lens s t a b Source #

Instances

Instances details

Field5 (a, b, c, d, e) (a, b, c, d, e') e e' Source #
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e) (a, b, c, d, e') e e' Source #
Field5 (a, b, c, d, e, f) (a, b, c, d, e', f) e e' Source #
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f) (a, b, c, d, e', f) e e' Source #
Field5 (a, b, c, d, e, f, g) (a, b, c, d, e', f, g) e e' Source #
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g) (a, b, c, d, e', f, g) e e' Source #
Field5 (a, b, c, d, e, f, g, h) (a, b, c, d, e', f, g, h) e e' Source #
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h) (a, b, c, d, e', f, g, h) e e' Source #
Field5 (a, b, c, d, e, f, g, h, i) (a, b, c, d, e', f, g, h, i) e e' Source #
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i) (a, b, c, d, e', f, g, h, i) e e' Source #
Field5 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e', f, g, h, i, j) e e' Source #
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e', f, g, h, i, j) e e' Source #
Field5 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e', f, g, h, i, j, kk) e e' Source #
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e', f, g, h, i, j, kk) e e' Source #
Field5 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e', f, g, h, i, j, kk, l) e e' Source #
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e', f, g, h, i, j, kk, l) e e' Source #
Field5 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e', f, g, h, i, j, kk, l, m) e e' Source #
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e', f, g, h, i, j, kk, l, m) e e' Source #
Field5 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n) e e' Source #
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n) e e' Source #
Field5 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o) e e' Source #
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o) e e' Source #
Field5 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o, p) e e' Source #
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o, p) e e' Source #
Field5 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o, p, q) e e' Source #
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o, p, q) e e' Source #
Field5 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o, p, q, r) e e' Source #
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o, p, q, r) e e' Source #
Field5 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o, p, q, r, s) e e' Source #
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o, p, q, r, s) e e' Source #

class Field6 s t a b | s -> a, t -> b, s b -> t, t a -> s where Source #

Provides access to the 6th element of a tuple.

Minimal complete definition

Nothing

Methods

_6 :: Lens s t a b Source #

Access the 6th field of a tuple.

default _6 :: (Generic s, Generic t, GIxed N5 (Rep s) (Rep t) a b) => Lens s t a b Source #

Instances

Instances details

Field6 (a, b, c, d, e, f) (a, b, c, d, e, f') f f' Source #
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f) (a, b, c, d, e, f') f f' Source #
Field6 (a, b, c, d, e, f, g) (a, b, c, d, e, f', g) f f' Source #
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g) (a, b, c, d, e, f', g) f f' Source #
Field6 (a, b, c, d, e, f, g, h) (a, b, c, d, e, f', g, h) f f' Source #
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h) (a, b, c, d, e, f', g, h) f f' Source #
Field6 (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f', g, h, i) f f' Source #
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f', g, h, i) f f' Source #
Field6 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f', g, h, i, j) f f' Source #
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f', g, h, i, j) f f' Source #
Field6 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f', g, h, i, j, kk) f f' Source #
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f', g, h, i, j, kk) f f' Source #
Field6 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f', g, h, i, j, kk, l) f f' Source #
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f', g, h, i, j, kk, l) f f' Source #
Field6 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f', g, h, i, j, kk, l, m) f f' Source #
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f', g, h, i, j, kk, l, m) f f' Source #
Field6 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n) f f' Source #
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n) f f' Source #
Field6 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o) f f' Source #
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o) f f' Source #
Field6 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o, p) f f' Source #
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o, p) f f' Source #
Field6 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o, p, q) f f' Source #
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o, p, q) f f' Source #
Field6 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o, p, q, r) f f' Source #
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o, p, q, r) f f' Source #
Field6 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o, p, q, r, s) f f' Source #
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o, p, q, r, s) f f' Source #

class Field7 s t a b | s -> a, t -> b, s b -> t, t a -> s where Source #

Provide access to the 7th field of a tuple.

Minimal complete definition

Nothing

Methods

_7 :: Lens s t a b Source #

Access the 7th field of a tuple.

default _7 :: (Generic s, Generic t, GIxed N6 (Rep s) (Rep t) a b) => Lens s t a b Source #

Instances

Instances details

Field7 (a, b, c, d, e, f, g) (a, b, c, d, e, f, g') g g' Source #
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g) (a, b, c, d, e, f, g') g g' Source #
Field7 (a, b, c, d, e, f, g, h) (a, b, c, d, e, f, g', h) g g' Source #
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h) (a, b, c, d, e, f, g', h) g g' Source #
Field7 (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f, g', h, i) g g' Source #
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f, g', h, i) g g' Source #
Field7 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g', h, i, j) g g' Source #
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g', h, i, j) g g' Source #
Field7 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g', h, i, j, kk) g g' Source #
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g', h, i, j, kk) g g' Source #
Field7 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g', h, i, j, kk, l) g g' Source #
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g', h, i, j, kk, l) g g' Source #
Field7 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g', h, i, j, kk, l, m) g g' Source #
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g', h, i, j, kk, l, m) g g' Source #
Field7 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n) g g' Source #
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n) g g' Source #
Field7 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o) g g' Source #
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o) g g' Source #
Field7 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o, p) g g' Source #
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o, p) g g' Source #
Field7 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o, p, q) g g' Source #
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o, p, q) g g' Source #
Field7 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o, p, q, r) g g' Source #
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o, p, q, r) g g' Source #
Field7 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o, p, q, r, s) g g' Source #
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o, p, q, r, s) g g' Source #

class Field8 s t a b | s -> a, t -> b, s b -> t, t a -> s where Source #

Provide access to the 8th field of a tuple.

Minimal complete definition

Nothing

Methods

_8 :: Lens s t a b Source #

Access the 8th field of a tuple.

default _8 :: (Generic s, Generic t, GIxed N7 (Rep s) (Rep t) a b) => Lens s t a b Source #

Instances

Instances details

Field8 (a, b, c, d, e, f, g, h) (a, b, c, d, e, f, g, h') h h' Source #
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h) (a, b, c, d, e, f, g, h') h h' Source #
Field8 (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f, g, h', i) h h' Source #
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f, g, h', i) h h' Source #
Field8 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g, h', i, j) h h' Source #
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g, h', i, j) h h' Source #
Field8 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g, h', i, j, kk) h h' Source #
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g, h', i, j, kk) h h' Source #
Field8 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h', i, j, kk, l) h h' Source #
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h', i, j, kk, l) h h' Source #
Field8 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h', i, j, kk, l, m) h h' Source #
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h', i, j, kk, l, m) h h' Source #
Field8 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n) h h' Source #
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n) h h' Source #
Field8 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o) h h' Source #
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o) h h' Source #
Field8 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o, p) h h' Source #
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o, p) h h' Source #
Field8 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o, p, q) h h' Source #
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o, p, q) h h' Source #
Field8 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o, p, q, r) h h' Source #
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o, p, q, r) h h' Source #
Field8 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o, p, q, r, s) h h' Source #
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o, p, q, r, s) h h' Source #

class Field9 s t a b | s -> a, t -> b, s b -> t, t a -> s where Source #

Provides access to the 9th field of a tuple.

Minimal complete definition

Nothing

Methods

_9 :: Lens s t a b Source #

Access the 9th field of a tuple.

default _9 :: (Generic s, Generic t, GIxed N8 (Rep s) (Rep t) a b) => Lens s t a b Source #

Instances

Instances details

Field9 (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f, g, h, i') i i' Source #
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f, g, h, i') i i' Source #
Field9 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g, h, i', j) i i' Source #
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g, h, i', j) i i' Source #
Field9 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g, h, i', j, kk) i i' Source #
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g, h, i', j, kk) i i' Source #
Field9 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h, i', j, kk, l) i i' Source #
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h, i', j, kk, l) i i' Source #
Field9 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i', j, kk, l, m) i i' Source #
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i', j, kk, l, m) i i' Source #
Field9 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n) i i' Source #
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n) i i' Source #
Field9 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o) i i' Source #
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o) i i' Source #
Field9 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o, p) i i' Source #
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o, p) i i' Source #
Field9 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o, p, q) i i' Source #
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o, p, q) i i' Source #
Field9 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o, p, q, r) i i' Source #
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o, p, q, r) i i' Source #
Field9 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o, p, q, r, s) i i' Source #
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o, p, q, r, s) i i' Source #

class Field10 s t a b | s -> a, t -> b, s b -> t, t a -> s where Source #

Provides access to the 10th field of a tuple.

Minimal complete definition

Nothing

Methods

_10 :: Lens s t a b Source #

Access the 10th field of a tuple.

default _10 :: (Generic s, Generic t, GIxed N9 (Rep s) (Rep t) a b) => Lens s t a b Source #

Instances

Instances details

Field10 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g, h, i, j') j j' Source #
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g, h, i, j') j j' Source #
Field10 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g, h, i, j', kk) j j' Source #
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g, h, i, j', kk) j j' Source #
Field10 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h, i, j', kk, l) j j' Source #
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h, i, j', kk, l) j j' Source #
Field10 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i, j', kk, l, m) j j' Source #
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i, j', kk, l, m) j j' Source #
Field10 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n) j j' Source #
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n) j j' Source #
Field10 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o) j j' Source #
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o) j j' Source #
Field10 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o, p) j j' Source #
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o, p) j j' Source #
Field10 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o, p, q) j j' Source #
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o, p, q) j j' Source #
Field10 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o, p, q, r) j j' Source #
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o, p, q, r) j j' Source #
Field10 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o, p, q, r, s) j j' Source #
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o, p, q, r, s) j j' Source #

class Field11 s t a b | s -> a, t -> b, s b -> t, t a -> s where Source #

Provides access to the 11th field of a tuple.

Minimal complete definition

Nothing

Methods

_11 :: Lens s t a b Source #

Access the 11th field of a tuple.

default _11 :: (Generic s, Generic t, GIxed N10 (Rep s) (Rep t) a b) => Lens s t a b Source #

Instances

Instances details

Field11 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g, h, i, j, kk') kk kk' Source #
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g, h, i, j, kk') kk kk' Source #
Field11 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h, i, j, kk', l) kk kk' Source #
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h, i, j, kk', l) kk kk' Source #
Field11 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i, j, kk', l, m) kk kk' Source #
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i, j, kk', l, m) kk kk' Source #
Field11 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n) kk kk' Source #
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n) kk kk' Source #
Field11 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o) kk kk' Source #
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o) kk kk' Source #
Field11 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o, p) kk kk' Source #
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o, p) kk kk' Source #
Field11 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o, p, q) kk kk' Source #
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o, p, q) kk kk' Source #
Field11 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o, p, q, r) kk kk' Source #
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o, p, q, r) kk kk' Source #
Field11 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o, p, q, r, s) kk kk' Source #
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o, p, q, r, s) kk kk' Source #

class Field12 s t a b | s -> a, t -> b, s b -> t, t a -> s where Source #

Provides access to the 12th field of a tuple.

Minimal complete definition

Nothing

Methods

_12 :: Lens s t a b Source #

Access the 12th field of a tuple.

default _12 :: (Generic s, Generic t, GIxed N11 (Rep s) (Rep t) a b) => Lens s t a b Source #

Instances

Instances details

Field12 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h, i, j, kk, l') l l' Source #
Instance details Defined in Control.Lens.Tuple Methods _12 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h, i, j, kk, l') l l' Source #
Field12 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i, j, kk, l', m) l l' Source #
Instance details Defined in Control.Lens.Tuple Methods _12 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i, j, kk, l', m) l l' Source #
Field12 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n) l l' Source #
Instance details Defined in Control.Lens.Tuple Methods _12 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n) l l' Source #
Field12 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o) l l' Source #
Instance details Defined in Control.Lens.Tuple Methods _12 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o) l l' Source #
Field12 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o, p) l l' Source #
Instance details Defined in Control.Lens.Tuple Methods _12 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o, p) l l' Source #
Field12 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o, p, q) l l' Source #
Instance details Defined in Control.Lens.Tuple Methods _12 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o, p, q) l l' Source #
Field12 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o, p, q, r) l l' Source #
Instance details Defined in Control.Lens.Tuple Methods _12 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o, p, q, r) l l' Source #
Field12 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o, p, q, r, s) l l' Source #
Instance details Defined in Control.Lens.Tuple Methods _12 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o, p, q, r, s) l l' Source #

class Field13 s t a b | s -> a, t -> b, s b -> t, t a -> s where Source #

Provides access to the 13th field of a tuple.

Minimal complete definition

Nothing

Methods

_13 :: Lens s t a b Source #

Access the 13th field of a tuple.

default _13 :: (Generic s, Generic t, GIxed N12 (Rep s) (Rep t) a b) => Lens s t a b Source #

Instances

Instances details

Field13 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i, j, kk, l, m') m m' Source #
Instance details Defined in Control.Lens.Tuple Methods _13 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i, j, kk, l, m') m m' Source #
Field13 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n) m m' Source #
Instance details Defined in Control.Lens.Tuple Methods _13 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n) m m' Source #
Field13 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o) m m' Source #
Instance details Defined in Control.Lens.Tuple Methods _13 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o) m m' Source #
Field13 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o, p) m m' Source #
Instance details Defined in Control.Lens.Tuple Methods _13 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o, p) m m' Source #
Field13 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o, p, q) m m' Source #
Instance details Defined in Control.Lens.Tuple Methods _13 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o, p, q) m m' Source #
Field13 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o, p, q, r) m m' Source #
Instance details Defined in Control.Lens.Tuple Methods _13 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o, p, q, r) m m' Source #
Field13 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o, p, q, r, s) m m' Source #
Instance details Defined in Control.Lens.Tuple Methods _13 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o, p, q, r, s) m m' Source #

class Field14 s t a b | s -> a, t -> b, s b -> t, t a -> s where Source #

Provides access to the 14th field of a tuple.

Minimal complete definition

Nothing

Methods

_14 :: Lens s t a b Source #

Access the 14th field of a tuple.

default _14 :: (Generic s, Generic t, GIxed N13 (Rep s) (Rep t) a b) => Lens s t a b Source #

Instances

Instances details

Field14 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n') n n' Source #
Instance details Defined in Control.Lens.Tuple Methods _14 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n') n n' Source #
Field14 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o) n n' Source #
Instance details Defined in Control.Lens.Tuple Methods _14 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o) n n' Source #
Field14 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o, p) n n' Source #
Instance details Defined in Control.Lens.Tuple Methods _14 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o, p) n n' Source #
Field14 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o, p, q) n n' Source #
Instance details Defined in Control.Lens.Tuple Methods _14 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o, p, q) n n' Source #
Field14 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o, p, q, r) n n' Source #
Instance details Defined in Control.Lens.Tuple Methods _14 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o, p, q, r) n n' Source #
Field14 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o, p, q, r, s) n n' Source #
Instance details Defined in Control.Lens.Tuple Methods _14 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o, p, q, r, s) n n' Source #

class Field15 s t a b | s -> a, t -> b, s b -> t, t a -> s where Source #

Provides access to the 15th field of a tuple.

Minimal complete definition

Nothing

Methods

_15 :: Lens s t a b Source #

Access the 15th field of a tuple.

default _15 :: (Generic s, Generic t, GIxed N14 (Rep s) (Rep t) a b) => Lens s t a b Source #

Instances

Instances details

Field15 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o') o o' Source #
Instance details Defined in Control.Lens.Tuple Methods _15 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o') o o' Source #
Field15 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o', p) o o' Source #
Instance details Defined in Control.Lens.Tuple Methods _15 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o', p) o o' Source #
Field15 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o', p, q) o o' Source #
Instance details Defined in Control.Lens.Tuple Methods _15 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o', p, q) o o' Source #
Field15 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o', p, q, r) o o' Source #
Instance details Defined in Control.Lens.Tuple Methods _15 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o', p, q, r) o o' Source #
Field15 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o', p, q, r, s) o o' Source #
Instance details Defined in Control.Lens.Tuple Methods _15 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o', p, q, r, s) o o' Source #

class Field16 s t a b | s -> a, t -> b, s b -> t, t a -> s where Source #

Provides access to the 16th field of a tuple.

Minimal complete definition

Nothing

Methods

_16 :: Lens s t a b Source #

Access the 16th field of a tuple.

default _16 :: (Generic s, Generic t, GIxed N15 (Rep s) (Rep t) a b) => Lens s t a b Source #

Instances

Instances details

Field16 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p') p p' Source #
Instance details Defined in Control.Lens.Tuple Methods _16 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p') p p' Source #
Field16 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p', q) p p' Source #
Instance details Defined in Control.Lens.Tuple Methods _16 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p', q) p p' Source #
Field16 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p', q, r) p p' Source #
Instance details Defined in Control.Lens.Tuple Methods _16 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p', q, r) p p' Source #
Field16 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p', q, r, s) p p' Source #
Instance details Defined in Control.Lens.Tuple Methods _16 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p', q, r, s) p p' Source #

class Field17 s t a b | s -> a, t -> b, s b -> t, t a -> s where Source #

Provides access to the 17th field of a tuple.

Minimal complete definition

Nothing

Methods

_17 :: Lens s t a b Source #

Access the 17th field of a tuple.

default _17 :: (Generic s, Generic t, GIxed N16 (Rep s) (Rep t) a b) => Lens s t a b Source #

Instances

Instances details

Field17 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q') q q' Source #
Instance details Defined in Control.Lens.Tuple Methods _17 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q') q q' Source #
Field17 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q', r) q q' Source #
Instance details Defined in Control.Lens.Tuple Methods _17 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q', r) q q' Source #
Field17 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q', r, s) q q' Source #
Instance details Defined in Control.Lens.Tuple Methods _17 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q', r, s) q q' Source #

class Field18 s t a b | s -> a, t -> b, s b -> t, t a -> s where Source #

Provides access to the 18th field of a tuple.

Minimal complete definition

Nothing

Methods

_18 :: Lens s t a b Source #

Access the 18th field of a tuple.

default _18 :: (Generic s, Generic t, GIxed N17 (Rep s) (Rep t) a b) => Lens s t a b Source #

Instances

Instances details

Field18 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r') r r' Source #
Instance details Defined in Control.Lens.Tuple Methods _18 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r') r r' Source #
Field18 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r', s) r r' Source #
Instance details Defined in Control.Lens.Tuple Methods _18 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r', s) r r' Source #

class Field19 s t a b | s -> a, t -> b, s b -> t, t a -> s where Source #

Provides access to the 19th field of a tuple.

Minimal complete definition

Nothing

Methods

_19 :: Lens s t a b Source #

Access the 19th field of a tuple.

default _19 :: (Generic s, Generic t, GIxed N18 (Rep s) (Rep t) a b) => Lens s t a b Source #

Instances

Instances details

Field19 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s') s s' Source #
Instance details Defined in Control.Lens.Tuple Methods _19 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s') s s' Source #

type Fold1 s a = forall f. (Contravariant f, Apply f) => (a -> f a) -> s -> f s Source #

A relevant Fold (aka Fold1) has one or more targets.

type IndexedFold1 i s a = forall p f. (Indexable i p, Contravariant f, Apply f) => p a (f a) -> s -> f s Source #

type IndexPreservingLens s t a b = forall p f. (Conjoined p, Functor f) => p a (f b) -> p s (f t) Source #

An IndexPreservingLens leaves any index it is composed with alone.

type IndexPreservingLens' s a = IndexPreservingLens s s a a Source #

type IndexPreservingLens' = Simple IndexPreservingLens

type IndexPreservingTraversal s t a b = forall p f. (Conjoined p, Applicative f) => p a (f b) -> p s (f t) Source #

An IndexPreservingTraversal leaves any index it is composed with alone.

type IndexPreservingTraversal' s a = IndexPreservingTraversal s s a a Source #

type IndexPreservingTraversal' = Simple IndexPreservingTraversal

type IndexPreservingTraversal1 s t a b = forall p f. (Conjoined p, Apply f) => p a (f b) -> p s (f t) Source #

type IndexPreservingTraversal1' s a = IndexPreservingTraversal1 s s a a Source #

type IndexPreservingSetter s t a b = forall p f. (Conjoined p, Settable f) => p a (f b) -> p s (f t) Source #

An IndexPreservingSetter can be composed with a IndexedSetter, IndexedTraversal or IndexedLens and leaves the index intact, yielding an IndexedSetter.

type IndexPreservingSetter' s a = IndexPreservingSetter s s a a Source #

type IndexedPreservingSetter' i = Simple IndexedPreservingSetter

type IndexPreservingGetter s a = forall p f. (Conjoined p, Contravariant f, Functor f) => p a (f a) -> p s (f s) Source #

An IndexPreservingGetter can be used as a Getter, but when composed with an IndexedTraversal, IndexedFold, or IndexedLens yields an IndexedFold, IndexedFold or IndexedGetter respectively.

type IndexPreservingFold s a = forall p f. (Conjoined p, Contravariant f, Applicative f) => p a (f a) -> p s (f s) Source #

An IndexPreservingFold can be used as a Fold, but when composed with an IndexedTraversal, IndexedFold, or IndexedLens yields an IndexedFold respectively.

type IndexPreservingFold1 s a = forall p f. (Conjoined p, Contravariant f, Apply f) => p a (f a) -> p s (f s) Source #

type Simple f s a = f s s a a Source #

A Simple Lens, Simple Traversal, ... can be used instead of a Lens,Traversal, ... whenever the type variables don't change upon setting a value.

_imagPart :: Simple Lens (Complex a) a
traversed :: Simple (IndexedTraversal Int) [a] a

Note: To use this alias in your own code with LensLike f or Setter, you may have to turn on LiberalTypeSynonyms.

This is commonly abbreviated as a "prime" marker, e.g. Lens' = Simple Lens.

type LensLike' f s a = LensLike f s s a a Source #

type LensLike' f = Simple (LensLike f)

type Over p f s t a b = p a (f b) -> s -> f t Source #

This is a convenient alias for use when you need to consume either indexed or non-indexed lens-likes based on context.

type Over' p f s a = Over p f s s a a Source #

This is a convenient alias for use when you need to consume either indexed or non-indexed lens-likes based on context.

type Over' p f = Simple (Over p f)

type IndexedLensLike i f s t a b = forall p. Indexable i p => p a (f b) -> s -> f t Source #

Convenient alias for constructing indexed lenses and their ilk.

type IndexedLensLike' i f s a = IndexedLensLike i f s s a a Source #

Convenient alias for constructing simple indexed lenses and their ilk.

type Optical p q f s t a b = p a (f b) -> q s (f t) Source #

type LensLike f s t a b = Optical (->) (->) f s t a b

type Over p f s t a b = Optical p (->) f s t a b

type Optic p f s t a b = Optical p p f s t a b

type Optical' p q f s a = Optical p q f s s a a Source #

type Optical' p q f s a = Simple (Optical p q f) s a

type Optic' p f s a = Optic p f s s a a Source #

type Optic' p f s a = Simple (Optic p f) s a

class Wrapped s => Rewrapped (s :: Type) (t :: Type) Source #

Instances

Instances details

t ~ NoMethodError => Rewrapped NoMethodError t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ PatternMatchFail => Rewrapped PatternMatchFail t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ RecConError => Rewrapped RecConError t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ RecSelError => Rewrapped RecSelError t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ RecUpdError => Rewrapped RecUpdError t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ TypeError => Rewrapped TypeError t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ All => Rewrapped All t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Any => Rewrapped Any t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped Errno t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CBool t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CChar t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CClock t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CDouble t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CFloat t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CInt t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CIntMax t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CIntPtr t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CLLong t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CLong t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CPtrdiff t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CSChar t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CSUSeconds t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CShort t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CSigAtomic t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CSize t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CTime t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CUChar t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CUInt t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CUIntMax t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CUIntPtr t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CULLong t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CULong t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CUSeconds t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CUShort t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CWchar t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ ErrorCall => Rewrapped ErrorCall t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ AssertionFailed => Rewrapped AssertionFailed t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ CompactionFailed => Rewrapped CompactionFailed t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CBlkCnt t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CBlkSize t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CCc t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CClockId t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CDev t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CFsBlkCnt t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CFsFilCnt t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CGid t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CId t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CIno t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CKey t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CMode t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CNlink t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped COff t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CPid t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CRLim t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CSpeed t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CSsize t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CTcflag t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CTimer t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped CUid t Source #
Instance details Defined in Control.Lens.Wrapped
Rewrapped Fd t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ IntSet => Rewrapped IntSet t Source #	Use `_Wrapping fromList`. unwrapping returns a sorted list.
Instance details Defined in Control.Lens.Wrapped
t ~ ZipList b => Rewrapped (ZipList a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Comparison b => Rewrapped (Comparison a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Equivalence b => Rewrapped (Equivalence a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Predicate b => Rewrapped (Predicate a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Identity b => Rewrapped (Identity a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ First b => Rewrapped (First a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Last b => Rewrapped (Last a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Down b => Rewrapped (Down a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ First b => Rewrapped (First a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Last b => Rewrapped (Last a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Max b => Rewrapped (Max a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Min b => Rewrapped (Min a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ WrappedMonoid b => Rewrapped (WrappedMonoid a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Dual b => Rewrapped (Dual a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Endo b => Rewrapped (Endo a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Product b => Rewrapped (Product a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Sum b => Rewrapped (Sum a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ NonEmpty b => Rewrapped (NonEmpty a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Par1 p' => Rewrapped (Par1 p) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ IntMap a' => Rewrapped (IntMap a) t Source #	Use `_Wrapping fromList`. unwrapping returns a sorted list.
Instance details Defined in Control.Lens.Wrapped
t ~ Seq a' => Rewrapped (Seq a) t Source #
Instance details Defined in Control.Lens.Wrapped
(t ~ Set a', Ord a) => Rewrapped (Set a) t Source #	Use `_Wrapping fromList`. unwrapping returns a sorted list.
Instance details Defined in Control.Lens.Wrapped
(t ~ HashSet a', Hashable a, Eq a) => Rewrapped (HashSet a) t Source #	Use `_Wrapping fromList`. Unwrapping returns some permutation of the list.
Instance details Defined in Control.Lens.Wrapped
t ~ Vector a' => Rewrapped (Vector a) t Source #
Instance details Defined in Control.Lens.Wrapped
(Prim a, t ~ Vector a') => Rewrapped (Vector a) t Source #
Instance details Defined in Control.Lens.Wrapped
(Storable a, t ~ Vector a') => Rewrapped (Vector a) t Source #
Instance details Defined in Control.Lens.Wrapped
(Unbox a, t ~ Vector a') => Rewrapped (Vector a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ WrappedMonad m' a' => Rewrapped (WrappedMonad m a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ ArrowMonad m' a' => Rewrapped (ArrowMonad m a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Op a' b' => Rewrapped (Op a b) t Source #
Instance details Defined in Control.Lens.Wrapped
(t ~ Map k' a', Ord k) => Rewrapped (Map k a) t Source #	Use `_Wrapping fromList`. unwrapping returns a sorted list.
Instance details Defined in Control.Lens.Wrapped
t ~ CatchT m' a' => Rewrapped (CatchT m a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Alt f' a' => Rewrapped (Alt f a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ CoiterT w' a' => Rewrapped (CoiterT w a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ IterT m' a' => Rewrapped (IterT m a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ MaybeApply f' a' => Rewrapped (MaybeApply f a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ WrappedApplicative f' a' => Rewrapped (WrappedApplicative f a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ MaybeT n b => Rewrapped (MaybeT m a) t Source #
Instance details Defined in Control.Lens.Wrapped
(t ~ HashMap k' a', Hashable k, Eq k) => Rewrapped (HashMap k a) t Source #	Use `_Wrapping fromList`. Unwrapping returns some permutation of the list.
Instance details Defined in Control.Lens.Wrapped
t ~ WrappedArrow a' b' c' => Rewrapped (WrappedArrow a b c) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Kleisli m' a' b' => Rewrapped (Kleisli m a b) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Const a' x' => Rewrapped (Const a x) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Ap g b => Rewrapped (Ap f a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Alt g b => Rewrapped (Alt f a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Rec1 f' p' => Rewrapped (Rec1 f p) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Fix p' a' => Rewrapped (Fix p a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Join p' a' => Rewrapped (Join p a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ TracedT m' w' a' => Rewrapped (TracedT m w a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Compose f' g' a' => Rewrapped (Compose f g a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ ComposeCF f' g' a' => Rewrapped (ComposeCF f g a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ ComposeFC f' g' a' => Rewrapped (ComposeFC f g a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ ApT f' g' a' => Rewrapped (ApT f g a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ CofreeT f' w' a' => Rewrapped (CofreeT f w a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ FreeT f' m' a' => Rewrapped (FreeT f m a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Static f' a' b' => Rewrapped (Static f a b) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Tagged s' a' => Rewrapped (Tagged s a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Backwards g b => Rewrapped (Backwards f a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ ExceptT e' m' a' => Rewrapped (ExceptT e m a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ IdentityT n b => Rewrapped (IdentityT m a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ ReaderT s n b => Rewrapped (ReaderT r m a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ StateT s' m' a' => Rewrapped (StateT s m a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ StateT s' m' a' => Rewrapped (StateT s m a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ WriterT w' m' a' => Rewrapped (WriterT w m a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ WriterT w' m' a' => Rewrapped (WriterT w m a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Constant a' b' => Rewrapped (Constant a b) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Reverse g b => Rewrapped (Reverse f a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ K1 i' c' p' => Rewrapped (K1 i c p) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Costar f' d' c' => Rewrapped (Costar f d c) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Forget r' a' b' => Rewrapped (Forget r a b) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Star f' d' c' => Rewrapped (Star f d c) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ ContT r' m' a' => Rewrapped (ContT r m a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Compose f' g' a' => Rewrapped (Compose f g a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ (f' :.: g') p' => Rewrapped ((f :.: g) p) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ M1 i' c' f' p' => Rewrapped (M1 i c f p) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Clown f' a' b' => Rewrapped (Clown f a b) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Flip p' a' b' => Rewrapped (Flip p a b) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Joker g' a' b' => Rewrapped (Joker g a b) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ WrappedBifunctor p' a' b' => Rewrapped (WrappedBifunctor p a b) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ WrappedArrow p' a' b' => Rewrapped (WrappedArrow p a b) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Semi m' a' b' => Rewrapped (Semi m a b) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ WrappedCategory k' a' b' => Rewrapped (WrappedCategory k6 a b) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Dual k' a' b' => Rewrapped (Dual k6 a b) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ RWST r' w' s' m' a' => Rewrapped (RWST r w s m a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ RWST r' w' s' m' a' => Rewrapped (RWST r w s m a) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Tannen f' p' a' b' => Rewrapped (Tannen f p a b) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Cayley f' p' a' b' => Rewrapped (Cayley f p a b) t Source #
Instance details Defined in Control.Lens.Wrapped
t ~ Biff p' f' g' a' b' => Rewrapped (Biff p f g a b) t Source #
Instance details Defined in Control.Lens.Wrapped

class (Rewrapped s t, Rewrapped t s) => Rewrapping s t Source #

Instances

Instances details

(Rewrapped s t, Rewrapped t s) => Rewrapping s t Source #
Instance details Defined in Control.Lens.Wrapped

type family Magnified (m :: Type -> Type) :: Type -> Type -> Type Source #

This type family is used by Magnify to describe the common effect type.

Instances

Instances details

type Magnified (IdentityT m) Source #
Instance details Defined in Control.Lens.Zoom type Magnified (IdentityT m) = Magnified m
type Magnified (ReaderT b m) Source #
Instance details Defined in Control.Lens.Zoom type Magnified (ReaderT b m) = Effect m
type Magnified ((->) b) Source #
Instance details Defined in Control.Lens.Zoom type Magnified ((->) b) = Const :: Type -> Type -> Type
type Magnified (RWST a w s m) Source #
Instance details Defined in Control.Lens.Zoom type Magnified (RWST a w s m) = EffectRWS w s m
type Magnified (RWST a w s m) Source #
Instance details Defined in Control.Lens.Zoom type Magnified (RWST a w s m) = EffectRWS w s m

class (Magnified m ~ Magnified n, MonadReader b m, MonadReader a n) => Magnify m n b a | m -> b, n -> a, m a -> n, n b -> m where Source #

This class allows us to use magnify part of the environment, changing the environment supplied by many different Monad transformers. Unlike zoom this can change the environment of a deeply nested Monad transformer.

Also, unlike zoom, this can be used with any valid Getter, but cannot be used with a Traversal or Fold.

Methods

magnify :: ((Functor (Magnified m c), Contravariant (Magnified m c)) => LensLike' (Magnified m c) a b) -> m c -> n c infixr 2 Source #

Run a monadic action in a larger environment than it was defined in, using a Getter.

This acts like local, but can in many cases change the type of the environment as well.

This is commonly used to lift actions in a simpler Reader Monad into a Monad with a larger environment type.

This can be used to edit pretty much any Monad transformer stack with an environment in it:

>>> (1,2) & magnify _2 (+1)
3

>>> flip Reader.runReader (1,2) $ magnify _1 Reader.ask
1

>>> flip Reader.runReader (1,2,[10..20]) $ magnify (_3._tail) Reader.ask
[11,12,13,14,15,16,17,18,19,20]

The type can be read as

  magnify :: LensLike' (Magnified m c) a b -> m c -> n c

but the higher-rank constraints make it easier to apply magnify to a Getter in highly-polymorphic code.

magnify :: Getter s a -> (a -> r) -> s -> r
magnify :: Monoid r => Fold s a   -> (a -> r) -> s -> r

magnify :: Monoid w                 => Getter s t -> RWS t w st c -> RWS s w st c
magnify :: (Monoid w, Monoid c) => Fold s a   -> RWS a w st c -> RWS s w st c
...

Instances

Instances details

Magnify m n b a => Magnify (IdentityT m) (IdentityT n) b a Source #
Instance details Defined in Control.Lens.Zoom Methods magnify :: ((Functor (Magnified (IdentityT m) c), Contravariant (Magnified (IdentityT m) c)) => LensLike' (Magnified (IdentityT m) c) a b) -> IdentityT m c -> IdentityT n c Source #
Monad m => Magnify (ReaderT b m) (ReaderT a m) b a Source #
Instance details Defined in Control.Lens.Zoom Methods magnify :: ((Functor (Magnified (ReaderT b m) c), Contravariant (Magnified (ReaderT b m) c)) => LensLike' (Magnified (ReaderT b m) c) a b) -> ReaderT b m c -> ReaderT a m c Source #
Magnify ((->) b) ((->) a) b a Source #	`magnify` = `views`
Instance details Defined in Control.Lens.Zoom Methods magnify :: ((Functor (Magnified ((->) b) c), Contravariant (Magnified ((->) b) c)) => LensLike' (Magnified ((->) b) c) a b) -> (b -> c) -> a -> c Source #
(Monad m, Monoid w) => Magnify (RWST b w s m) (RWST a w s m) b a Source #
Instance details Defined in Control.Lens.Zoom Methods magnify :: ((Functor (Magnified (RWST b w s m) c), Contravariant (Magnified (RWST b w s m) c)) => LensLike' (Magnified (RWST b w s m) c) a b) -> RWST b w s m c -> RWST a w s m c Source #
(Monad m, Monoid w) => Magnify (RWST b w s m) (RWST a w s m) b a Source #
Instance details Defined in Control.Lens.Zoom Methods magnify :: ((Functor (Magnified (RWST b w s m) c), Contravariant (Magnified (RWST b w s m) c)) => LensLike' (Magnified (RWST b w s m) c) a b) -> RWST b w s m c -> RWST a w s m c Source #

type family Zoomed (m :: Type -> Type) :: Type -> Type -> Type Source #

This type family is used by Zoom to describe the common effect type.

Instances

Instances details

type Zoomed (MaybeT m) Source #
Instance details Defined in Control.Lens.Zoom type Zoomed (MaybeT m) = FocusingMay (Zoomed m)
type Zoomed (FreeT f m) Source #
Instance details Defined in Control.Lens.Zoom type Zoomed (FreeT f m) = FocusingFree f m (Zoomed m)
type Zoomed (ExceptT e m) Source #
Instance details Defined in Control.Lens.Zoom type Zoomed (ExceptT e m) = FocusingErr e (Zoomed m)
type Zoomed (IdentityT m) Source #
Instance details Defined in Control.Lens.Zoom type Zoomed (IdentityT m) = Zoomed m
type Zoomed (ReaderT e m) Source #
Instance details Defined in Control.Lens.Zoom type Zoomed (ReaderT e m) = Zoomed m
type Zoomed (StateT s z) Source #
Instance details Defined in Control.Lens.Zoom type Zoomed (StateT s z) = Focusing z
type Zoomed (StateT s z) Source #
Instance details Defined in Control.Lens.Zoom type Zoomed (StateT s z) = Focusing z
type Zoomed (WriterT w m) Source #
Instance details Defined in Control.Lens.Zoom type Zoomed (WriterT w m) = FocusingPlus w (Zoomed m)
type Zoomed (WriterT w m) Source #
Instance details Defined in Control.Lens.Zoom type Zoomed (WriterT w m) = FocusingPlus w (Zoomed m)
type Zoomed (RWST r w s z) Source #
Instance details Defined in Control.Lens.Zoom type Zoomed (RWST r w s z) = FocusingWith w z
type Zoomed (RWST r w s z) Source #
Instance details Defined in Control.Lens.Zoom type Zoomed (RWST r w s z) = FocusingWith w z

newtype ReifiedTraversal s t a b Source #

A form of Traversal that can be stored monomorphically in a container.

Constructors

Traversal
Fields runTraversal :: Traversal s t a b

type ReifiedLens' s a = ReifiedLens s s a a Source #

type ReifiedLens' = Simple ReifiedLens

newtype ReifiedIndexedLens i s t a b Source #

Reify an IndexedLens so it can be stored safely in a container.

Constructors

IndexedLens
Fields runIndexedLens :: IndexedLens i s t a b

type ReifiedIndexedLens' i s a = ReifiedIndexedLens i s s a a Source #

type ReifiedIndexedLens' i = Simple (ReifiedIndexedLens i)

newtype ReifiedIndexedTraversal i s t a b Source #

Reify an IndexedTraversal so it can be stored safely in a container.

Constructors

IndexedTraversal
Fields runIndexedTraversal :: IndexedTraversal i s t a b

type ReifiedIndexedTraversal' i s a = ReifiedIndexedTraversal i s s a a Source #

type ReifiedIndexedTraversal' i = Simple (ReifiedIndexedTraversal i)

type ReifiedTraversal' s a = ReifiedTraversal s s a a Source #

type ReifiedTraversal' = Simple ReifiedTraversal

newtype ReifiedGetter s a Source #

Reify a Getter so it can be stored safely in a container.

This can also be useful when combining getters in novel ways, as ReifiedGetter is isomorphic to (->) and provides similar instances.

>>> ("hello","world","!!!")^.runGetter ((,) <$> Getter _2 <*> Getter (_1.to length))
("world",5)

Constructors

Getter
Fields runGetter :: Getter s a

Instances

Instances details

Arrow ReifiedGetter Source #
Instance details Defined in Control.Lens.Reified Methods arr :: (b -> c) -> ReifiedGetter b c # first :: ReifiedGetter b c -> ReifiedGetter (b, d) (c, d) # second :: ReifiedGetter b c -> ReifiedGetter (d, b) (d, c) # (***) :: ReifiedGetter b c -> ReifiedGetter b' c' -> ReifiedGetter (b, b') (c, c') # (&&&) :: ReifiedGetter b c -> ReifiedGetter b c' -> ReifiedGetter b (c, c') #
ArrowApply ReifiedGetter Source #
Instance details Defined in Control.Lens.Reified Methods app :: ReifiedGetter (ReifiedGetter b c, b) c #
ArrowChoice ReifiedGetter Source #
Instance details Defined in Control.Lens.Reified Methods left :: ReifiedGetter b c -> ReifiedGetter (Either b d) (Either c d) # right :: ReifiedGetter b c -> ReifiedGetter (Either d b) (Either d c) # (+++) :: ReifiedGetter b c -> ReifiedGetter b' c' -> ReifiedGetter (Either b b') (Either c c') # (\|\|\|) :: ReifiedGetter b d -> ReifiedGetter c d -> ReifiedGetter (Either b c) d #
ArrowLoop ReifiedGetter Source #
Instance details Defined in Control.Lens.Reified Methods loop :: ReifiedGetter (b, d) (c, d) -> ReifiedGetter b c #
Conjoined ReifiedGetter Source #
Instance details Defined in Control.Lens.Reified Methods distrib :: Functor f => ReifiedGetter a b -> ReifiedGetter (f a) (f b) Source # conjoined :: (ReifiedGetter ~ (->) => q (a -> b) r) -> q (ReifiedGetter a b) r -> q (ReifiedGetter a b) r Source #
Choice ReifiedGetter Source #
Instance details Defined in Control.Lens.Reified Methods left' :: ReifiedGetter a b -> ReifiedGetter (Either a c) (Either b c) # right' :: ReifiedGetter a b -> ReifiedGetter (Either c a) (Either c b) #
Closed ReifiedGetter Source #
Instance details Defined in Control.Lens.Reified Methods closed :: ReifiedGetter a b -> ReifiedGetter (x -> a) (x -> b) #
Corepresentable ReifiedGetter Source #
Instance details Defined in Control.Lens.Reified Associated Types type Corep ReifiedGetter :: Type -> Type # Methods cotabulate :: (Corep ReifiedGetter d -> c) -> ReifiedGetter d c #
Representable ReifiedGetter Source #
Instance details Defined in Control.Lens.Reified Associated Types type Rep ReifiedGetter :: Type -> Type # Methods tabulate :: (d -> Rep ReifiedGetter c) -> ReifiedGetter d c #
Costrong ReifiedGetter Source #
Instance details Defined in Control.Lens.Reified Methods unfirst :: ReifiedGetter (a, d) (b, d) -> ReifiedGetter a b # unsecond :: ReifiedGetter (d, a) (d, b) -> ReifiedGetter a b #
Strong ReifiedGetter Source #
Instance details Defined in Control.Lens.Reified Methods first' :: ReifiedGetter a b -> ReifiedGetter (a, c) (b, c) # second' :: ReifiedGetter a b -> ReifiedGetter (c, a) (c, b) #
Profunctor ReifiedGetter Source #
Instance details Defined in Control.Lens.Reified Methods dimap :: (a -> b) -> (c -> d) -> ReifiedGetter b c -> ReifiedGetter a d # lmap :: (a -> b) -> ReifiedGetter b c -> ReifiedGetter a c # rmap :: (b -> c) -> ReifiedGetter a b -> ReifiedGetter a c # (#.) :: forall a b c q. Coercible c b => q b c -> ReifiedGetter a b -> ReifiedGetter a c # (.#) :: forall a b c q. Coercible b a => ReifiedGetter b c -> q a b -> ReifiedGetter a c #
Category ReifiedGetter Source #
Instance details Defined in Control.Lens.Reified Methods id :: forall (a :: k). ReifiedGetter a a # (.) :: forall (b :: k) (c :: k) (a :: k). ReifiedGetter b c -> ReifiedGetter a b -> ReifiedGetter a c #
Cosieve ReifiedGetter Identity Source #
Instance details Defined in Control.Lens.Reified Methods cosieve :: ReifiedGetter a b -> Identity a -> b #
Sieve ReifiedGetter Identity Source #
Instance details Defined in Control.Lens.Reified Methods sieve :: ReifiedGetter a b -> a -> Identity b #
MonadReader s (ReifiedGetter s) Source #
Instance details Defined in Control.Lens.Reified Methods ask :: ReifiedGetter s s # local :: (s -> s) -> ReifiedGetter s a -> ReifiedGetter s a # reader :: (s -> a) -> ReifiedGetter s a #
Applicative (ReifiedGetter s) Source #
Instance details Defined in Control.Lens.Reified Methods pure :: a -> ReifiedGetter s a # (<>) :: ReifiedGetter s (a -> b) -> ReifiedGetter s a -> ReifiedGetter s b # liftA2 :: (a -> b -> c) -> ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s c # (>) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s b # (<*) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s a #
Functor (ReifiedGetter s) Source #
Instance details Defined in Control.Lens.Reified Methods fmap :: (a -> b) -> ReifiedGetter s a -> ReifiedGetter s b # (<$) :: a -> ReifiedGetter s b -> ReifiedGetter s a #
Monad (ReifiedGetter s) Source #
Instance details Defined in Control.Lens.Reified Methods (>>=) :: ReifiedGetter s a -> (a -> ReifiedGetter s b) -> ReifiedGetter s b # (>>) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s b # return :: a -> ReifiedGetter s a #
Monoid s => Comonad (ReifiedGetter s) Source #
Instance details Defined in Control.Lens.Reified Methods extract :: ReifiedGetter s a -> a # duplicate :: ReifiedGetter s a -> ReifiedGetter s (ReifiedGetter s a) # extend :: (ReifiedGetter s a -> b) -> ReifiedGetter s a -> ReifiedGetter s b #
Monoid s => ComonadApply (ReifiedGetter s) Source #
Instance details Defined in Control.Lens.Reified Methods (<@>) :: ReifiedGetter s (a -> b) -> ReifiedGetter s a -> ReifiedGetter s b # (@>) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s b # (<@) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s a #
Distributive (ReifiedGetter s) Source #
Instance details Defined in Control.Lens.Reified Methods distribute :: Functor f => f (ReifiedGetter s a) -> ReifiedGetter s (f a) # collect :: Functor f => (a -> ReifiedGetter s b) -> f a -> ReifiedGetter s (f b) # distributeM :: Monad m => m (ReifiedGetter s a) -> ReifiedGetter s (m a) # collectM :: Monad m => (a -> ReifiedGetter s b) -> m a -> ReifiedGetter s (m b) #
Apply (ReifiedGetter s) Source #
Instance details Defined in Control.Lens.Reified Methods (<.>) :: ReifiedGetter s (a -> b) -> ReifiedGetter s a -> ReifiedGetter s b # (.>) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s b # (<.) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s a # liftF2 :: (a -> b -> c) -> ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s c #
Bind (ReifiedGetter s) Source #
Instance details Defined in Control.Lens.Reified Methods (>>-) :: ReifiedGetter s a -> (a -> ReifiedGetter s b) -> ReifiedGetter s b # join :: ReifiedGetter s (ReifiedGetter s a) -> ReifiedGetter s a #
Semigroup s => Extend (ReifiedGetter s) Source #
Instance details Defined in Control.Lens.Reified Methods duplicated :: ReifiedGetter s a -> ReifiedGetter s (ReifiedGetter s a) # extended :: (ReifiedGetter s a -> b) -> ReifiedGetter s a -> ReifiedGetter s b #
type Corep ReifiedGetter Source #
Instance details Defined in Control.Lens.Reified type Corep ReifiedGetter = Identity
type Rep ReifiedGetter Source #
Instance details Defined in Control.Lens.Reified type Rep ReifiedGetter = Identity

newtype ReifiedIndexedGetter i s a Source #

Reify an IndexedGetter so it can be stored safely in a container.

Constructors

IndexedGetter
Fields runIndexedGetter :: IndexedGetter i s a

Instances

Instances details

Representable (ReifiedIndexedGetter i) Source #
Instance details Defined in Control.Lens.Reified Associated Types type Rep (ReifiedIndexedGetter i) :: Type -> Type # Methods tabulate :: (d -> Rep (ReifiedIndexedGetter i) c) -> ReifiedIndexedGetter i d c #
Strong (ReifiedIndexedGetter i) Source #
Instance details Defined in Control.Lens.Reified Methods first' :: ReifiedIndexedGetter i a b -> ReifiedIndexedGetter i (a, c) (b, c) # second' :: ReifiedIndexedGetter i a b -> ReifiedIndexedGetter i (c, a) (c, b) #
Profunctor (ReifiedIndexedGetter i) Source #
Instance details Defined in Control.Lens.Reified Methods dimap :: (a -> b) -> (c -> d) -> ReifiedIndexedGetter i b c -> ReifiedIndexedGetter i a d # lmap :: (a -> b) -> ReifiedIndexedGetter i b c -> ReifiedIndexedGetter i a c # rmap :: (b -> c) -> ReifiedIndexedGetter i a b -> ReifiedIndexedGetter i a c # (#.) :: forall a b c q. Coercible c b => q b c -> ReifiedIndexedGetter i a b -> ReifiedIndexedGetter i a c # (.#) :: forall a b c q. Coercible b a => ReifiedIndexedGetter i b c -> q a b -> ReifiedIndexedGetter i a c #
Sieve (ReifiedIndexedGetter i) ((,) i) Source #
Instance details Defined in Control.Lens.Reified Methods sieve :: ReifiedIndexedGetter i a b -> a -> (i, b) #
Functor (ReifiedIndexedGetter i s) Source #
Instance details Defined in Control.Lens.Reified Methods fmap :: (a -> b) -> ReifiedIndexedGetter i s a -> ReifiedIndexedGetter i s b # (<$) :: a -> ReifiedIndexedGetter i s b -> ReifiedIndexedGetter i s a #
Semigroup i => Apply (ReifiedIndexedGetter i s) Source #
Instance details Defined in Control.Lens.Reified Methods (<.>) :: ReifiedIndexedGetter i s (a -> b) -> ReifiedIndexedGetter i s a -> ReifiedIndexedGetter i s b # (.>) :: ReifiedIndexedGetter i s a -> ReifiedIndexedGetter i s b -> ReifiedIndexedGetter i s b # (<.) :: ReifiedIndexedGetter i s a -> ReifiedIndexedGetter i s b -> ReifiedIndexedGetter i s a # liftF2 :: (a -> b -> c) -> ReifiedIndexedGetter i s a -> ReifiedIndexedGetter i s b -> ReifiedIndexedGetter i s c #
type Rep (ReifiedIndexedGetter i) Source #
Instance details Defined in Control.Lens.Reified type Rep (ReifiedIndexedGetter i) = (,) i

newtype ReifiedFold s a Source #

Reify a Fold so it can be stored safely in a container.

This can also be useful for creatively combining folds as ReifiedFold s is isomorphic to ReaderT s [] and provides similar instances.

>>> ("hello","world")^..runFold ((,) <$> Fold _2 <*> Fold both)
[("world","hello"),("world","world")]

Constructors

Fold
Fields runFold :: Fold s a

Instances

Instances details

Arrow ReifiedFold Source #
Instance details Defined in Control.Lens.Reified Methods arr :: (b -> c) -> ReifiedFold b c # first :: ReifiedFold b c -> ReifiedFold (b, d) (c, d) # second :: ReifiedFold b c -> ReifiedFold (d, b) (d, c) # (***) :: ReifiedFold b c -> ReifiedFold b' c' -> ReifiedFold (b, b') (c, c') # (&&&) :: ReifiedFold b c -> ReifiedFold b c' -> ReifiedFold b (c, c') #
ArrowApply ReifiedFold Source #
Instance details Defined in Control.Lens.Reified Methods app :: ReifiedFold (ReifiedFold b c, b) c #
ArrowChoice ReifiedFold Source #
Instance details Defined in Control.Lens.Reified Methods left :: ReifiedFold b c -> ReifiedFold (Either b d) (Either c d) # right :: ReifiedFold b c -> ReifiedFold (Either d b) (Either d c) # (+++) :: ReifiedFold b c -> ReifiedFold b' c' -> ReifiedFold (Either b b') (Either c c') # (\|\|\|) :: ReifiedFold b d -> ReifiedFold c d -> ReifiedFold (Either b c) d #
Choice ReifiedFold Source #
Instance details Defined in Control.Lens.Reified Methods left' :: ReifiedFold a b -> ReifiedFold (Either a c) (Either b c) # right' :: ReifiedFold a b -> ReifiedFold (Either c a) (Either c b) #
Representable ReifiedFold Source #
Instance details Defined in Control.Lens.Reified Associated Types type Rep ReifiedFold :: Type -> Type # Methods tabulate :: (d -> Rep ReifiedFold c) -> ReifiedFold d c #
Strong ReifiedFold Source #
Instance details Defined in Control.Lens.Reified Methods first' :: ReifiedFold a b -> ReifiedFold (a, c) (b, c) # second' :: ReifiedFold a b -> ReifiedFold (c, a) (c, b) #
Profunctor ReifiedFold Source #
Instance details Defined in Control.Lens.Reified Methods dimap :: (a -> b) -> (c -> d) -> ReifiedFold b c -> ReifiedFold a d # lmap :: (a -> b) -> ReifiedFold b c -> ReifiedFold a c # rmap :: (b -> c) -> ReifiedFold a b -> ReifiedFold a c # (#.) :: forall a b c q. Coercible c b => q b c -> ReifiedFold a b -> ReifiedFold a c # (.#) :: forall a b c q. Coercible b a => ReifiedFold b c -> q a b -> ReifiedFold a c #
Category ReifiedFold Source #
Instance details Defined in Control.Lens.Reified Methods id :: forall (a :: k). ReifiedFold a a # (.) :: forall (b :: k) (c :: k) (a :: k). ReifiedFold b c -> ReifiedFold a b -> ReifiedFold a c #
Sieve ReifiedFold List Source #
Instance details Defined in Control.Lens.Reified Methods sieve :: ReifiedFold a b -> a -> [b] #
MonadReader s (ReifiedFold s) Source #
Instance details Defined in Control.Lens.Reified Methods ask :: ReifiedFold s s # local :: (s -> s) -> ReifiedFold s a -> ReifiedFold s a # reader :: (s -> a) -> ReifiedFold s a #
Alternative (ReifiedFold s) Source #
Instance details Defined in Control.Lens.Reified Methods empty :: ReifiedFold s a # (<\|>) :: ReifiedFold s a -> ReifiedFold s a -> ReifiedFold s a # some :: ReifiedFold s a -> ReifiedFold s [a] # many :: ReifiedFold s a -> ReifiedFold s [a] #
Applicative (ReifiedFold s) Source #
Instance details Defined in Control.Lens.Reified Methods pure :: a -> ReifiedFold s a # (<>) :: ReifiedFold s (a -> b) -> ReifiedFold s a -> ReifiedFold s b # liftA2 :: (a -> b -> c) -> ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s c # (>) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s b # (<*) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s a #
Functor (ReifiedFold s) Source #
Instance details Defined in Control.Lens.Reified Methods fmap :: (a -> b) -> ReifiedFold s a -> ReifiedFold s b # (<$) :: a -> ReifiedFold s b -> ReifiedFold s a #
Monad (ReifiedFold s) Source #
Instance details Defined in Control.Lens.Reified Methods (>>=) :: ReifiedFold s a -> (a -> ReifiedFold s b) -> ReifiedFold s b # (>>) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s b # return :: a -> ReifiedFold s a #
MonadPlus (ReifiedFold s) Source #
Instance details Defined in Control.Lens.Reified Methods mzero :: ReifiedFold s a # mplus :: ReifiedFold s a -> ReifiedFold s a -> ReifiedFold s a #
Alt (ReifiedFold s) Source #
Instance details Defined in Control.Lens.Reified Methods (<!>) :: ReifiedFold s a -> ReifiedFold s a -> ReifiedFold s a # some :: Applicative (ReifiedFold s) => ReifiedFold s a -> ReifiedFold s [a] # many :: Applicative (ReifiedFold s) => ReifiedFold s a -> ReifiedFold s [a] #
Apply (ReifiedFold s) Source #
Instance details Defined in Control.Lens.Reified Methods (<.>) :: ReifiedFold s (a -> b) -> ReifiedFold s a -> ReifiedFold s b # (.>) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s b # (<.) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s a # liftF2 :: (a -> b -> c) -> ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s c #
Bind (ReifiedFold s) Source #
Instance details Defined in Control.Lens.Reified Methods (>>-) :: ReifiedFold s a -> (a -> ReifiedFold s b) -> ReifiedFold s b # join :: ReifiedFold s (ReifiedFold s a) -> ReifiedFold s a #
Plus (ReifiedFold s) Source #
Instance details Defined in Control.Lens.Reified Methods zero :: ReifiedFold s a #
Monoid (ReifiedFold s a) Source #
Instance details Defined in Control.Lens.Reified Methods mempty :: ReifiedFold s a # mappend :: ReifiedFold s a -> ReifiedFold s a -> ReifiedFold s a # mconcat :: [ReifiedFold s a] -> ReifiedFold s a #
Semigroup (ReifiedFold s a) Source #
Instance details Defined in Control.Lens.Reified Methods (<>) :: ReifiedFold s a -> ReifiedFold s a -> ReifiedFold s a # sconcat :: NonEmpty (ReifiedFold s a) -> ReifiedFold s a # stimes :: Integral b => b -> ReifiedFold s a -> ReifiedFold s a #
type Rep ReifiedFold Source #
Instance details Defined in Control.Lens.Reified type Rep ReifiedFold = List

newtype ReifiedIndexedFold i s a Source #

Constructors

IndexedFold
Fields runIndexedFold :: IndexedFold i s a

Instances

Instances details

Representable (ReifiedIndexedFold i) Source #
Instance details Defined in Control.Lens.Reified Associated Types type Rep (ReifiedIndexedFold i) :: Type -> Type # Methods tabulate :: (d -> Rep (ReifiedIndexedFold i) c) -> ReifiedIndexedFold i d c #
Strong (ReifiedIndexedFold i) Source #
Instance details Defined in Control.Lens.Reified Methods first' :: ReifiedIndexedFold i a b -> ReifiedIndexedFold i (a, c) (b, c) # second' :: ReifiedIndexedFold i a b -> ReifiedIndexedFold i (c, a) (c, b) #
Profunctor (ReifiedIndexedFold i) Source #
Instance details Defined in Control.Lens.Reified Methods dimap :: (a -> b) -> (c -> d) -> ReifiedIndexedFold i b c -> ReifiedIndexedFold i a d # lmap :: (a -> b) -> ReifiedIndexedFold i b c -> ReifiedIndexedFold i a c # rmap :: (b -> c) -> ReifiedIndexedFold i a b -> ReifiedIndexedFold i a c # (#.) :: forall a b c q. Coercible c b => q b c -> ReifiedIndexedFold i a b -> ReifiedIndexedFold i a c # (.#) :: forall a b c q. Coercible b a => ReifiedIndexedFold i b c -> q a b -> ReifiedIndexedFold i a c #
Sieve (ReifiedIndexedFold i) (Compose List ((,) i)) Source #
Instance details Defined in Control.Lens.Reified Methods sieve :: ReifiedIndexedFold i a b -> a -> Compose List ((,) i) b #
Functor (ReifiedIndexedFold i s) Source #
Instance details Defined in Control.Lens.Reified Methods fmap :: (a -> b) -> ReifiedIndexedFold i s a -> ReifiedIndexedFold i s b # (<$) :: a -> ReifiedIndexedFold i s b -> ReifiedIndexedFold i s a #
Alt (ReifiedIndexedFold i s) Source #
Instance details Defined in Control.Lens.Reified Methods (<!>) :: ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a # some :: Applicative (ReifiedIndexedFold i s) => ReifiedIndexedFold i s a -> ReifiedIndexedFold i s [a] # many :: Applicative (ReifiedIndexedFold i s) => ReifiedIndexedFold i s a -> ReifiedIndexedFold i s [a] #
Plus (ReifiedIndexedFold i s) Source #
Instance details Defined in Control.Lens.Reified Methods zero :: ReifiedIndexedFold i s a #
Monoid (ReifiedIndexedFold i s a) Source #
Instance details Defined in Control.Lens.Reified Methods mempty :: ReifiedIndexedFold i s a # mappend :: ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a # mconcat :: [ReifiedIndexedFold i s a] -> ReifiedIndexedFold i s a #
Semigroup (ReifiedIndexedFold i s a) Source #
Instance details Defined in Control.Lens.Reified Methods (<>) :: ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a # sconcat :: NonEmpty (ReifiedIndexedFold i s a) -> ReifiedIndexedFold i s a # stimes :: Integral b => b -> ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a #
type Rep (ReifiedIndexedFold i) Source #
Instance details Defined in Control.Lens.Reified type Rep (ReifiedIndexedFold i) = Compose List ((,) i)

newtype ReifiedSetter s t a b Source #

Reify a Setter so it can be stored safely in a container.

Constructors

Setter
Fields runSetter :: Setter s t a b

type ReifiedSetter' s a = ReifiedSetter s s a a Source #

type ReifiedSetter' = Simple ReifiedSetter

newtype ReifiedIndexedSetter i s t a b Source #

Reify an IndexedSetter so it can be stored safely in a container.

Constructors

IndexedSetter
Fields runIndexedSetter :: IndexedSetter i s t a b

type ReifiedIndexedSetter' i s a = ReifiedIndexedSetter i s s a a Source #

type ReifiedIndexedSetter' i = Simple (ReifiedIndexedSetter i)

newtype ReifiedIso s t a b Source #

Reify an Iso so it can be stored safely in a container.

Constructors

Iso
Fields runIso :: Iso s t a b

type ReifiedIso' s a = ReifiedIso s s a a Source #

type ReifiedIso' = Simple ReifiedIso

newtype ReifiedPrism s t a b Source #

Reify a Prism so it can be stored safely in a container.

Constructors

Prism
Fields runPrism :: Prism s t a b

type ReifiedPrism' s a = ReifiedPrism s s a a Source #

type ReifiedPrism' = Simple ReifiedPrism

pattern List :: IsList l => [Item l] -> l Source #

pattern Empty :: AsEmpty s => s Source #

pattern Strict :: Strict s t => t -> s Source #

pattern Lazy :: Strict t s => t -> s Source #

pattern Wrapped :: Rewrapped s s => Unwrapped s -> s Source #

pattern Swapped :: Swap p => p b a -> p a b Source #

pattern Reversed :: Reversing t => t -> t Source #

pattern Unwrapped :: Rewrapped t t => t -> Unwrapped t Source #

strict :: Strict lazy strict => Iso' lazy strict Source #

An Iso between the lazy variant of a structure and its strict counterpart.

strict = from lazy

only :: Eq a => a -> Prism' a () Source #

This Prism compares for exact equality with a given value.

>>> only 4 # ()
4

>>> 5 ^? only 4
Nothing

index :: (Indexable i p, Eq i, Applicative f) => i -> Optical' p (Indexed i) f a a Source #

This allows you to filter an IndexedFold, IndexedGetter, IndexedTraversal or IndexedLens based on an index.

>>> ["hello","the","world","!!!"]^?traversed.index 2
Just "world"

indices :: (Indexable i p, Applicative f) => (i -> Bool) -> Optical' p (Indexed i) f a a Source #

This allows you to filter an IndexedFold, IndexedGetter, IndexedTraversal or IndexedLens based on a predicate on the indices.

>>> ["hello","the","world","!!!"]^..traversed.indices even
["hello","world"]

>>> over (traversed.indices (>0)) Prelude.reverse $ ["He","was","stressed","o_O"]
["He","saw","desserts","O_o"]

lazy :: Strict lazy strict => Iso' strict lazy Source #

An Iso between the strict variant of a structure and its lazy counterpart.

lazy = from strict

uncons :: Cons s s a a => s -> Maybe (a, s) Source #

Attempt to extract the left-most element from a container, and a version of the container without that element.

>>> uncons []
Nothing

>>> uncons [a, b, c]
Just (a,[b,c])

from :: AnIso s t a b -> Iso b a t s Source #

Invert an isomorphism.

from (from l) ≡ l

to :: (Profunctor p, Contravariant f) => (s -> a) -> Optic' p f s a Source #

Build an (index-preserving) Getter from an arbitrary Haskell function.

to f . to g ≡ to (g . f)

a ^. to f ≡ f a

>>> a ^.to f
f a

>>> ("hello","world")^.to snd
"world"

>>> 5^.to succ
6

>>> (0, -5)^._2.to abs
5

to :: (s -> a) -> IndexPreservingGetter s a

cons :: Cons s s a a => a -> s -> s infixr 5 Source #

cons an element onto a container.

>>> cons a []
[a]

>>> cons a [b, c]
[a,b,c]

>>> cons a (Seq.fromList [])
fromList [a]

>>> cons a (Seq.fromList [b, c])
fromList [a,b,c]

snoc :: Snoc s s a a => s -> a -> s infixl 5 Source #

snoc an element onto the end of a container.

>>> snoc (Seq.fromList []) a
fromList [a]

>>> snoc (Seq.fromList [b, c]) a
fromList [b,c,a]

>>> snoc (LazyT.pack "hello") '!'
"hello!"

unsnoc :: Snoc s s a a => s -> Maybe (s, a) Source #

Attempt to extract the right-most element from a container, and a version of the container without that element.

>>> unsnoc (LazyT.pack "hello!")
Just ("hello",'!')

>>> unsnoc (LazyT.pack "")
Nothing

>>> unsnoc (Seq.fromList [b,c,a])
Just (fromList [b,c],a)

>>> unsnoc (Seq.fromList [])
Nothing

levels :: Applicative f => Traversing (->) f s t a b -> IndexedLensLike Int f s t (Level () a) (Level () b) Source #

This provides a breadth-first Traversal or Fold of the individual levels of any other Traversal or Fold via iterative deepening depth-first search. The levels are returned to you in a compressed format.

This can permit us to extract the levels directly:

>>> ["hello","world"]^..levels (traverse.traverse)
[Zero,Zero,One () 'h',Two 0 (One () 'e') (One () 'w'),Two 0 (One () 'l') (One () 'o'),Two 0 (One () 'l') (One () 'r'),Two 0 (One () 'o') (One () 'l'),One () 'd']

But we can also traverse them in turn:

>>> ["hello","world"]^..levels (traverse.traverse).traverse
"hewlolrold"

We can use this to traverse to a fixed depth in the tree of (<*>) used in the Traversal:

>>> ["hello","world"] & taking 4 (levels (traverse.traverse)).traverse %~ toUpper
["HEllo","World"]

Or we can use it to traverse the first n elements in found in that Traversal regardless of the depth at which they were found.

>>> ["hello","world"] & taking 4 (levels (traverse.traverse).traverse) %~ toUpper
["HELlo","World"]

The resulting Traversal of the levels which is indexed by the depth of each Level.

>>> ["dog","cat"]^@..levels (traverse.traverse) <. traverse
[(2,'d'),(3,'o'),(3,'c'),(4,'g'),(4,'a'),(5,'t')]

levels :: Traversal s t a b      -> IndexedTraversal Int s t (Level () a) (Level () b)
levels :: Fold s a               -> IndexedFold Int s (Level () a)

Note: Internally this is implemented by using an illegal Applicative, as it extracts information in an order that violates the Applicative laws.

chosen :: IndexPreservingLens (Either a a) (Either b b) a b Source #

This is a Lens that updates either side of an Either, where both sides have the same type.

chosen ≡ choosing id id

>>> Left a^.chosen
a

>>> Right a^.chosen
a

>>> Right "hello"^.chosen
"hello"

>>> Right a & chosen *~ b
Right (a * b)

chosen :: Lens (Either a a) (Either b b) a b
chosen f (Left a)  = Left <$> f a
chosen f (Right a) = Right <$> f a

traverseOf_ :: Functor f => Getting (Traversed r f) s a -> (a -> f r) -> s -> f () Source #

Traverse over all of the targets of a Fold (or Getter), computing an Applicative (or Functor)-based answer, but unlike traverseOf do not construct a new structure. traverseOf_ generalizes traverse_ to work over any Fold.

When passed a Getter, traverseOf_ can work over any Functor, but when passed a Fold, traverseOf_ requires an Applicative.

>>> traverseOf_ both putStrLn ("hello","world")
hello
world

traverse_ ≡ traverseOf_ folded

traverseOf_ _2 :: Functor f => (c -> f r) -> (d, c) -> f ()
traverseOf_ _Left :: Applicative f => (a -> f b) -> Either a c -> f ()

itraverseOf_ l ≡ traverseOf_ l . Indexed

The rather specific signature of traverseOf_ allows it to be used as if the signature was any of:

traverseOf_ :: Functor f     => Getter s a     -> (a -> f r) -> s -> f ()
traverseOf_ :: Applicative f => Fold s a       -> (a -> f r) -> s -> f ()
traverseOf_ :: Functor f     => Lens' s a      -> (a -> f r) -> s -> f ()
traverseOf_ :: Functor f     => Iso' s a       -> (a -> f r) -> s -> f ()
traverseOf_ :: Applicative f => Traversal' s a -> (a -> f r) -> s -> f ()
traverseOf_ :: Applicative f => Prism' s a     -> (a -> f r) -> s -> f ()

foldlOf' :: Getting (Endo (Endo r)) s a -> (r -> a -> r) -> r -> s -> r Source #

Fold over the elements of a structure, associating to the left, but strictly.

foldl' ≡ foldlOf' folded

foldlOf' :: Getter s a     -> (r -> a -> r) -> r -> s -> r
foldlOf' :: Fold s a       -> (r -> a -> r) -> r -> s -> r
foldlOf' :: Iso' s a       -> (r -> a -> r) -> r -> s -> r
foldlOf' :: Lens' s a      -> (r -> a -> r) -> r -> s -> r
foldlOf' :: Traversal' s a -> (r -> a -> r) -> r -> s -> r

mapMOf_ :: Monad m => Getting (Sequenced r m) s a -> (a -> m r) -> s -> m () Source #

Map each target of a Fold on a structure to a monadic action, evaluate these actions from left to right, and ignore the results.

>>> mapMOf_ both putStrLn ("hello","world")
hello
world

mapM_ ≡ mapMOf_ folded

mapMOf_ :: Monad m => Getter s a     -> (a -> m r) -> s -> m ()
mapMOf_ :: Monad m => Fold s a       -> (a -> m r) -> s -> m ()
mapMOf_ :: Monad m => Lens' s a      -> (a -> m r) -> s -> m ()
mapMOf_ :: Monad m => Iso' s a       -> (a -> m r) -> s -> m ()
mapMOf_ :: Monad m => Traversal' s a -> (a -> m r) -> s -> m ()
mapMOf_ :: Monad m => Prism' s a     -> (a -> m r) -> s -> m ()

ifor :: (TraversableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f (t b) #

Traverse with an index (and the arguments flipped).

for a ≡ ifor a . const
ifor ≡ flip itraverse

imapM :: (TraversableWithIndex i t, Monad m) => (i -> a -> m b) -> t a -> m (t b) #

Map each element of a structure to a monadic action, evaluate these actions from left to right, and collect the results, with access the index.

When you don't need access to the index mapM is more liberal in what it can accept.

mapM ≡ imapM . const

iforM :: (TraversableWithIndex i t, Monad m) => t a -> (i -> a -> m b) -> m (t b) #

Map each element of a structure to a monadic action, evaluate these actions from left to right, and collect the results, with access its position (and the arguments flipped).

forM a ≡ iforM a . const
iforM ≡ flip imapM

imapAccumR :: TraversableWithIndex i t => (i -> s -> a -> (s, b)) -> s -> t a -> (s, t b) #

Generalizes mapAccumR to add access to the index.

imapAccumR accumulates state from right to left.

mapAccumR ≡ imapAccumR . const

imapAccumL :: TraversableWithIndex i t => (i -> s -> a -> (s, b)) -> s -> t a -> (s, t b) #

Generalizes mapAccumL to add access to the index.

imapAccumL accumulates state from left to right.

mapAccumL ≡ imapAccumL . const

iany :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool #

Return whether or not any element in a container satisfies a predicate, with access to the index i.

When you don't need access to the index then any is more flexible in what it accepts.

any ≡ iany . const

iall :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool #

Return whether or not all elements in a container satisfy a predicate, with access to the index i.

When you don't need access to the index then all is more flexible in what it accepts.

all ≡ iall . const

inone :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool #

Return whether or not none of the elements in a container satisfy a predicate, with access to the index i.

When you don't need access to the index then none is more flexible in what it accepts.

none ≡ inone . const
inone f ≡ not . iany f

none :: Foldable f => (a -> Bool) -> f a -> Bool #

Determines whether no elements of the structure satisfy the predicate.

none f ≡ not . any f

itraverse_ :: (FoldableWithIndex i t, Applicative f) => (i -> a -> f b) -> t a -> f () #

Traverse elements with access to the index i, discarding the results.

When you don't need access to the index then traverse_ is more flexible in what it accepts.

traverse_ l = itraverse . const

ifor_ :: (FoldableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f () #

Traverse elements with access to the index i, discarding the results (with the arguments flipped).

ifor_ ≡ flip itraverse_

When you don't need access to the index then for_ is more flexible in what it accepts.

for_ a ≡ ifor_ a . const

imapM_ :: (FoldableWithIndex i t, Monad m) => (i -> a -> m b) -> t a -> m () #

Run monadic actions for each target of an IndexedFold or IndexedTraversal with access to the index, discarding the results.

When you don't need access to the index then mapMOf_ is more flexible in what it accepts.

mapM_ ≡ imapM . const

iforM_ :: (FoldableWithIndex i t, Monad m) => t a -> (i -> a -> m b) -> m () #

Run monadic actions for each target of an IndexedFold or IndexedTraversal with access to the index, discarding the results (with the arguments flipped).

iforM_ ≡ flip imapM_

When you don't need access to the index then forM_ is more flexible in what it accepts.

forM_ a ≡ iforM a . const

iconcatMap :: FoldableWithIndex i f => (i -> a -> [b]) -> f a -> [b] #

Concatenate the results of a function of the elements of an indexed container with access to the index.

When you don't need access to the index then concatMap is more flexible in what it accepts.

concatMap ≡ iconcatMap . const
iconcatMap ≡ ifoldMap

ifind :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Maybe (i, a) #

Searches a container with a predicate that is also supplied the index, returning the left-most element of the structure matching the predicate, or Nothing if there is no such element.

When you don't need access to the index then find is more flexible in what it accepts.

find ≡ ifind . const

ifoldrM :: (FoldableWithIndex i f, Monad m) => (i -> a -> b -> m b) -> b -> f a -> m b #

Monadic fold right over the elements of a structure with an index.

When you don't need access to the index then foldrM is more flexible in what it accepts.

foldrM ≡ ifoldrM . const

ifoldlM :: (FoldableWithIndex i f, Monad m) => (i -> b -> a -> m b) -> b -> f a -> m b #

Monadic fold over the elements of a structure with an index, associating to the left.

When you don't need access to the index then foldlM is more flexible in what it accepts.

foldlM ≡ ifoldlM . const

itoList :: FoldableWithIndex i f => f a -> [(i, a)] #

Extract the key-value pairs from a structure.

When you don't need access to the indices in the result, then toList is more flexible in what it accepts.

toList ≡ map snd . itoList

swapped :: Swap p => Iso (p a b) (p c d) (p b a) (p d c) Source #

swapped . swapped ≡ id
first f . swapped = swapped . second f
second g . swapped = swapped . first g
bimap f g . swapped = swapped . bimap g f

>>> (1,2)^.swapped
(2,1)

foldBy :: Foldable t => (a -> a -> a) -> a -> t a -> a #

Fold a value using its Foldable instance using explicitly provided Monoid operations. This is like fold where the Monoid instance can be manually specified.

foldBy mappend mempty ≡ fold

>>> foldBy (++) [] ["hello","world"]
"helloworld"

foldMapBy :: Foldable t => (r -> r -> r) -> r -> (a -> r) -> t a -> r #

Fold a value using its Foldable instance using explicitly provided Monoid operations. This is like foldMap where the Monoid instance can be manually specified.

foldMapBy mappend mempty ≡ foldMap

>>> foldMapBy (+) 0 length ["hello","world"]
10

traverseBy :: Traversable t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (a -> f b) -> t a -> f (t b) #

Traverse a container using its Traversable instance using explicitly provided Applicative operations. This is like traverse where the Applicative instance can be manually specified.

sequenceBy :: Traversable t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> t (f a) -> f (t a) #

Sequence a container using its Traversable instance using explicitly provided Applicative operations. This is like sequence where the Applicative instance can be manually specified.

over :: ASetter s t a b -> (a -> b) -> s -> t Source #

Modify the target of a Lens or all the targets of a Setter or Traversal with a function.

fmap ≡ over mapped
fmapDefault ≡ over traverse
sets . over ≡ id
over . sets ≡ id

Given any valid Setter l, you can also rely on the law:

over l f . over l g = over l (f . g)

e.g.

>>> over mapped f (over mapped g [a,b,c]) == over mapped (f . g) [a,b,c]
True

Another way to view over is to say that it transforms a Setter into a "semantic editor combinator".

>>> over mapped f (Just a)
Just (f a)

>>> over mapped (*10) [1,2,3]
[10,20,30]

>>> over _1 f (a,b)
(f a,b)

>>> over _1 show (10,20)
("10",20)

over :: Setter s t a b -> (a -> b) -> s -> t
over :: ASetter s t a b -> (a -> b) -> s -> t

elements :: Traversable t => (Int -> Bool) -> IndexedTraversal' Int (t a) a Source #

Traverse elements of a Traversable container where their ordinal positions match a predicate.

elements ≡ elementsOf traverse

transform :: Plated a => (a -> a) -> a -> a Source #

Transform every element in the tree, in a bottom-up manner.

For example, replacing negative literals with literals:

negLits = transform $ \x -> case x of
  Neg (Lit i) -> Lit (negate i)
  _           -> x

set :: ASetter s t a b -> b -> s -> t Source #

Replace the target of a Lens or all of the targets of a Setter or Traversal with a constant value.

(<$) ≡ set mapped

>>> set _2 "hello" (1,())
(1,"hello")

>>> set mapped () [1,2,3,4]
[(),(),(),()]

Note: Attempting to set a Fold or Getter will fail at compile time with an relatively nice error message.

set :: Setter s t a b    -> b -> s -> t
set :: Iso s t a b       -> b -> s -> t
set :: Lens s t a b      -> b -> s -> t
set :: Traversal s t a b -> b -> s -> t

sans :: At m => Index m -> m -> m Source #

Delete the value associated with a key in a Map-like container

sans k = at k .~ Nothing

iat :: At m => Index m -> IndexedLens' (Index m) m (Maybe (IxValue m)) Source #

An indexed version of at.

>>> Map.fromList [(1,"world")] ^@. iat 1
(1,Just "world")

>>> iat 1 %@~ (\i x -> if odd i then Just "hello" else Nothing) $ Map.empty
fromList [(1,"hello")]

>>> iat 2 %@~ (\i x -> if odd i then Just "hello" else Nothing) $ Map.empty
fromList []

ixAt :: At m => Index m -> Traversal' m (IxValue m) Source #

A definition of ix for types with an At instance. This is the default if you don't specify a definition for ix.

iix :: Ixed m => Index m -> IndexedTraversal' (Index m) m (IxValue m) Source #

An indexed version of ix.

>>> Seq.fromList [a,b,c,d] & iix 2 %@~ f'
fromList [a,b,f' 2 c,d]

>>> Seq.fromList [a,b,c,d] & iix 2 .@~ h
fromList [a,b,h 2,d]

>>> Seq.fromList [a,b,c,d] ^@? iix 2
Just (2,c)

>>> Seq.fromList [] ^@? iix 2
Nothing

icontains :: Contains m => Index m -> IndexedLens' (Index m) m Bool Source #

An indexed version of contains.

>>> IntSet.fromList [1,2,3,4] ^@. icontains 3
(3,True)

>>> IntSet.fromList [1,2,3,4] ^@. icontains 5
(5,False)

>>> IntSet.fromList [1,2,3,4] & icontains 3 %@~ \i x -> if odd i then not x else x
fromList [1,2,4]

>>> IntSet.fromList [1,2,3,4] & icontains 3 %@~ \i x -> if even i then not x else x
fromList [1,2,3,4]

_head :: Cons s s a a => Traversal' s a Source #

A Traversal reading and writing to the head of a non-empty container.

>>> [a,b,c]^? _head
Just a

>>> [a,b,c] & _head .~ d
[d,b,c]

>>> [a,b,c] & _head %~ f
[f a,b,c]

>>> [] & _head %~ f
[]

>>> [1,2,3]^?!_head
1

>>> []^?_head
Nothing

>>> [1,2]^?_head
Just 1

>>> [] & _head .~ 1
[]

>>> [0] & _head .~ 2
[2]

>>> [0,1] & _head .~ 2
[2,1]

This isn't limited to lists.

For instance you can also traverse the head of a Seq:

>>> Seq.fromList [a,b,c,d] & _head %~ f
fromList [f a,b,c,d]

>>> Seq.fromList [] ^? _head
Nothing

>>> Seq.fromList [a,b,c,d] ^? _head
Just a

_head :: Traversal' [a] a
_head :: Traversal' (Seq a) a
_head :: Traversal' (Vector a) a

_tail :: Cons s s a a => Traversal' s s Source #

A Traversal reading and writing to the tail of a non-empty container.

>>> [a,b] & _tail .~ [c,d,e]
[a,c,d,e]

>>> [] & _tail .~ [a,b]
[]

>>> [a,b,c,d,e] & _tail.traverse %~ f
[a,f b,f c,f d,f e]

>>> [1,2] & _tail .~ [3,4,5]
[1,3,4,5]

>>> [] & _tail .~ [1,2]
[]

>>> [a,b,c]^?_tail
Just [b,c]

>>> [1,2]^?!_tail
[2]

>>> "hello"^._tail
"ello"

>>> ""^._tail
""

This isn't limited to lists. For instance you can also traverse the tail of a Seq.

>>> Seq.fromList [a,b] & _tail .~ Seq.fromList [c,d,e]
fromList [a,c,d,e]

>>> Seq.fromList [a,b,c] ^? _tail
Just (fromList [b,c])

>>> Seq.fromList [] ^? _tail
Nothing

_tail :: Traversal' [a] [a]
_tail :: Traversal' (Seq a) (Seq a)
_tail :: Traversal' (Vector a) (Vector a)

_init :: Snoc s s a a => Traversal' s s Source #

A Traversal reading and replacing all but the a last element of a non-empty container.

>>> [a,b,c,d]^?_init
Just [a,b,c]

>>> []^?_init
Nothing

>>> [a,b] & _init .~ [c,d,e]
[c,d,e,b]

>>> [] & _init .~ [a,b]
[]

>>> [a,b,c,d] & _init.traverse %~ f
[f a,f b,f c,d]

>>> [1,2,3]^?_init
Just [1,2]

>>> [1,2,3,4]^?!_init
[1,2,3]

>>> "hello"^._init
"hell"

>>> ""^._init
""

_init :: Traversal' [a] [a]
_init :: Traversal' (Seq a) (Seq a)
_init :: Traversal' (Vector a) (Vector a)

_last :: Snoc s s a a => Traversal' s a Source #

A Traversal reading and writing to the last element of a non-empty container.

>>> [a,b,c]^?!_last
c

>>> []^?_last
Nothing

>>> [a,b,c] & _last %~ f
[a,b,f c]

>>> [1,2]^?_last
Just 2

>>> [] & _last .~ 1
[]

>>> [0] & _last .~ 2
[2]

>>> [0,1] & _last .~ 2
[0,2]

This Traversal is not limited to lists, however. We can also work with other containers, such as a Vector.

>>> Vector.fromList "abcde" ^? _last
Just 'e'

>>> Vector.empty ^? _last
Nothing

>>> (Vector.fromList "abcde" & _last .~ 'Q') == Vector.fromList "abcdQ"
True

_last :: Traversal' [a] a
_last :: Traversal' (Seq a) a
_last :: Traversal' (Vector a) a

simply :: forall p f s a rep (r :: TYPE rep). (Optic' p f s a -> r) -> Optic' p f s a -> r Source #

This is an adverb that can be used to modify many other Lens combinators to make them require simple lenses, simple traversals, simple prisms or simple isos as input.

runEq :: AnEquality s t a b -> Identical s t a b Source #

Extract a witness of type Equality.

substEq :: forall s t a b rep (r :: TYPE rep). AnEquality s t a b -> ((s ~ a, t ~ b) => r) -> r Source #

Substituting types with Equality.

mapEq :: forall k1 k2 (s :: k1) (t :: k2) (a :: k1) (b :: k2) (f :: k1 -> Type). AnEquality s t a b -> f s -> f a Source #

We can use Equality to do substitution into anything.

fromEq :: AnEquality s t a b -> Equality b a t s Source #

Equality is symmetric.

simple :: Equality' a a Source #

Composition with this isomorphism is occasionally useful when your Lens, Traversal or Iso has a constraint on an unused argument to force that argument to agree with the type of a used argument and avoid ScopedTypeVariables or other ugliness.

equality :: (s :~: a) -> (b :~: t) -> Equality s t a b Source #

Construct an Equality from explicit equality evidence.

equality' :: (a :~: b) -> Equality' a b Source #

A Simple version of equality

withEquality :: forall s t a b rep (r :: TYPE rep). AnEquality s t a b -> ((s :~: a) -> (b :~: t) -> r) -> r Source #

A version of substEq that provides explicit, rather than implicit, equality evidence.

underEquality :: AnEquality s t a b -> p t s -> p b a Source #

The opposite of working overEquality is working underEquality.

overEquality :: AnEquality s t a b -> p a b -> p s t Source #

Recover a "profunctor lens" form of equality. Reverses fromLeibniz.

fromLeibniz :: (Identical a b a b -> Identical a b s t) -> Equality s t a b Source #

Convert a "profunctor lens" form of equality to an equality. Reverses overEquality.

The type should be understood as

fromLeibniz :: (forall p. p a b -> p s t) -> Equality s t a b

fromLeibniz' :: ((s :~: s) -> s :~: a) -> Equality' s a Source #

Convert Leibniz equality to equality. Reverses mapEq in Simple cases.

The type should be understood as

fromLeibniz' :: (forall f. f s -> f a) -> Equality' s a

cloneEquality :: AnEquality s t a b -> Equality s t a b Source #

pre :: Getting (First a) s a -> IndexPreservingGetter s (Maybe a) Source #

This converts a Fold to a IndexPreservingGetter that returns the first element, if it exists, as a Maybe.

pre :: Getter s a     -> IndexPreservingGetter s (Maybe a)
pre :: Fold s a       -> IndexPreservingGetter s (Maybe a)
pre :: Traversal' s a -> IndexPreservingGetter s (Maybe a)
pre :: Lens' s a      -> IndexPreservingGetter s (Maybe a)
pre :: Iso' s a       -> IndexPreservingGetter s (Maybe a)
pre :: Prism' s a     -> IndexPreservingGetter s (Maybe a)

ipre :: IndexedGetting i (First (i, a)) s a -> IndexPreservingGetter s (Maybe (i, a)) Source #

This converts an IndexedFold to an IndexPreservingGetter that returns the first index and element, if they exist, as a Maybe.

ipre :: IndexedGetter i s a     -> IndexPreservingGetter s (Maybe (i, a))
ipre :: IndexedFold i s a       -> IndexPreservingGetter s (Maybe (i, a))
ipre :: IndexedTraversal' i s a -> IndexPreservingGetter s (Maybe (i, a))
ipre :: IndexedLens' i s a      -> IndexPreservingGetter s (Maybe (i, a))

preview :: MonadReader s m => Getting (First a) s a -> m (Maybe a) Source #

Retrieve the first value targeted by a Fold or Traversal (or Just the result from a Getter or Lens). See also firstOf and ^?, which are similar with some subtle differences (explained below).

listToMaybe . toList ≡ preview folded

preview = view . pre

Unlike ^?, this function uses a MonadReader to read the value to be focused in on. This allows one to pass the value as the last argument by using the MonadReader instance for (->) s However, it may also be used as part of some deeply nested transformer stack.

preview uses a monoidal value to obtain the result. This means that it generally has good performance, but can occasionally cause space leaks or even stack overflows on some data types. There is another function, firstOf, which avoids these issues at the cost of a slight constant performance cost and a little less flexibility.

It may be helpful to think of preview as having one of the following more specialized types:

preview :: Getter s a     -> s -> Maybe a
preview :: Fold s a       -> s -> Maybe a
preview :: Lens' s a      -> s -> Maybe a
preview :: Iso' s a       -> s -> Maybe a
preview :: Traversal' s a -> s -> Maybe a

preview :: MonadReader s m => Getter s a     -> m (Maybe a)
preview :: MonadReader s m => Fold s a       -> m (Maybe a)
preview :: MonadReader s m => Lens' s a      -> m (Maybe a)
preview :: MonadReader s m => Iso' s a       -> m (Maybe a)
preview :: MonadReader s m => Traversal' s a -> m (Maybe a)

previews :: MonadReader s m => Getting (First r) s a -> (a -> r) -> m (Maybe r) Source #

Retrieve a function of the first value targeted by a Fold or Traversal (or Just the result from a Getter or Lens).

This is usually applied in the Reader Monad (->) s.

ipreview :: MonadReader s m => IndexedGetting i (First (i, a)) s a -> m (Maybe (i, a)) Source #

Retrieve the first index and value targeted by a Fold or Traversal (or Just the result from a Getter or Lens). See also (^@?).

ipreview = view . ipre

This is usually applied in the Reader Monad (->) s.

ipreview :: IndexedGetter i s a     -> s -> Maybe (i, a)
ipreview :: IndexedFold i s a       -> s -> Maybe (i, a)
ipreview :: IndexedLens' i s a      -> s -> Maybe (i, a)
ipreview :: IndexedTraversal' i s a -> s -> Maybe (i, a)

However, it may be useful to think of its full generality when working with a Monad transformer stack:

ipreview :: MonadReader s m => IndexedGetter s a     -> m (Maybe (i, a))
ipreview :: MonadReader s m => IndexedFold s a       -> m (Maybe (i, a))
ipreview :: MonadReader s m => IndexedLens' s a      -> m (Maybe (i, a))
ipreview :: MonadReader s m => IndexedTraversal' s a -> m (Maybe (i, a))

ipreviews :: MonadReader s m => IndexedGetting i (First r) s a -> (i -> a -> r) -> m (Maybe r) Source #

Retrieve a function of the first index and value targeted by an IndexedFold or IndexedTraversal (or Just the result from an IndexedGetter or IndexedLens). See also (^@?).

ipreviews = views . ipre

This is usually applied in the Reader Monad (->) s.

ipreviews :: IndexedGetter i s a     -> (i -> a -> r) -> s -> Maybe r
ipreviews :: IndexedFold i s a       -> (i -> a -> r) -> s -> Maybe r
ipreviews :: IndexedLens' i s a      -> (i -> a -> r) -> s -> Maybe r
ipreviews :: IndexedTraversal' i s a -> (i -> a -> r) -> s -> Maybe r

However, it may be useful to think of its full generality when working with a Monad transformer stack:

ipreviews :: MonadReader s m => IndexedGetter i s a     -> (i -> a -> r) -> m (Maybe r)
ipreviews :: MonadReader s m => IndexedFold i s a       -> (i -> a -> r) -> m (Maybe r)
ipreviews :: MonadReader s m => IndexedLens' i s a      -> (i -> a -> r) -> m (Maybe r)
ipreviews :: MonadReader s m => IndexedTraversal' i s a -> (i -> a -> r) -> m (Maybe r)

preuse :: MonadState s m => Getting (First a) s a -> m (Maybe a) Source #

Retrieve the first value targeted by a Fold or Traversal (or Just the result from a Getter or Lens) into the current state.

preuse = use . pre

preuse :: MonadState s m => Getter s a     -> m (Maybe a)
preuse :: MonadState s m => Fold s a       -> m (Maybe a)
preuse :: MonadState s m => Lens' s a      -> m (Maybe a)
preuse :: MonadState s m => Iso' s a       -> m (Maybe a)
preuse :: MonadState s m => Traversal' s a -> m (Maybe a)

preuses :: MonadState s m => Getting (First r) s a -> (a -> r) -> m (Maybe r) Source #

Retrieve a function of the first value targeted by a Fold or Traversal (or Just the result from a Getter or Lens) into the current state.

preuses = uses . pre

preuses :: MonadState s m => Getter s a     -> (a -> r) -> m (Maybe r)
preuses :: MonadState s m => Fold s a       -> (a -> r) -> m (Maybe r)
preuses :: MonadState s m => Lens' s a      -> (a -> r) -> m (Maybe r)
preuses :: MonadState s m => Iso' s a       -> (a -> r) -> m (Maybe r)
preuses :: MonadState s m => Traversal' s a -> (a -> r) -> m (Maybe r)

ipreuse :: MonadState s m => IndexedGetting i (First (i, a)) s a -> m (Maybe (i, a)) Source #

Retrieve the first index and value targeted by an IndexedFold or IndexedTraversal (or Just the index and result from an IndexedGetter or IndexedLens) into the current state.

ipreuse = use . ipre

ipreuse :: MonadState s m => IndexedGetter i s a     -> m (Maybe (i, a))
ipreuse :: MonadState s m => IndexedFold i s a       -> m (Maybe (i, a))
ipreuse :: MonadState s m => IndexedLens' i s a      -> m (Maybe (i, a))
ipreuse :: MonadState s m => IndexedTraversal' i s a -> m (Maybe (i, a))

ipreuses :: MonadState s m => IndexedGetting i (First r) s a -> (i -> a -> r) -> m (Maybe r) Source #

Retrieve a function of the first index and value targeted by an IndexedFold or IndexedTraversal (or a function of Just the index and result from an IndexedGetter or IndexedLens) into the current state.

ipreuses = uses . ipre

ipreuses :: MonadState s m => IndexedGetter i s a     -> (i -> a -> r) -> m (Maybe r)
ipreuses :: MonadState s m => IndexedFold i s a       -> (i -> a -> r) -> m (Maybe r)
ipreuses :: MonadState s m => IndexedLens' i s a      -> (i -> a -> r) -> m (Maybe r)
ipreuses :: MonadState s m => IndexedTraversal' i s a -> (i -> a -> r) -> m (Maybe r)

has :: Getting Any s a -> s -> Bool Source #

Check to see if this Fold or Traversal matches 1 or more entries.

>>> has (element 0) []
False

>>> has _Left (Left 12)
True

>>> has _Right (Left 12)
False

This will always return True for a Lens or Getter.

>>> has _1 ("hello","world")
True

has :: Getter s a     -> s -> Bool
has :: Fold s a       -> s -> Bool
has :: Iso' s a       -> s -> Bool
has :: Lens' s a      -> s -> Bool
has :: Traversal' s a -> s -> Bool

hasn't :: Getting All s a -> s -> Bool Source #

Check to see if this Fold or Traversal has no matches.

>>> hasn't _Left (Right 12)
True

>>> hasn't _Left (Left 12)
False

folding :: Foldable f => (s -> f a) -> Fold s a Source #

Obtain a Fold by lifting an operation that returns a Foldable result.

This can be useful to lift operations from Data.List and elsewhere into a Fold.

>>> [1,2,3,4]^..folding reverse
[4,3,2,1]

ifolding :: (Foldable f, Indexable i p, Contravariant g, Applicative g) => (s -> f (i, a)) -> Over p g s t a b Source #

foldring :: (Contravariant f, Applicative f) => ((a -> f a -> f a) -> f a -> s -> f a) -> LensLike f s t a b Source #

Obtain a Fold by lifting foldr like function.

>>> [1,2,3,4]^..foldring foldr
[1,2,3,4]

ifoldring :: (Indexable i p, Contravariant f, Applicative f) => ((i -> a -> f a -> f a) -> f a -> s -> f a) -> Over p f s t a b Source #

Obtain FoldWithIndex by lifting ifoldr like function.

folded :: Foldable f => IndexedFold Int (f a) a Source #

Obtain a Fold from any Foldable indexed by ordinal position.

>>> Just 3^..folded
[3]

>>> Nothing^..folded
[]

>>> [(1,2),(3,4)]^..folded.both
[1,2,3,4]

folded64 :: Foldable f => IndexedFold Int64 (f a) a Source #

Obtain a Fold from any Foldable indexed by ordinal position.

unfolded :: (b -> Maybe (a, b)) -> Fold b a Source #

Build a Fold that unfolds its values from a seed.

unfoldr ≡ toListOf . unfolded

>>> 10^..unfolded (\b -> if b == 0 then Nothing else Just (b, b-1))
[10,9,8,7,6,5,4,3,2,1]

iterated :: Apply f => (a -> a) -> LensLike' f a a Source #

x ^. iterated f returns an infinite Fold1 of repeated applications of f to x.

toListOf (iterated f) a ≡ iterate f a

iterated :: (a -> a) -> Fold1 a a

filtered :: (Choice p, Applicative f) => (a -> Bool) -> Optic' p f a a Source #

Obtain a Fold that can be composed with to filter another Lens, Iso, Getter, Fold (or Traversal).

Note: This is not a legal Traversal, unless you are very careful not to invalidate the predicate on the target.

Note: This is also not a legal Prism, unless you are very careful not to inject a value that fails the predicate.

As a counter example, consider that given evens = filtered even the second Traversal law is violated:

over evens succ . over evens succ /= over evens (succ . succ)

So, in order for this to qualify as a legal Traversal you can only use it for actions that preserve the result of the predicate!

>>> [1..10]^..folded.filtered even
[2,4,6,8,10]

This will preserve an index if it is present.

filteredBy :: (Indexable i p, Applicative f) => Getting (First i) a i -> p a (f a) -> a -> f a Source #

Obtain a potentially empty IndexedTraversal by taking the first element from another, potentially empty Fold and using it as an index.

The resulting optic can be composed with to filter another Lens, Iso, Getter, Fold (or Traversal).

>>> [(Just 2, 3), (Nothing, 4)] & mapped . filteredBy (_1 . _Just) <. _2 %@~ (*) :: [(Maybe Int, Int)]
[(Just 2,6),(Nothing,4)]

filteredBy :: Fold a i -> IndexedTraversal' i a a

Note: As with filtered, this is not a legal IndexedTraversal, unless you are very careful not to invalidate the predicate on the target!

backwards :: (Profunctor p, Profunctor q) => Optical p q (Backwards f) s t a b -> Optical p q f s t a b Source #

This allows you to traverse the elements of a pretty much any LensLike construction in the opposite order.

This will preserve indexes on Indexed types and will give you the elements of a (finite) Fold or Traversal in the opposite order.

This has no practical impact on a Getter, Setter, Lens or Iso.

NB: To write back through an Iso, you want to use from. Similarly, to write back through an Prism, you want to use re.

repeated :: Apply f => LensLike' f a a Source #

Form a Fold1 by repeating the input forever.

repeat ≡ toListOf repeated

>>> timingOut $ 5^..taking 20 repeated
[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]

repeated :: Fold1 a a

replicated :: Int -> Fold a a Source #

A Fold that replicates its input n times.

replicate n ≡ toListOf (replicated n)

>>> 5^..replicated 20
[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]

cycled :: Apply f => LensLike f s t a b -> LensLike f s t a b Source #

Transform a non-empty Fold into a Fold1 that loops over its elements over and over.

>>> timingOut $ [1,2,3]^..taking 7 (cycled traverse)
[1,2,3,1,2,3,1]

cycled :: Fold1 s a -> Fold1 s a

takingWhile :: (Conjoined p, Applicative f) => (a -> Bool) -> Over p (TakingWhile p f a a) s t a a -> Over p f s t a a Source #

Obtain a Fold by taking elements from another Fold, Lens, Iso, Getter or Traversal while a predicate holds.

takeWhile p ≡ toListOf (takingWhile p folded)

>>> timingOut $ toListOf (takingWhile (<=3) folded) [1..]
[1,2,3]

takingWhile :: (a -> Bool) -> Fold s a                         -> Fold s a
takingWhile :: (a -> Bool) -> Getter s a                       -> Fold s a
takingWhile :: (a -> Bool) -> Traversal' s a                   -> Fold s a -- * See note below
takingWhile :: (a -> Bool) -> Lens' s a                        -> Fold s a -- * See note below
takingWhile :: (a -> Bool) -> Prism' s a                       -> Fold s a -- * See note below
takingWhile :: (a -> Bool) -> Iso' s a                         -> Fold s a -- * See note below
takingWhile :: (a -> Bool) -> IndexedTraversal' i s a          -> IndexedFold i s a -- * See note below
takingWhile :: (a -> Bool) -> IndexedLens' i s a               -> IndexedFold i s a -- * See note below
takingWhile :: (a -> Bool) -> IndexedFold i s a                -> IndexedFold i s a
takingWhile :: (a -> Bool) -> IndexedGetter i s a              -> IndexedFold i s a

Note: When applied to a Traversal, takingWhile yields something that can be used as if it were a Traversal, but which is not a Traversal per the laws, unless you are careful to ensure that you do not invalidate the predicate when writing back through it.

droppingWhile :: (Conjoined p, Profunctor q, Applicative f) => (a -> Bool) -> Optical p q (Compose (State Bool) f) s t a a -> Optical p q f s t a a Source #

Obtain a Fold by dropping elements from another Fold, Lens, Iso, Getter or Traversal while a predicate holds.

dropWhile p ≡ toListOf (droppingWhile p folded)

>>> toListOf (droppingWhile (<=3) folded) [1..6]
[4,5,6]

>>> toListOf (droppingWhile (<=3) folded) [1,6,1]
[6,1]

droppingWhile :: (a -> Bool) -> Fold s a                         -> Fold s a
droppingWhile :: (a -> Bool) -> Getter s a                       -> Fold s a
droppingWhile :: (a -> Bool) -> Traversal' s a                   -> Fold s a                -- see notes
droppingWhile :: (a -> Bool) -> Lens' s a                        -> Fold s a                -- see notes
droppingWhile :: (a -> Bool) -> Prism' s a                       -> Fold s a                -- see notes
droppingWhile :: (a -> Bool) -> Iso' s a                         -> Fold s a                -- see notes

droppingWhile :: (a -> Bool) -> IndexPreservingTraversal' s a    -> IndexPreservingFold s a -- see notes
droppingWhile :: (a -> Bool) -> IndexPreservingLens' s a         -> IndexPreservingFold s a -- see notes
droppingWhile :: (a -> Bool) -> IndexPreservingGetter s a        -> IndexPreservingFold s a
droppingWhile :: (a -> Bool) -> IndexPreservingFold s a          -> IndexPreservingFold s a

droppingWhile :: (a -> Bool) -> IndexedTraversal' i s a          -> IndexedFold i s a       -- see notes
droppingWhile :: (a -> Bool) -> IndexedLens' i s a               -> IndexedFold i s a       -- see notes
droppingWhile :: (a -> Bool) -> IndexedGetter i s a              -> IndexedFold i s a
droppingWhile :: (a -> Bool) -> IndexedFold i s a                -> IndexedFold i s a

Note: Many uses of this combinator will yield something that meets the types, but not the laws of a valid Traversal or IndexedTraversal. The Traversal and IndexedTraversal laws are only satisfied if the new values you assign to the first target also does not pass the predicate! Otherwise subsequent traversals will visit fewer elements and Traversal fusion is not sound.

So for any traversal t and predicate p, droppingWhile p t may not be lawful, but (dropping 1 . droppingWhile p) t is. For example:

>>> let l  :: Traversal' [Int] Int; l  = droppingWhile (<= 1) traverse
>>> let l' :: Traversal' [Int] Int; l' = dropping 1 l

l is not a lawful setter because over l f . over l g ≢ over l (f . g):

>>> [1,2,3] & l .~ 0 & l .~ 4
[1,0,0]
>>> [1,2,3] & l .~ 4
[1,4,4]

l' on the other hand behaves lawfully:

>>> [1,2,3] & l' .~ 0 & l' .~ 4
[1,2,4]
>>> [1,2,3] & l' .~ 4
[1,2,4]

worded :: Applicative f => IndexedLensLike' Int f String String Source #

A Fold over the individual words of a String.

worded :: Fold String String
worded :: Traversal' String String

worded :: IndexedFold Int String String
worded :: IndexedTraversal' Int String String

Note: This function type-checks as a Traversal but it doesn't satisfy the laws. It's only valid to use it when you don't insert any whitespace characters while traversing, and if your original String contains only isolated space characters (and no other characters that count as space, such as non-breaking spaces).

lined :: Applicative f => IndexedLensLike' Int f String String Source #

A Fold over the individual lines of a String.

lined :: Fold String String
lined :: Traversal' String String

lined :: IndexedFold Int String String
lined :: IndexedTraversal' Int String String

Note: This function type-checks as a Traversal but it doesn't satisfy the laws. It's only valid to use it when you don't insert any newline characters while traversing, and if your original String contains only isolated newline characters.

foldMapOf :: Getting r s a -> (a -> r) -> s -> r Source #

Map each part of a structure viewed through a Lens, Getter, Fold or Traversal to a monoid and combine the results.

>>> foldMapOf (folded . both . _Just) Sum [(Just 21, Just 21)]
Sum {getSum = 42}

foldMap = foldMapOf folded

foldMapOf ≡ views
ifoldMapOf l = foldMapOf l . Indexed

foldMapOf ::                Getter s a      -> (a -> r) -> s -> r
foldMapOf :: Monoid r    => Fold s a        -> (a -> r) -> s -> r
foldMapOf :: Semigroup r => Fold1 s a       -> (a -> r) -> s -> r
foldMapOf ::                Lens' s a       -> (a -> r) -> s -> r
foldMapOf ::                Iso' s a        -> (a -> r) -> s -> r
foldMapOf :: Monoid r    => Traversal' s a  -> (a -> r) -> s -> r
foldMapOf :: Semigroup r => Traversal1' s a -> (a -> r) -> s -> r
foldMapOf :: Monoid r    => Prism' s a      -> (a -> r) -> s -> r

foldMapOf :: Getting r s a -> (a -> r) -> s -> r

foldOf :: Getting a s a -> s -> a Source #

Combine the elements of a structure viewed through a Lens, Getter, Fold or Traversal using a monoid.

>>> foldOf (folded.folded) [[Sum 1,Sum 4],[Sum 8, Sum 8],[Sum 21]]
Sum {getSum = 42}

fold = foldOf folded

foldOf ≡ view

foldOf ::             Getter s m     -> s -> m
foldOf :: Monoid m => Fold s m       -> s -> m
foldOf ::             Lens' s m      -> s -> m
foldOf ::             Iso' s m       -> s -> m
foldOf :: Monoid m => Traversal' s m -> s -> m
foldOf :: Monoid m => Prism' s m     -> s -> m

foldrOf :: Getting (Endo r) s a -> (a -> r -> r) -> r -> s -> r Source #

Right-associative fold of parts of a structure that are viewed through a Lens, Getter, Fold or Traversal.

foldr ≡ foldrOf folded

foldrOf :: Getter s a     -> (a -> r -> r) -> r -> s -> r
foldrOf :: Fold s a       -> (a -> r -> r) -> r -> s -> r
foldrOf :: Lens' s a      -> (a -> r -> r) -> r -> s -> r
foldrOf :: Iso' s a       -> (a -> r -> r) -> r -> s -> r
foldrOf :: Traversal' s a -> (a -> r -> r) -> r -> s -> r
foldrOf :: Prism' s a     -> (a -> r -> r) -> r -> s -> r

ifoldrOf l ≡ foldrOf l . Indexed

foldrOf :: Getting (Endo r) s a -> (a -> r -> r) -> r -> s -> r

foldlOf :: Getting (Dual (Endo r)) s a -> (r -> a -> r) -> r -> s -> r Source #

Left-associative fold of the parts of a structure that are viewed through a Lens, Getter, Fold or Traversal.

foldl ≡ foldlOf folded

foldlOf :: Getter s a     -> (r -> a -> r) -> r -> s -> r
foldlOf :: Fold s a       -> (r -> a -> r) -> r -> s -> r
foldlOf :: Lens' s a      -> (r -> a -> r) -> r -> s -> r
foldlOf :: Iso' s a       -> (r -> a -> r) -> r -> s -> r
foldlOf :: Traversal' s a -> (r -> a -> r) -> r -> s -> r
foldlOf :: Prism' s a     -> (r -> a -> r) -> r -> s -> r

toListOf :: Getting (Endo [a]) s a -> s -> [a] Source #

Extract a list of the targets of a Fold. See also (^..).

toList ≡ toListOf folded
(^..) ≡ flip toListOf

toNonEmptyOf :: Getting (NonEmptyDList a) s a -> s -> NonEmpty a Source #

Extract a NonEmpty of the targets of Fold1.

>>> toNonEmptyOf both1 ("hello", "world")
"hello" :| ["world"]

toNonEmptyOf :: Getter s a      -> s -> NonEmpty a
toNonEmptyOf :: Fold1 s a       -> s -> NonEmpty a
toNonEmptyOf :: Lens' s a       -> s -> NonEmpty a
toNonEmptyOf :: Iso' s a        -> s -> NonEmpty a
toNonEmptyOf :: Traversal1' s a -> s -> NonEmpty a

altOf :: Applicative f => Getting (Alt f a) s a -> s -> f a Source #

Calls pure on the target of a Lens, Getter, or Iso.

Calls pure on the targets of a Traversal, Fold, or Prism, and combines them with <|> (or empty if none). Intuitively, it collects targets into an Alternative until the container fills up or it runs out of targets, whichever comes first.

Generalizes toListOf and (^?).

>>> altOf both ("hello", "world") :: [String]
["hello","world"]
>>> altOf both ("hello", "world") :: Maybe String
Just "hello"

altOf :: Applicative f => Lens' s a      -> s -> f a
altOf :: Applicative f => Getter s a     -> s -> f a
altOf :: Applicative f => Iso' s a       -> s -> f a

altOf :: Alternative f => Traversal' s a -> s -> f a
altOf :: Alternative f => Fold s a       -> s -> f a
altOf :: Alternative f => Prism' s a     -> s -> f a

anyOf :: Getting Any s a -> (a -> Bool) -> s -> Bool Source #

Returns True if any target of a Fold satisfies a predicate.

>>> anyOf both (=='x') ('x','y')
True
>>> import Data.Data.Lens
>>> anyOf biplate (== "world") (((),2::Int),"hello",("world",11::Int))
True

any ≡ anyOf folded

ianyOf l ≡ anyOf l . Indexed

anyOf :: Getter s a     -> (a -> Bool) -> s -> Bool
anyOf :: Fold s a       -> (a -> Bool) -> s -> Bool
anyOf :: Lens' s a      -> (a -> Bool) -> s -> Bool
anyOf :: Iso' s a       -> (a -> Bool) -> s -> Bool
anyOf :: Traversal' s a -> (a -> Bool) -> s -> Bool
anyOf :: Prism' s a     -> (a -> Bool) -> s -> Bool

allOf :: Getting All s a -> (a -> Bool) -> s -> Bool Source #

Returns True if every target of a Fold satisfies a predicate.

>>> allOf both (>=3) (4,5)
True
>>> allOf folded (>=2) [1..10]
False

all ≡ allOf folded

iallOf l = allOf l . Indexed

allOf :: Getter s a     -> (a -> Bool) -> s -> Bool
allOf :: Fold s a       -> (a -> Bool) -> s -> Bool
allOf :: Lens' s a      -> (a -> Bool) -> s -> Bool
allOf :: Iso' s a       -> (a -> Bool) -> s -> Bool
allOf :: Traversal' s a -> (a -> Bool) -> s -> Bool
allOf :: Prism' s a     -> (a -> Bool) -> s -> Bool

noneOf :: Getting Any s a -> (a -> Bool) -> s -> Bool Source #

Returns True only if no targets of a Fold satisfy a predicate.

>>> noneOf each (is _Nothing) (Just 3, Just 4, Just 5)
True
>>> noneOf (folded.folded) (<10) [[13,99,20],[3,71,42]]
False

inoneOf l = noneOf l . Indexed

noneOf :: Getter s a     -> (a -> Bool) -> s -> Bool
noneOf :: Fold s a       -> (a -> Bool) -> s -> Bool
noneOf :: Lens' s a      -> (a -> Bool) -> s -> Bool
noneOf :: Iso' s a       -> (a -> Bool) -> s -> Bool
noneOf :: Traversal' s a -> (a -> Bool) -> s -> Bool
noneOf :: Prism' s a     -> (a -> Bool) -> s -> Bool

andOf :: Getting All s Bool -> s -> Bool Source #

Returns True if every target of a Fold is True.

>>> andOf both (True,False)
False
>>> andOf both (True,True)
True

and ≡ andOf folded

andOf :: Getter s Bool     -> s -> Bool
andOf :: Fold s Bool       -> s -> Bool
andOf :: Lens' s Bool      -> s -> Bool
andOf :: Iso' s Bool       -> s -> Bool
andOf :: Traversal' s Bool -> s -> Bool
andOf :: Prism' s Bool     -> s -> Bool

orOf :: Getting Any s Bool -> s -> Bool Source #

Returns True if any target of a Fold is True.

>>> orOf both (True,False)
True
>>> orOf both (False,False)
False

or ≡ orOf folded

orOf :: Getter s Bool     -> s -> Bool
orOf :: Fold s Bool       -> s -> Bool
orOf :: Lens' s Bool      -> s -> Bool
orOf :: Iso' s Bool       -> s -> Bool
orOf :: Traversal' s Bool -> s -> Bool
orOf :: Prism' s Bool     -> s -> Bool

productOf :: Num a => Getting (Endo (Endo a)) s a -> s -> a Source #

Calculate the Product of every number targeted by a Fold.

>>> productOf both (4,5)
20
>>> productOf folded [1,2,3,4,5]
120

product ≡ productOf folded

This operation may be more strict than you would expect. If you want a lazier version use ala Product . foldMapOf

productOf :: Num a => Getter s a     -> s -> a
productOf :: Num a => Fold s a       -> s -> a
productOf :: Num a => Lens' s a      -> s -> a
productOf :: Num a => Iso' s a       -> s -> a
productOf :: Num a => Traversal' s a -> s -> a
productOf :: Num a => Prism' s a     -> s -> a

sumOf :: Num a => Getting (Endo (Endo a)) s a -> s -> a Source #

Calculate the Sum of every number targeted by a Fold.

>>> sumOf both (5,6)
11
>>> sumOf folded [1,2,3,4]
10
>>> sumOf (folded.both) [(1,2),(3,4)]
10
>>> import Data.Data.Lens
>>> sumOf biplate [(1::Int,[]),(2,[(3::Int,4::Int)])] :: Int
10

sum ≡ sumOf folded

This operation may be more strict than you would expect. If you want a lazier version use ala Sum . foldMapOf

sumOf _1 :: Num a => (a, b) -> a
sumOf (folded . _1) :: (Foldable f, Num a) => f (a, b) -> a

sumOf :: Num a => Getter s a     -> s -> a
sumOf :: Num a => Fold s a       -> s -> a
sumOf :: Num a => Lens' s a      -> s -> a
sumOf :: Num a => Iso' s a       -> s -> a
sumOf :: Num a => Traversal' s a -> s -> a
sumOf :: Num a => Prism' s a     -> s -> a

forOf_ :: Functor f => Getting (Traversed r f) s a -> s -> (a -> f r) -> f () Source #

Traverse over all of the targets of a Fold (or Getter), computing an Applicative (or Functor)-based answer, but unlike forOf do not construct a new structure. forOf_ generalizes for_ to work over any Fold.

When passed a Getter, forOf_ can work over any Functor, but when passed a Fold, forOf_ requires an Applicative.

for_ ≡ forOf_ folded

>>> forOf_ both ("hello","world") putStrLn
hello
world

The rather specific signature of forOf_ allows it to be used as if the signature was any of:

iforOf_ l s ≡ forOf_ l s . Indexed

forOf_ :: Functor f     => Getter s a     -> s -> (a -> f r) -> f ()
forOf_ :: Applicative f => Fold s a       -> s -> (a -> f r) -> f ()
forOf_ :: Functor f     => Lens' s a      -> s -> (a -> f r) -> f ()
forOf_ :: Functor f     => Iso' s a       -> s -> (a -> f r) -> f ()
forOf_ :: Applicative f => Traversal' s a -> s -> (a -> f r) -> f ()
forOf_ :: Applicative f => Prism' s a     -> s -> (a -> f r) -> f ()

sequenceAOf_ :: Functor f => Getting (Traversed a f) s (f a) -> s -> f () Source #

Evaluate each action in observed by a Fold on a structure from left to right, ignoring the results.

sequenceA_ ≡ sequenceAOf_ folded

>>> sequenceAOf_ both (putStrLn "hello",putStrLn "world")
hello
world

sequenceAOf_ :: Functor f     => Getter s (f a)     -> s -> f ()
sequenceAOf_ :: Applicative f => Fold s (f a)       -> s -> f ()
sequenceAOf_ :: Functor f     => Lens' s (f a)      -> s -> f ()
sequenceAOf_ :: Functor f     => Iso' s (f a)       -> s -> f ()
sequenceAOf_ :: Applicative f => Traversal' s (f a) -> s -> f ()
sequenceAOf_ :: Applicative f => Prism' s (f a)     -> s -> f ()

traverse1Of_ :: Functor f => Getting (TraversedF r f) s a -> (a -> f r) -> s -> f () Source #

Traverse over all of the targets of a Fold1, computing an Apply based answer.

As long as you have Applicative or Functor effect you are better using traverseOf_. The traverse1Of_ is useful only when you have genuine Apply effect.

>>> traverse1Of_ both1 (\ks -> Map.fromList [ (k, ()) | k <- ks ]) ("abc", "bcd")
fromList [('b',()),('c',())]

traverse1Of_ :: Apply f => Fold1 s a -> (a -> f r) -> s -> f ()

Since: 4.16

for1Of_ :: Functor f => Getting (TraversedF r f) s a -> s -> (a -> f r) -> f () Source #

See forOf_ and traverse1Of_.

>>> for1Of_ both1 ("abc", "bcd") (\ks -> Map.fromList [ (k, ()) | k <- ks ])
fromList [('b',()),('c',())]

for1Of_ :: Apply f => Fold1 s a -> s -> (a -> f r) -> f ()

Since: 4.16

sequence1Of_ :: Functor f => Getting (TraversedF a f) s (f a) -> s -> f () Source #

See sequenceAOf_ and traverse1Of_.

sequence1Of_ :: Apply f => Fold1 s (f a) -> s -> f ()

Since: 4.16

forMOf_ :: Monad m => Getting (Sequenced r m) s a -> s -> (a -> m r) -> m () Source #

forMOf_ is mapMOf_ with two of its arguments flipped.

>>> forMOf_ both ("hello","world") putStrLn
hello
world

forM_ ≡ forMOf_ folded

forMOf_ :: Monad m => Getter s a     -> s -> (a -> m r) -> m ()
forMOf_ :: Monad m => Fold s a       -> s -> (a -> m r) -> m ()
forMOf_ :: Monad m => Lens' s a      -> s -> (a -> m r) -> m ()
forMOf_ :: Monad m => Iso' s a       -> s -> (a -> m r) -> m ()
forMOf_ :: Monad m => Traversal' s a -> s -> (a -> m r) -> m ()
forMOf_ :: Monad m => Prism' s a     -> s -> (a -> m r) -> m ()

sequenceOf_ :: Monad m => Getting (Sequenced a m) s (m a) -> s -> m () Source #

Evaluate each monadic action referenced by a Fold on the structure from left to right, and ignore the results.

>>> sequenceOf_ both (putStrLn "hello",putStrLn "world")
hello
world

sequence_ ≡ sequenceOf_ folded

sequenceOf_ :: Monad m => Getter s (m a)     -> s -> m ()
sequenceOf_ :: Monad m => Fold s (m a)       -> s -> m ()
sequenceOf_ :: Monad m => Lens' s (m a)      -> s -> m ()
sequenceOf_ :: Monad m => Iso' s (m a)       -> s -> m ()
sequenceOf_ :: Monad m => Traversal' s (m a) -> s -> m ()
sequenceOf_ :: Monad m => Prism' s (m a)     -> s -> m ()

asumOf :: Alternative f => Getting (Endo (f a)) s (f a) -> s -> f a Source #

The sum of a collection of actions, generalizing concatOf.

>>> asumOf both ("hello","world")
"helloworld"

>>> asumOf each (Nothing, Just "hello", Nothing)
Just "hello"

asum ≡ asumOf folded

asumOf :: Alternative f => Getter s (f a)     -> s -> f a
asumOf :: Alternative f => Fold s (f a)       -> s -> f a
asumOf :: Alternative f => Lens' s (f a)      -> s -> f a
asumOf :: Alternative f => Iso' s (f a)       -> s -> f a
asumOf :: Alternative f => Traversal' s (f a) -> s -> f a
asumOf :: Alternative f => Prism' s (f a)     -> s -> f a

msumOf :: MonadPlus m => Getting (Endo (m a)) s (m a) -> s -> m a Source #

The sum of a collection of actions, generalizing concatOf.

>>> msumOf both ("hello","world")
"helloworld"

>>> msumOf each (Nothing, Just "hello", Nothing)
Just "hello"

msum ≡ msumOf folded

msumOf :: MonadPlus m => Getter s (m a)     -> s -> m a
msumOf :: MonadPlus m => Fold s (m a)       -> s -> m a
msumOf :: MonadPlus m => Lens' s (m a)      -> s -> m a
msumOf :: MonadPlus m => Iso' s (m a)       -> s -> m a
msumOf :: MonadPlus m => Traversal' s (m a) -> s -> m a
msumOf :: MonadPlus m => Prism' s (m a)     -> s -> m a

concatMapOf :: Getting [r] s a -> (a -> [r]) -> s -> [r] Source #

Map a function over all the targets of a Fold of a container and concatenate the resulting lists.

>>> concatMapOf both (\x -> [x, x + 1]) (1,3)
[1,2,3,4]

concatMap ≡ concatMapOf folded

concatMapOf :: Getter s a     -> (a -> [r]) -> s -> [r]
concatMapOf :: Fold s a       -> (a -> [r]) -> s -> [r]
concatMapOf :: Lens' s a      -> (a -> [r]) -> s -> [r]
concatMapOf :: Iso' s a       -> (a -> [r]) -> s -> [r]
concatMapOf :: Traversal' s a -> (a -> [r]) -> s -> [r]

concatOf :: Getting [r] s [r] -> s -> [r] Source #

Concatenate all of the lists targeted by a Fold into a longer list.

>>> concatOf both ("pan","ama")
"panama"

concat ≡ concatOf folded
concatOf ≡ view

concatOf :: Getter s [r]     -> s -> [r]
concatOf :: Fold s [r]       -> s -> [r]
concatOf :: Iso' s [r]       -> s -> [r]
concatOf :: Lens' s [r]      -> s -> [r]
concatOf :: Traversal' s [r] -> s -> [r]

elemOf :: Eq a => Getting Any s a -> a -> s -> Bool Source #

Does the element occur anywhere within a given Fold of the structure?

>>> elemOf both "hello" ("hello","world")
True

elem ≡ elemOf folded

elemOf :: Eq a => Getter s a     -> a -> s -> Bool
elemOf :: Eq a => Fold s a       -> a -> s -> Bool
elemOf :: Eq a => Lens' s a      -> a -> s -> Bool
elemOf :: Eq a => Iso' s a       -> a -> s -> Bool
elemOf :: Eq a => Traversal' s a -> a -> s -> Bool
elemOf :: Eq a => Prism' s a     -> a -> s -> Bool

notElemOf :: Eq a => Getting All s a -> a -> s -> Bool Source #

Does the element not occur anywhere within a given Fold of the structure?

>>> notElemOf each 'd' ('a','b','c')
True

>>> notElemOf each 'a' ('a','b','c')
False

notElem ≡ notElemOf folded

notElemOf :: Eq a => Getter s a     -> a -> s -> Bool
notElemOf :: Eq a => Fold s a       -> a -> s -> Bool
notElemOf :: Eq a => Iso' s a       -> a -> s -> Bool
notElemOf :: Eq a => Lens' s a      -> a -> s -> Bool
notElemOf :: Eq a => Traversal' s a -> a -> s -> Bool
notElemOf :: Eq a => Prism' s a     -> a -> s -> Bool

lengthOf :: Getting (Endo (Endo Int)) s a -> s -> Int Source #

Calculate the number of targets there are for a Fold in a given container.

Note: This can be rather inefficient for large containers and just like length, this will not terminate for infinite folds.

length ≡ lengthOf folded

>>> lengthOf _1 ("hello",())
1

>>> lengthOf traverse [1..10]
10

>>> lengthOf (traverse.traverse) [[1,2],[3,4],[5,6]]
6

lengthOf (folded . folded) :: (Foldable f, Foldable g) => f (g a) -> Int

lengthOf :: Getter s a     -> s -> Int
lengthOf :: Fold s a       -> s -> Int
lengthOf :: Lens' s a      -> s -> Int
lengthOf :: Iso' s a       -> s -> Int
lengthOf :: Traversal' s a -> s -> Int

nullOf :: Getting All s a -> s -> Bool Source #

Returns True if this Fold or Traversal has no targets in the given container.

Note: nullOf on a valid Iso, Lens or Getter should always return False.

null ≡ nullOf folded

This may be rather inefficient compared to the null check of many containers.

>>> nullOf _1 (1,2)
False

>>> nullOf ignored ()
True

>>> nullOf traverse []
True

>>> nullOf (element 20) [1..10]
True

nullOf (folded . _1 . folded) :: (Foldable f, Foldable g) => f (g a, b) -> Bool

nullOf :: Getter s a     -> s -> Bool
nullOf :: Fold s a       -> s -> Bool
nullOf :: Iso' s a       -> s -> Bool
nullOf :: Lens' s a      -> s -> Bool
nullOf :: Traversal' s a -> s -> Bool

notNullOf :: Getting Any s a -> s -> Bool Source #

Returns True if this Fold or Traversal has any targets in the given container.

A more "conversational" alias for this combinator is has.

Note: notNullOf on a valid Iso, Lens or Getter should always return True.

not . null ≡ notNullOf folded

This may be rather inefficient compared to the not . null check of many containers.

>>> notNullOf _1 (1,2)
True

>>> notNullOf traverse [1..10]
True

>>> notNullOf folded []
False

>>> notNullOf (element 20) [1..10]
False

notNullOf (folded . _1 . folded) :: (Foldable f, Foldable g) => f (g a, b) -> Bool

notNullOf :: Getter s a     -> s -> Bool
notNullOf :: Fold s a       -> s -> Bool
notNullOf :: Iso' s a       -> s -> Bool
notNullOf :: Lens' s a      -> s -> Bool
notNullOf :: Traversal' s a -> s -> Bool

firstOf :: Getting (Leftmost a) s a -> s -> Maybe a Source #

Retrieve the First entry of a Fold or Traversal or retrieve Just the result from a Getter or Lens.

The answer is computed in a manner that leaks space less than preview or ^?' and gives you back access to the outermost Just constructor more quickly, but does so in a way that builds an intermediate structure, and thus may have worse constant factors. This also means that it can not be used in any MonadReader, but must instead have s passed as its last argument, unlike preview.

Note: this could been named headOf.

>>> firstOf traverse [1..10]
Just 1

>>> firstOf both (1,2)
Just 1

>>> firstOf ignored ()
Nothing

firstOf :: Getter s a     -> s -> Maybe a
firstOf :: Fold s a       -> s -> Maybe a
firstOf :: Lens' s a      -> s -> Maybe a
firstOf :: Iso' s a       -> s -> Maybe a
firstOf :: Traversal' s a -> s -> Maybe a

first1Of :: Getting (First a) s a -> s -> a Source #

Retrieve the First entry of a Fold1 or Traversal1 or the result from a Getter or Lens.

>>> first1Of traverse1 (1 :| [2..10])
1

>>> first1Of both1 (1,2)
1

Note: this is different from ^..

>>> first1Of traverse1 ([1,2] :| [[3,4],[5,6]])
[1,2]

>>> ([1,2] :| [[3,4],[5,6]]) ^. traverse1
[1,2,3,4,5,6]

first1Of :: Getter s a      -> s -> a
first1Of :: Fold1 s a       -> s -> a
first1Of :: Lens' s a       -> s -> a
first1Of :: Iso' s a        -> s -> a
first1Of :: Traversal1' s a -> s -> a

lastOf :: Getting (Rightmost a) s a -> s -> Maybe a Source #

Retrieve the Last entry of a Fold or Traversal or retrieve Just the result from a Getter or Lens.

The answer is computed in a manner that leaks space less than ala Last . foldMapOf and gives you back access to the outermost Just constructor more quickly, but may have worse constant factors.

>>> lastOf traverse [1..10]
Just 10

>>> lastOf both (1,2)
Just 2

>>> lastOf ignored ()
Nothing

lastOf :: Getter s a     -> s -> Maybe a
lastOf :: Fold s a       -> s -> Maybe a
lastOf :: Lens' s a      -> s -> Maybe a
lastOf :: Iso' s a       -> s -> Maybe a
lastOf :: Traversal' s a -> s -> Maybe a

last1Of :: Getting (Last a) s a -> s -> a Source #

Retrieve the Last entry of a Fold1 or Traversal1 or retrieve the result from a Getter or Lens.o

>>> last1Of traverse1 (1 :| [2..10])
10

>>> last1Of both1 (1,2)
2

last1Of :: Getter s a      -> s -> Maybe a
last1Of :: Fold1 s a       -> s -> Maybe a
last1Of :: Lens' s a       -> s -> Maybe a
last1Of :: Iso' s a        -> s -> Maybe a
last1Of :: Traversal1' s a -> s -> Maybe a

maximumOf :: Ord a => Getting (Endo (Endo (Maybe a))) s a -> s -> Maybe a Source #

Obtain the maximum element (if any) targeted by a Fold or Traversal safely.

Note: maximumOf on a valid Iso, Lens or Getter will always return Just a value.

>>> maximumOf traverse [1..10]
Just 10

>>> maximumOf traverse []
Nothing

>>> maximumOf (folded.filtered even) [1,4,3,6,7,9,2]
Just 6

maximum ≡ fromMaybe (error "empty") . maximumOf folded

In the interest of efficiency, This operation has semantics more strict than strictly necessary. rmap getMax (foldMapOf l Max) has lazier semantics but could leak memory.

maximumOf :: Ord a => Getter s a     -> s -> Maybe a
maximumOf :: Ord a => Fold s a       -> s -> Maybe a
maximumOf :: Ord a => Iso' s a       -> s -> Maybe a
maximumOf :: Ord a => Lens' s a      -> s -> Maybe a
maximumOf :: Ord a => Traversal' s a -> s -> Maybe a

maximum1Of :: Ord a => Getting (Max a) s a -> s -> a Source #

Obtain the maximum element targeted by a Fold1 or Traversal1.

>>> maximum1Of traverse1 (1 :| [2..10])
10

maximum1Of :: Ord a => Getter s a      -> s -> a
maximum1Of :: Ord a => Fold1 s a       -> s -> a
maximum1Of :: Ord a => Iso' s a        -> s -> a
maximum1Of :: Ord a => Lens' s a       -> s -> a
maximum1Of :: Ord a => Traversal1' s a -> s -> a

minimumOf :: Ord a => Getting (Endo (Endo (Maybe a))) s a -> s -> Maybe a Source #

Obtain the minimum element (if any) targeted by a Fold or Traversal safely.

Note: minimumOf on a valid Iso, Lens or Getter will always return Just a value.

>>> minimumOf traverse [1..10]
Just 1

>>> minimumOf traverse []
Nothing

>>> minimumOf (folded.filtered even) [1,4,3,6,7,9,2]
Just 2

minimum ≡ fromMaybe (error "empty") . minimumOf folded

In the interest of efficiency, This operation has semantics more strict than strictly necessary. rmap getMin (foldMapOf l Min) has lazier semantics but could leak memory.

minimumOf :: Ord a => Getter s a     -> s -> Maybe a
minimumOf :: Ord a => Fold s a       -> s -> Maybe a
minimumOf :: Ord a => Iso' s a       -> s -> Maybe a
minimumOf :: Ord a => Lens' s a      -> s -> Maybe a
minimumOf :: Ord a => Traversal' s a -> s -> Maybe a

minimum1Of :: Ord a => Getting (Min a) s a -> s -> a Source #

Obtain the minimum element targeted by a Fold1 or Traversal1.

>>> minimum1Of traverse1 (1 :| [2..10])
1

minimum1Of :: Ord a => Getter s a      -> s -> a
minimum1Of :: Ord a => Fold1 s a       -> s -> a
minimum1Of :: Ord a => Iso' s a        -> s -> a
minimum1Of :: Ord a => Lens' s a       -> s -> a
minimum1Of :: Ord a => Traversal1' s a -> s -> a

maximumByOf :: Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> Ordering) -> s -> Maybe a Source #

Obtain the maximum element (if any) targeted by a Fold, Traversal, Lens, Iso, or Getter according to a user supplied Ordering.

>>> maximumByOf traverse (compare `on` length) ["mustard","relish","ham"]
Just "mustard"

In the interest of efficiency, This operation has semantics more strict than strictly necessary.

maximumBy cmp ≡ fromMaybe (error "empty") . maximumByOf folded cmp

maximumByOf :: Getter s a     -> (a -> a -> Ordering) -> s -> Maybe a
maximumByOf :: Fold s a       -> (a -> a -> Ordering) -> s -> Maybe a
maximumByOf :: Iso' s a       -> (a -> a -> Ordering) -> s -> Maybe a
maximumByOf :: Lens' s a      -> (a -> a -> Ordering) -> s -> Maybe a
maximumByOf :: Traversal' s a -> (a -> a -> Ordering) -> s -> Maybe a

minimumByOf :: Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> Ordering) -> s -> Maybe a Source #

Obtain the minimum element (if any) targeted by a Fold, Traversal, Lens, Iso or Getter according to a user supplied Ordering.

In the interest of efficiency, This operation has semantics more strict than strictly necessary.

>>> minimumByOf traverse (compare `on` length) ["mustard","relish","ham"]
Just "ham"

minimumBy cmp ≡ fromMaybe (error "empty") . minimumByOf folded cmp

minimumByOf :: Getter s a     -> (a -> a -> Ordering) -> s -> Maybe a
minimumByOf :: Fold s a       -> (a -> a -> Ordering) -> s -> Maybe a
minimumByOf :: Iso' s a       -> (a -> a -> Ordering) -> s -> Maybe a
minimumByOf :: Lens' s a      -> (a -> a -> Ordering) -> s -> Maybe a
minimumByOf :: Traversal' s a -> (a -> a -> Ordering) -> s -> Maybe a

findOf :: Getting (Endo (Maybe a)) s a -> (a -> Bool) -> s -> Maybe a Source #

The findOf function takes a Lens (or Getter, Iso, Fold, or Traversal), a predicate and a structure and returns the leftmost element of the structure matching the predicate, or Nothing if there is no such element.

>>> findOf each even (1,3,4,6)
Just 4

>>> findOf folded even [1,3,5,7]
Nothing

findOf :: Getter s a     -> (a -> Bool) -> s -> Maybe a
findOf :: Fold s a       -> (a -> Bool) -> s -> Maybe a
findOf :: Iso' s a       -> (a -> Bool) -> s -> Maybe a
findOf :: Lens' s a      -> (a -> Bool) -> s -> Maybe a
findOf :: Traversal' s a -> (a -> Bool) -> s -> Maybe a

find ≡ findOf folded
ifindOf l ≡ findOf l . Indexed

A simpler version that didn't permit indexing, would be:

findOf :: Getting (Endo (Maybe a)) s a -> (a -> Bool) -> s -> Maybe a
findOf l p = foldrOf l (a y -> if p a then Just a else y) Nothing

findMOf :: Monad m => Getting (Endo (m (Maybe a))) s a -> (a -> m Bool) -> s -> m (Maybe a) Source #

The findMOf function takes a Lens (or Getter, Iso, Fold, or Traversal), a monadic predicate and a structure and returns in the monad the leftmost element of the structure matching the predicate, or Nothing if there is no such element.

>>> findMOf each ( \x -> print ("Checking " ++ show x) >> return (even x)) (1,3,4,6)
"Checking 1"
"Checking 3"
"Checking 4"
Just 4

>>> findMOf each ( \x -> print ("Checking " ++ show x) >> return (even x)) (1,3,5,7)
"Checking 1"
"Checking 3"
"Checking 5"
"Checking 7"
Nothing

findMOf :: (Monad m, Getter s a)     -> (a -> m Bool) -> s -> m (Maybe a)
findMOf :: (Monad m, Fold s a)       -> (a -> m Bool) -> s -> m (Maybe a)
findMOf :: (Monad m, Iso' s a)       -> (a -> m Bool) -> s -> m (Maybe a)
findMOf :: (Monad m, Lens' s a)      -> (a -> m Bool) -> s -> m (Maybe a)
findMOf :: (Monad m, Traversal' s a) -> (a -> m Bool) -> s -> m (Maybe a)

findMOf folded :: (Monad m, Foldable f) => (a -> m Bool) -> f a -> m (Maybe a)
ifindMOf l ≡ findMOf l . Indexed

A simpler version that didn't permit indexing, would be:

findMOf :: Monad m => Getting (Endo (m (Maybe a))) s a -> (a -> m Bool) -> s -> m (Maybe a)
findMOf l p = foldrOf l (a y -> p a >>= x -> if x then return (Just a) else y) $ return Nothing

foldrOf' :: Getting (Dual (Endo (Endo r))) s a -> (a -> r -> r) -> r -> s -> r Source #

Strictly fold right over the elements of a structure.

foldr' ≡ foldrOf' folded

foldrOf' :: Getter s a     -> (a -> r -> r) -> r -> s -> r
foldrOf' :: Fold s a       -> (a -> r -> r) -> r -> s -> r
foldrOf' :: Iso' s a       -> (a -> r -> r) -> r -> s -> r
foldrOf' :: Lens' s a      -> (a -> r -> r) -> r -> s -> r
foldrOf' :: Traversal' s a -> (a -> r -> r) -> r -> s -> r

foldr1Of :: HasCallStack => Getting (Endo (Maybe a)) s a -> (a -> a -> a) -> s -> a Source #

A variant of foldrOf that has no base case and thus may only be applied to lenses and structures such that the Lens views at least one element of the structure.

>>> foldr1Of each (+) (1,2,3,4)
10

foldr1Of l f ≡ foldr1 f . toListOf l
foldr1 ≡ foldr1Of folded

foldr1Of :: Getter s a     -> (a -> a -> a) -> s -> a
foldr1Of :: Fold s a       -> (a -> a -> a) -> s -> a
foldr1Of :: Iso' s a       -> (a -> a -> a) -> s -> a
foldr1Of :: Lens' s a      -> (a -> a -> a) -> s -> a
foldr1Of :: Traversal' s a -> (a -> a -> a) -> s -> a

foldl1Of :: HasCallStack => Getting (Dual (Endo (Maybe a))) s a -> (a -> a -> a) -> s -> a Source #

A variant of foldlOf that has no base case and thus may only be applied to lenses and structures such that the Lens views at least one element of the structure.

>>> foldl1Of each (+) (1,2,3,4)
10

foldl1Of l f ≡ foldl1 f . toListOf l
foldl1 ≡ foldl1Of folded

foldl1Of :: Getter s a     -> (a -> a -> a) -> s -> a
foldl1Of :: Fold s a       -> (a -> a -> a) -> s -> a
foldl1Of :: Iso' s a       -> (a -> a -> a) -> s -> a
foldl1Of :: Lens' s a      -> (a -> a -> a) -> s -> a
foldl1Of :: Traversal' s a -> (a -> a -> a) -> s -> a

foldr1Of' :: HasCallStack => Getting (Dual (Endo (Endo (Maybe a)))) s a -> (a -> a -> a) -> s -> a Source #

A variant of foldrOf' that has no base case and thus may only be applied to folds and structures such that the fold views at least one element of the structure.

foldr1Of l f ≡ foldr1 f . toListOf l

foldr1Of' :: Getter s a     -> (a -> a -> a) -> s -> a
foldr1Of' :: Fold s a       -> (a -> a -> a) -> s -> a
foldr1Of' :: Iso' s a       -> (a -> a -> a) -> s -> a
foldr1Of' :: Lens' s a      -> (a -> a -> a) -> s -> a
foldr1Of' :: Traversal' s a -> (a -> a -> a) -> s -> a

foldl1Of' :: HasCallStack => Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> a) -> s -> a Source #

A variant of foldlOf' that has no base case and thus may only be applied to folds and structures such that the fold views at least one element of the structure.

foldl1Of' l f ≡ foldl1' f . toListOf l

foldl1Of' :: Getter s a     -> (a -> a -> a) -> s -> a
foldl1Of' :: Fold s a       -> (a -> a -> a) -> s -> a
foldl1Of' :: Iso' s a       -> (a -> a -> a) -> s -> a
foldl1Of' :: Lens' s a      -> (a -> a -> a) -> s -> a
foldl1Of' :: Traversal' s a -> (a -> a -> a) -> s -> a

foldrMOf :: Monad m => Getting (Dual (Endo (r -> m r))) s a -> (a -> r -> m r) -> r -> s -> m r Source #

Monadic fold over the elements of a structure, associating to the right, i.e. from right to left.

foldrM ≡ foldrMOf folded

foldrMOf :: Monad m => Getter s a     -> (a -> r -> m r) -> r -> s -> m r
foldrMOf :: Monad m => Fold s a       -> (a -> r -> m r) -> r -> s -> m r
foldrMOf :: Monad m => Iso' s a       -> (a -> r -> m r) -> r -> s -> m r
foldrMOf :: Monad m => Lens' s a      -> (a -> r -> m r) -> r -> s -> m r
foldrMOf :: Monad m => Traversal' s a -> (a -> r -> m r) -> r -> s -> m r

foldlMOf :: Monad m => Getting (Endo (r -> m r)) s a -> (r -> a -> m r) -> r -> s -> m r Source #

Monadic fold over the elements of a structure, associating to the left, i.e. from left to right.

foldlM ≡ foldlMOf folded

foldlMOf :: Monad m => Getter s a     -> (r -> a -> m r) -> r -> s -> m r
foldlMOf :: Monad m => Fold s a       -> (r -> a -> m r) -> r -> s -> m r
foldlMOf :: Monad m => Iso' s a       -> (r -> a -> m r) -> r -> s -> m r
foldlMOf :: Monad m => Lens' s a      -> (r -> a -> m r) -> r -> s -> m r
foldlMOf :: Monad m => Traversal' s a -> (r -> a -> m r) -> r -> s -> m r

lookupOf :: Eq k => Getting (Endo (Maybe v)) s (k, v) -> k -> s -> Maybe v Source #

The lookupOf function takes a Fold (or Getter, Traversal, Lens, Iso, etc.), a key, and a structure containing key/value pairs. It returns the first value corresponding to the given key. This function generalizes lookup to work on an arbitrary Fold instead of lists.

>>> lookupOf folded 4 [(2, 'a'), (4, 'b'), (4, 'c')]
Just 'b'

>>> lookupOf each 2 [(2, 'a'), (4, 'b'), (4, 'c')]
Just 'a'

lookupOf :: Eq k => Fold s (k,v) -> k -> s -> Maybe v

ifoldMapOf :: IndexedGetting i m s a -> (i -> a -> m) -> s -> m Source #

Fold an IndexedFold or IndexedTraversal by mapping indices and values to an arbitrary Monoid with access to the i.

When you don't need access to the index then foldMapOf is more flexible in what it accepts.

foldMapOf l ≡ ifoldMapOf l . const

ifoldMapOf ::             IndexedGetter i s a     -> (i -> a -> m) -> s -> m
ifoldMapOf :: Monoid m => IndexedFold i s a       -> (i -> a -> m) -> s -> m
ifoldMapOf ::             IndexedLens' i s a      -> (i -> a -> m) -> s -> m
ifoldMapOf :: Monoid m => IndexedTraversal' i s a -> (i -> a -> m) -> s -> m

ifoldrOf :: IndexedGetting i (Endo r) s a -> (i -> a -> r -> r) -> r -> s -> r Source #

Right-associative fold of parts of a structure that are viewed through an IndexedFold or IndexedTraversal with access to the i.

When you don't need access to the index then foldrOf is more flexible in what it accepts.

foldrOf l ≡ ifoldrOf l . const

ifoldrOf :: IndexedGetter i s a     -> (i -> a -> r -> r) -> r -> s -> r
ifoldrOf :: IndexedFold i s a       -> (i -> a -> r -> r) -> r -> s -> r
ifoldrOf :: IndexedLens' i s a      -> (i -> a -> r -> r) -> r -> s -> r
ifoldrOf :: IndexedTraversal' i s a -> (i -> a -> r -> r) -> r -> s -> r

ifoldlOf :: IndexedGetting i (Dual (Endo r)) s a -> (i -> r -> a -> r) -> r -> s -> r Source #

Left-associative fold of the parts of a structure that are viewed through an IndexedFold or IndexedTraversal with access to the i.

When you don't need access to the index then foldlOf is more flexible in what it accepts.

foldlOf l ≡ ifoldlOf l . const

ifoldlOf :: IndexedGetter i s a     -> (i -> r -> a -> r) -> r -> s -> r
ifoldlOf :: IndexedFold i s a       -> (i -> r -> a -> r) -> r -> s -> r
ifoldlOf :: IndexedLens' i s a      -> (i -> r -> a -> r) -> r -> s -> r
ifoldlOf :: IndexedTraversal' i s a -> (i -> r -> a -> r) -> r -> s -> r

ianyOf :: IndexedGetting i Any s a -> (i -> a -> Bool) -> s -> Bool Source #

Return whether or not any element viewed through an IndexedFold or IndexedTraversal satisfy a predicate, with access to the i.

When you don't need access to the index then anyOf is more flexible in what it accepts.

anyOf l ≡ ianyOf l . const

ianyOf :: IndexedGetter i s a     -> (i -> a -> Bool) -> s -> Bool
ianyOf :: IndexedFold i s a       -> (i -> a -> Bool) -> s -> Bool
ianyOf :: IndexedLens' i s a      -> (i -> a -> Bool) -> s -> Bool
ianyOf :: IndexedTraversal' i s a -> (i -> a -> Bool) -> s -> Bool

iallOf :: IndexedGetting i All s a -> (i -> a -> Bool) -> s -> Bool Source #

Return whether or not all elements viewed through an IndexedFold or IndexedTraversal satisfy a predicate, with access to the i.

When you don't need access to the index then allOf is more flexible in what it accepts.

allOf l ≡ iallOf l . const

iallOf :: IndexedGetter i s a     -> (i -> a -> Bool) -> s -> Bool
iallOf :: IndexedFold i s a       -> (i -> a -> Bool) -> s -> Bool
iallOf :: IndexedLens' i s a      -> (i -> a -> Bool) -> s -> Bool
iallOf :: IndexedTraversal' i s a -> (i -> a -> Bool) -> s -> Bool

inoneOf :: IndexedGetting i Any s a -> (i -> a -> Bool) -> s -> Bool Source #

Return whether or not none of the elements viewed through an IndexedFold or IndexedTraversal satisfy a predicate, with access to the i.

When you don't need access to the index then noneOf is more flexible in what it accepts.

noneOf l ≡ inoneOf l . const

inoneOf :: IndexedGetter i s a     -> (i -> a -> Bool) -> s -> Bool
inoneOf :: IndexedFold i s a       -> (i -> a -> Bool) -> s -> Bool
inoneOf :: IndexedLens' i s a      -> (i -> a -> Bool) -> s -> Bool
inoneOf :: IndexedTraversal' i s a -> (i -> a -> Bool) -> s -> Bool

itraverseOf_ :: Functor f => IndexedGetting i (Traversed r f) s a -> (i -> a -> f r) -> s -> f () Source #

Traverse the targets of an IndexedFold or IndexedTraversal with access to the i, discarding the results.

When you don't need access to the index then traverseOf_ is more flexible in what it accepts.

traverseOf_ l ≡ itraverseOf l . const

itraverseOf_ :: Functor f     => IndexedGetter i s a     -> (i -> a -> f r) -> s -> f ()
itraverseOf_ :: Applicative f => IndexedFold i s a       -> (i -> a -> f r) -> s -> f ()
itraverseOf_ :: Functor f     => IndexedLens' i s a      -> (i -> a -> f r) -> s -> f ()
itraverseOf_ :: Applicative f => IndexedTraversal' i s a -> (i -> a -> f r) -> s -> f ()

iforOf_ :: Functor f => IndexedGetting i (Traversed r f) s a -> s -> (i -> a -> f r) -> f () Source #

Traverse the targets of an IndexedFold or IndexedTraversal with access to the index, discarding the results (with the arguments flipped).

iforOf_ ≡ flip . itraverseOf_

When you don't need access to the index then forOf_ is more flexible in what it accepts.

forOf_ l a ≡ iforOf_ l a . const

iforOf_ :: Functor f     => IndexedGetter i s a     -> s -> (i -> a -> f r) -> f ()
iforOf_ :: Applicative f => IndexedFold i s a       -> s -> (i -> a -> f r) -> f ()
iforOf_ :: Functor f     => IndexedLens' i s a      -> s -> (i -> a -> f r) -> f ()
iforOf_ :: Applicative f => IndexedTraversal' i s a -> s -> (i -> a -> f r) -> f ()

imapMOf_ :: Monad m => IndexedGetting i (Sequenced r m) s a -> (i -> a -> m r) -> s -> m () Source #

Run monadic actions for each target of an IndexedFold or IndexedTraversal with access to the index, discarding the results.

When you don't need access to the index then mapMOf_ is more flexible in what it accepts.

mapMOf_ l ≡ imapMOf l . const

imapMOf_ :: Monad m => IndexedGetter i s a     -> (i -> a -> m r) -> s -> m ()
imapMOf_ :: Monad m => IndexedFold i s a       -> (i -> a -> m r) -> s -> m ()
imapMOf_ :: Monad m => IndexedLens' i s a      -> (i -> a -> m r) -> s -> m ()
imapMOf_ :: Monad m => IndexedTraversal' i s a -> (i -> a -> m r) -> s -> m ()

iforMOf_ :: Monad m => IndexedGetting i (Sequenced r m) s a -> s -> (i -> a -> m r) -> m () Source #

Run monadic actions for each target of an IndexedFold or IndexedTraversal with access to the index, discarding the results (with the arguments flipped).

iforMOf_ ≡ flip . imapMOf_

When you don't need access to the index then forMOf_ is more flexible in what it accepts.

forMOf_ l a ≡ iforMOf l a . const

iforMOf_ :: Monad m => IndexedGetter i s a     -> s -> (i -> a -> m r) -> m ()
iforMOf_ :: Monad m => IndexedFold i s a       -> s -> (i -> a -> m r) -> m ()
iforMOf_ :: Monad m => IndexedLens' i s a      -> s -> (i -> a -> m r) -> m ()
iforMOf_ :: Monad m => IndexedTraversal' i s a -> s -> (i -> a -> m r) -> m ()

iconcatMapOf :: IndexedGetting i [r] s a -> (i -> a -> [r]) -> s -> [r] Source #

Concatenate the results of a function of the elements of an IndexedFold or IndexedTraversal with access to the index.

When you don't need access to the index then concatMapOf is more flexible in what it accepts.

concatMapOf l ≡ iconcatMapOf l . const
iconcatMapOf ≡ ifoldMapOf

iconcatMapOf :: IndexedGetter i s a     -> (i -> a -> [r]) -> s -> [r]
iconcatMapOf :: IndexedFold i s a       -> (i -> a -> [r]) -> s -> [r]
iconcatMapOf :: IndexedLens' i s a      -> (i -> a -> [r]) -> s -> [r]
iconcatMapOf :: IndexedTraversal' i s a -> (i -> a -> [r]) -> s -> [r]

ifindOf :: IndexedGetting i (Endo (Maybe a)) s a -> (i -> a -> Bool) -> s -> Maybe a Source #

The ifindOf function takes an IndexedFold or IndexedTraversal, a predicate that is also supplied the index, a structure and returns the left-most element of the structure matching the predicate, or Nothing if there is no such element.

When you don't need access to the index then findOf is more flexible in what it accepts.

findOf l ≡ ifindOf l . const

ifindOf :: IndexedGetter i s a     -> (i -> a -> Bool) -> s -> Maybe a
ifindOf :: IndexedFold i s a       -> (i -> a -> Bool) -> s -> Maybe a
ifindOf :: IndexedLens' i s a      -> (i -> a -> Bool) -> s -> Maybe a
ifindOf :: IndexedTraversal' i s a -> (i -> a -> Bool) -> s -> Maybe a

ifindMOf :: Monad m => IndexedGetting i (Endo (m (Maybe a))) s a -> (i -> a -> m Bool) -> s -> m (Maybe a) Source #

The ifindMOf function takes an IndexedFold or IndexedTraversal, a monadic predicate that is also supplied the index, a structure and returns in the monad the left-most element of the structure matching the predicate, or Nothing if there is no such element.

When you don't need access to the index then findMOf is more flexible in what it accepts.

findMOf l ≡ ifindMOf l . const

ifindMOf :: Monad m => IndexedGetter i s a     -> (i -> a -> m Bool) -> s -> m (Maybe a)
ifindMOf :: Monad m => IndexedFold i s a       -> (i -> a -> m Bool) -> s -> m (Maybe a)
ifindMOf :: Monad m => IndexedLens' i s a      -> (i -> a -> m Bool) -> s -> m (Maybe a)
ifindMOf :: Monad m => IndexedTraversal' i s a -> (i -> a -> m Bool) -> s -> m (Maybe a)

ifoldrOf' :: IndexedGetting i (Dual (Endo (r -> r))) s a -> (i -> a -> r -> r) -> r -> s -> r Source #

Strictly fold right over the elements of a structure with an index.

When you don't need access to the index then foldrOf' is more flexible in what it accepts.

foldrOf' l ≡ ifoldrOf' l . const

ifoldrOf' :: IndexedGetter i s a     -> (i -> a -> r -> r) -> r -> s -> r
ifoldrOf' :: IndexedFold i s a       -> (i -> a -> r -> r) -> r -> s -> r
ifoldrOf' :: IndexedLens' i s a      -> (i -> a -> r -> r) -> r -> s -> r
ifoldrOf' :: IndexedTraversal' i s a -> (i -> a -> r -> r) -> r -> s -> r

ifoldlOf' :: IndexedGetting i (Endo (r -> r)) s a -> (i -> r -> a -> r) -> r -> s -> r Source #

Fold over the elements of a structure with an index, associating to the left, but strictly.

When you don't need access to the index then foldlOf' is more flexible in what it accepts.

foldlOf' l ≡ ifoldlOf' l . const

ifoldlOf' :: IndexedGetter i s a       -> (i -> r -> a -> r) -> r -> s -> r
ifoldlOf' :: IndexedFold i s a         -> (i -> r -> a -> r) -> r -> s -> r
ifoldlOf' :: IndexedLens' i s a        -> (i -> r -> a -> r) -> r -> s -> r
ifoldlOf' :: IndexedTraversal' i s a   -> (i -> r -> a -> r) -> r -> s -> r

ifoldrMOf :: Monad m => IndexedGetting i (Dual (Endo (r -> m r))) s a -> (i -> a -> r -> m r) -> r -> s -> m r Source #

Monadic fold right over the elements of a structure with an index.

When you don't need access to the index then foldrMOf is more flexible in what it accepts.

foldrMOf l ≡ ifoldrMOf l . const

ifoldrMOf :: Monad m => IndexedGetter i s a     -> (i -> a -> r -> m r) -> r -> s -> m r
ifoldrMOf :: Monad m => IndexedFold i s a       -> (i -> a -> r -> m r) -> r -> s -> m r
ifoldrMOf :: Monad m => IndexedLens' i s a      -> (i -> a -> r -> m r) -> r -> s -> m r
ifoldrMOf :: Monad m => IndexedTraversal' i s a -> (i -> a -> r -> m r) -> r -> s -> m r

ifoldlMOf :: Monad m => IndexedGetting i (Endo (r -> m r)) s a -> (i -> r -> a -> m r) -> r -> s -> m r Source #

Monadic fold over the elements of a structure with an index, associating to the left.

When you don't need access to the index then foldlMOf is more flexible in what it accepts.

foldlMOf l ≡ ifoldlMOf l . const

ifoldlMOf :: Monad m => IndexedGetter i s a     -> (i -> r -> a -> m r) -> r -> s -> m r
ifoldlMOf :: Monad m => IndexedFold i s a       -> (i -> r -> a -> m r) -> r -> s -> m r
ifoldlMOf :: Monad m => IndexedLens' i s a      -> (i -> r -> a -> m r) -> r -> s -> m r
ifoldlMOf :: Monad m => IndexedTraversal' i s a -> (i -> r -> a -> m r) -> r -> s -> m r

itoListOf :: IndexedGetting i (Endo [(i, a)]) s a -> s -> [(i, a)] Source #

Extract the key-value pairs from a structure.

When you don't need access to the indices in the result, then toListOf is more flexible in what it accepts.

toListOf l ≡ map snd . itoListOf l

itoListOf :: IndexedGetter i s a     -> s -> [(i,a)]
itoListOf :: IndexedFold i s a       -> s -> [(i,a)]
itoListOf :: IndexedLens' i s a      -> s -> [(i,a)]
itoListOf :: IndexedTraversal' i s a -> s -> [(i,a)]

elemIndexOf :: Eq a => IndexedGetting i (First i) s a -> a -> s -> Maybe i Source #

Retrieve the index of the first value targeted by a IndexedFold or IndexedTraversal which is equal to a given value.

elemIndex ≡ elemIndexOf folded

elemIndexOf :: Eq a => IndexedFold i s a       -> a -> s -> Maybe i
elemIndexOf :: Eq a => IndexedTraversal' i s a -> a -> s -> Maybe i

elemIndicesOf :: Eq a => IndexedGetting i (Endo [i]) s a -> a -> s -> [i] Source #

Retrieve the indices of the values targeted by a IndexedFold or IndexedTraversal which are equal to a given value.

elemIndices ≡ elemIndicesOf folded

elemIndicesOf :: Eq a => IndexedFold i s a       -> a -> s -> [i]
elemIndicesOf :: Eq a => IndexedTraversal' i s a -> a -> s -> [i]

findIndexOf :: IndexedGetting i (First i) s a -> (a -> Bool) -> s -> Maybe i Source #

Retrieve the index of the first value targeted by a IndexedFold or IndexedTraversal which satisfies a predicate.

findIndex ≡ findIndexOf folded

findIndexOf :: IndexedFold i s a       -> (a -> Bool) -> s -> Maybe i
findIndexOf :: IndexedTraversal' i s a -> (a -> Bool) -> s -> Maybe i

findIndicesOf :: IndexedGetting i (Endo [i]) s a -> (a -> Bool) -> s -> [i] Source #

Retrieve the indices of the values targeted by a IndexedFold or IndexedTraversal which satisfy a predicate.

findIndices ≡ findIndicesOf folded

findIndicesOf :: IndexedFold i s a       -> (a -> Bool) -> s -> [i]
findIndicesOf :: IndexedTraversal' i s a -> (a -> Bool) -> s -> [i]

ifiltered :: (Indexable i p, Applicative f) => (i -> a -> Bool) -> Optical' p (Indexed i) f a a Source #

Filter an IndexedFold or IndexedGetter, obtaining an IndexedFold.

>>> [0,0,0,5,5,5]^..traversed.ifiltered (\i a -> i <= a)
[0,5,5,5]

Compose with ifiltered to filter another IndexedLens, IndexedIso, IndexedGetter, IndexedFold (or IndexedTraversal) with access to both the value and the index.

Note: As with filtered, this is not a legal IndexedTraversal, unless you are very careful not to invalidate the predicate on the target!

itakingWhile :: (Indexable i p, Profunctor q, Contravariant f, Applicative f) => (i -> a -> Bool) -> Optical' (Indexed i) q (Const (Endo (f s))) s a -> Optical' p q f s a Source #

Obtain an IndexedFold by taking elements from another IndexedFold, IndexedLens, IndexedGetter or IndexedTraversal while a predicate holds.

itakingWhile :: (i -> a -> Bool) -> IndexedFold i s a          -> IndexedFold i s a
itakingWhile :: (i -> a -> Bool) -> IndexedTraversal' i s a    -> IndexedFold i s a
itakingWhile :: (i -> a -> Bool) -> IndexedLens' i s a         -> IndexedFold i s a
itakingWhile :: (i -> a -> Bool) -> IndexedGetter i s a        -> IndexedFold i s a

Note: Applying itakingWhile to an IndexedLens or IndexedTraversal will still allow you to use it as a pseudo-IndexedTraversal, but if you change the value of any target to one where the predicate returns False, then you will break the Traversal laws and Traversal fusion will no longer be sound.

idroppingWhile :: (Indexable i p, Profunctor q, Applicative f) => (i -> a -> Bool) -> Optical (Indexed i) q (Compose (State Bool) f) s t a a -> Optical p q f s t a a Source #

Obtain an IndexedFold by dropping elements from another IndexedFold, IndexedLens, IndexedGetter or IndexedTraversal while a predicate holds.

idroppingWhile :: (i -> a -> Bool) -> IndexedFold i s a          -> IndexedFold i s a
idroppingWhile :: (i -> a -> Bool) -> IndexedTraversal' i s a    -> IndexedFold i s a -- see notes
idroppingWhile :: (i -> a -> Bool) -> IndexedLens' i s a         -> IndexedFold i s a -- see notes
idroppingWhile :: (i -> a -> Bool) -> IndexedGetter i s a        -> IndexedFold i s a

Note: As with droppingWhile applying idroppingWhile to an IndexedLens or IndexedTraversal will still allow you to use it as a pseudo-IndexedTraversal, but if you change the value of the first target to one where the predicate returns True, then you will break the Traversal laws and Traversal fusion will no longer be sound.

foldByOf :: Fold s a -> (a -> a -> a) -> a -> s -> a Source #

Fold a value using a specified Fold and Monoid operations. This is like foldBy where the Foldable instance can be manually specified.

foldByOf folded ≡ foldBy

foldByOf :: Getter s a     -> (a -> a -> a) -> a -> s -> a
foldByOf :: Fold s a       -> (a -> a -> a) -> a -> s -> a
foldByOf :: Lens' s a      -> (a -> a -> a) -> a -> s -> a
foldByOf :: Traversal' s a -> (a -> a -> a) -> a -> s -> a
foldByOf :: Iso' s a       -> (a -> a -> a) -> a -> s -> a

>>> foldByOf both (++) [] ("hello","world")
"helloworld"

foldMapByOf :: Fold s a -> (r -> r -> r) -> r -> (a -> r) -> s -> r Source #

Fold a value using a specified Fold and Monoid operations. This is like foldMapBy where the Foldable instance can be manually specified.

foldMapByOf folded ≡ foldMapBy

foldMapByOf :: Getter s a     -> (r -> r -> r) -> r -> (a -> r) -> s -> r
foldMapByOf :: Fold s a       -> (r -> r -> r) -> r -> (a -> r) -> s -> r
foldMapByOf :: Traversal' s a -> (r -> r -> r) -> r -> (a -> r) -> s -> r
foldMapByOf :: Lens' s a      -> (r -> r -> r) -> r -> (a -> r) -> s -> r
foldMapByOf :: Iso' s a       -> (r -> r -> r) -> r -> (a -> r) -> s -> r

>>> foldMapByOf both (+) 0 length ("hello","world")
10

ito :: (Indexable i p, Contravariant f) => (s -> (i, a)) -> Over' p f s a Source #

ito :: (s -> (i, a)) -> IndexedGetter i s a

like :: (Profunctor p, Contravariant f, Functor f) => a -> Optic' p f s a Source #

Build an constant-valued (index-preserving) Getter from an arbitrary Haskell value.

like a . like b ≡ like b
a ^. like b ≡ b
a ^. like b ≡ a ^. to (const b)

This can be useful as a second case failing a Fold e.g. foo failing like 0

like :: a -> IndexPreservingGetter s a

ilike :: (Indexable i p, Contravariant f, Functor f) => i -> a -> Over' p f s a Source #

ilike :: i -> a -> IndexedGetter i s a

view :: MonadReader s m => Getting a s a -> m a Source #

View the value pointed to by a Getter, Iso or Lens or the result of folding over all the results of a Fold or Traversal that points at a monoidal value.

view . to ≡ id

>>> view (to f) a
f a

>>> view _2 (1,"hello")
"hello"

>>> view (to succ) 5
6

>>> view (_2._1) ("hello",("world","!!!"))
"world"

As view is commonly used to access the target of a Getter or obtain a monoidal summary of the targets of a Fold, It may be useful to think of it as having one of these more restricted signatures:

view ::             Getter s a     -> s -> a
view :: Monoid m => Fold s m       -> s -> m
view ::             Iso' s a       -> s -> a
view ::             Lens' s a      -> s -> a
view :: Monoid m => Traversal' s m -> s -> m

In a more general setting, such as when working with a Monad transformer stack you can use:

view :: MonadReader s m             => Getter s a     -> m a
view :: (MonadReader s m, Monoid a) => Fold s a       -> m a
view :: MonadReader s m             => Iso' s a       -> m a
view :: MonadReader s m             => Lens' s a      -> m a
view :: (MonadReader s m, Monoid a) => Traversal' s a -> m a

views :: MonadReader s m => LensLike' (Const r) s a -> (a -> r) -> m r Source #

View a function of the value pointed to by a Getter or Lens or the result of folding over the result of mapping the targets of a Fold or Traversal.

views l f ≡ view (l . to f)

>>> views (to f) g a
g (f a)

>>> views _2 length (1,"hello")
5

As views is commonly used to access the target of a Getter or obtain a monoidal summary of the targets of a Fold, It may be useful to think of it as having one of these more restricted signatures:

views ::             Getter s a     -> (a -> r) -> s -> r
views :: Monoid m => Fold s a       -> (a -> m) -> s -> m
views ::             Iso' s a       -> (a -> r) -> s -> r
views ::             Lens' s a      -> (a -> r) -> s -> r
views :: Monoid m => Traversal' s a -> (a -> m) -> s -> m

In a more general setting, such as when working with a Monad transformer stack you can use:

views :: MonadReader s m             => Getter s a     -> (a -> r) -> m r
views :: (MonadReader s m, Monoid r) => Fold s a       -> (a -> r) -> m r
views :: MonadReader s m             => Iso' s a       -> (a -> r) -> m r
views :: MonadReader s m             => Lens' s a      -> (a -> r) -> m r
views :: (MonadReader s m, Monoid r) => Traversal' s a -> (a -> r) -> m r

views :: MonadReader s m => Getting r s a -> (a -> r) -> m r

use :: MonadState s m => Getting a s a -> m a Source #

Use the target of a Lens, Iso, or Getter in the current state, or use a summary of a Fold or Traversal that points to a monoidal value.

>>> evalState (use _1) (a,b)
a

>>> evalState (use _1) ("hello","world")
"hello"

use :: MonadState s m             => Getter s a     -> m a
use :: (MonadState s m, Monoid r) => Fold s r       -> m r
use :: MonadState s m             => Iso' s a       -> m a
use :: MonadState s m             => Lens' s a      -> m a
use :: (MonadState s m, Monoid r) => Traversal' s r -> m r

uses :: MonadState s m => LensLike' (Const r) s a -> (a -> r) -> m r Source #

Use the target of a Lens, Iso or Getter in the current state, or use a summary of a Fold or Traversal that points to a monoidal value.

>>> evalState (uses _1 length) ("hello","world")
5

uses :: MonadState s m             => Getter s a     -> (a -> r) -> m r
uses :: (MonadState s m, Monoid r) => Fold s a       -> (a -> r) -> m r
uses :: MonadState s m             => Lens' s a      -> (a -> r) -> m r
uses :: MonadState s m             => Iso' s a       -> (a -> r) -> m r
uses :: (MonadState s m, Monoid r) => Traversal' s a -> (a -> r) -> m r

uses :: MonadState s m => Getting r s t a b -> (a -> r) -> m r

listening :: MonadWriter w m => Getting u w u -> m a -> m (a, u) Source #

This is a generalized form of listen that only extracts the portion of the log that is focused on by a Getter. If given a Fold or a Traversal then a monoidal summary of the parts of the log that are visited will be returned.

listening :: MonadWriter w m             => Getter w u     -> m a -> m (a, u)
listening :: MonadWriter w m             => Lens' w u      -> m a -> m (a, u)
listening :: MonadWriter w m             => Iso' w u       -> m a -> m (a, u)
listening :: (MonadWriter w m, Monoid u) => Fold w u       -> m a -> m (a, u)
listening :: (MonadWriter w m, Monoid u) => Traversal' w u -> m a -> m (a, u)
listening :: (MonadWriter w m, Monoid u) => Prism' w u     -> m a -> m (a, u)

listenings :: MonadWriter w m => Getting v w u -> (u -> v) -> m a -> m (a, v) Source #

This is a generalized form of listen that only extracts the portion of the log that is focused on by a Getter. If given a Fold or a Traversal then a monoidal summary of the parts of the log that are visited will be returned.

listenings :: MonadWriter w m             => Getter w u     -> (u -> v) -> m a -> m (a, v)
listenings :: MonadWriter w m             => Lens' w u      -> (u -> v) -> m a -> m (a, v)
listenings :: MonadWriter w m             => Iso' w u       -> (u -> v) -> m a -> m (a, v)
listenings :: (MonadWriter w m, Monoid v) => Fold w u       -> (u -> v) -> m a -> m (a, v)
listenings :: (MonadWriter w m, Monoid v) => Traversal' w u -> (u -> v) -> m a -> m (a, v)
listenings :: (MonadWriter w m, Monoid v) => Prism' w u     -> (u -> v) -> m a -> m (a, v)

iview :: MonadReader s m => IndexedGetting i (i, a) s a -> m (i, a) Source #

View the index and value of an IndexedGetter into the current environment as a pair.

When applied to an IndexedFold the result will most likely be a nonsensical monoidal summary of the indices tupled with a monoidal summary of the values and probably not whatever it is you wanted.

iviews :: MonadReader s m => IndexedGetting i r s a -> (i -> a -> r) -> m r Source #

View a function of the index and value of an IndexedGetter into the current environment.

When applied to an IndexedFold the result will be a monoidal summary instead of a single answer.

iviews ≡ ifoldMapOf

iuse :: MonadState s m => IndexedGetting i (i, a) s a -> m (i, a) Source #

Use the index and value of an IndexedGetter into the current state as a pair.

When applied to an IndexedFold the result will most likely be a nonsensical monoidal summary of the indices tupled with a monoidal summary of the values and probably not whatever it is you wanted.

iuses :: MonadState s m => IndexedGetting i r s a -> (i -> a -> r) -> m r Source #

Use a function of the index and value of an IndexedGetter into the current state.

When applied to an IndexedFold the result will be a monoidal summary instead of a single answer.

ilistening :: MonadWriter w m => IndexedGetting i (i, u) w u -> m a -> m (a, (i, u)) Source #

This is a generalized form of listen that only extracts the portion of the log that is focused on by a Getter. If given a Fold or a Traversal then a monoidal summary of the parts of the log that are visited will be returned.

ilistening :: MonadWriter w m             => IndexedGetter i w u     -> m a -> m (a, (i, u))
ilistening :: MonadWriter w m             => IndexedLens' i w u      -> m a -> m (a, (i, u))
ilistening :: (MonadWriter w m, Monoid u) => IndexedFold i w u       -> m a -> m (a, (i, u))
ilistening :: (MonadWriter w m, Monoid u) => IndexedTraversal' i w u -> m a -> m (a, (i, u))

ilistenings :: MonadWriter w m => IndexedGetting i v w u -> (i -> u -> v) -> m a -> m (a, v) Source #

This is a generalized form of listen that only extracts the portion of the log that is focused on by a Getter. If given a Fold or a Traversal then a monoidal summary of the parts of the log that are visited will be returned.

ilistenings :: MonadWriter w m             => IndexedGetter w u     -> (i -> u -> v) -> m a -> m (a, v)
ilistenings :: MonadWriter w m             => IndexedLens' w u      -> (i -> u -> v) -> m a -> m (a, v)
ilistenings :: (MonadWriter w m, Monoid v) => IndexedFold w u       -> (i -> u -> v) -> m a -> m (a, v)
ilistenings :: (MonadWriter w m, Monoid v) => IndexedTraversal' w u -> (i -> u -> v) -> m a -> m (a, v)

getting :: (Profunctor p, Profunctor q, Functor f, Contravariant f) => Optical p q f s t a b -> Optical' p q f s a Source #

Coerce a Getter-compatible Optical to an Optical'. This is useful when using a Traversal that is not simple as a Getter or a Fold.

getting :: Traversal s t a b          -> Fold s a
getting :: Lens s t a b               -> Getter s a
getting :: IndexedTraversal i s t a b -> IndexedFold i s a
getting :: IndexedLens i s t a b      -> IndexedGetter i s a

selfIndex :: Indexable a p => p a fb -> a -> fb Source #

Use a value itself as its own index. This is essentially an indexed version of id.

Note: When used to modify the value, this can break the index requirements assumed by indices and similar, so this is only properly an IndexedGetter, but it can be used as more.

selfIndex :: IndexedGetter a a b

reindexed :: Indexable j p => (i -> j) -> (Indexed i a b -> r) -> p a b -> r Source #

Remap the index.

icompose :: Indexable p c => (i -> j -> p) -> (Indexed i s t -> r) -> (Indexed j a b -> s -> t) -> c a b -> r Source #

Composition of Indexed functions with a user supplied function for combining indices.

indexing :: Indexable Int p => ((a -> Indexing f b) -> s -> Indexing f t) -> p a (f b) -> s -> f t Source #

Transform a Traversal into an IndexedTraversal or a Fold into an IndexedFold, etc.

indexing :: Traversal s t a b -> IndexedTraversal Int s t a b
indexing :: Prism s t a b     -> IndexedTraversal Int s t a b
indexing :: Lens s t a b      -> IndexedLens Int  s t a b
indexing :: Iso s t a b       -> IndexedLens Int s t a b
indexing :: Fold s a          -> IndexedFold Int s a
indexing :: Getter s a        -> IndexedGetter Int s a

indexing :: Indexable Int p => LensLike (Indexing f) s t a b -> Over p f s t a b

indexing64 :: Indexable Int64 p => ((a -> Indexing64 f b) -> s -> Indexing64 f t) -> p a (f b) -> s -> f t Source #

Transform a Traversal into an IndexedTraversal or a Fold into an IndexedFold, etc.

This combinator is like indexing except that it handles large traversals and folds gracefully.

indexing64 :: Traversal s t a b -> IndexedTraversal Int64 s t a b
indexing64 :: Prism s t a b     -> IndexedTraversal Int64 s t a b
indexing64 :: Lens s t a b      -> IndexedLens Int64 s t a b
indexing64 :: Iso s t a b       -> IndexedLens Int64 s t a b
indexing64 :: Fold s a          -> IndexedFold Int64 s a
indexing64 :: Getter s a        -> IndexedGetter Int64 s a

indexing64 :: Indexable Int64 p => LensLike (Indexing64 f) s t a b -> Over p f s t a b

imapped :: FunctorWithIndex i f => IndexedSetter i (f a) (f b) a b Source #

The IndexedSetter for a FunctorWithIndex.

If you don't need access to the index, then mapped is more flexible in what it accepts.

ifolded :: FoldableWithIndex i f => IndexedFold i (f a) a Source #

The IndexedFold of a FoldableWithIndex container.

ifolded . asIndex is a fold over the keys of a FoldableWithIndex.

>>> Data.Map.fromList [(2, "hello"), (1, "world")]^..ifolded.asIndex
[1,2]

withIndex :: (Indexable i p, Functor f) => p (i, s) (f (j, t)) -> Indexed i s (f t) Source #

Fold a container with indices returning both the indices and the values.

The result is only valid to compose in a Traversal, if you don't edit the index as edits to the index have no effect.

>>> [10, 20, 30] ^.. ifolded . withIndex
[(0,10),(1,20),(2,30)]

>>> [10, 20, 30] ^.. ifolded . withIndex . alongside negated (re _Show)
[(0,"10"),(-1,"20"),(-2,"30")]

asIndex :: (Indexable i p, Contravariant f, Functor f) => p i (f i) -> Indexed i s (f s) Source #

When composed with an IndexedFold or IndexedTraversal this yields an (Indexed) Fold of the indices.

itraversed :: TraversableWithIndex i t => IndexedTraversal i (t a) (t b) a b Source #

The IndexedTraversal of a TraversableWithIndex container.

ifoldMapBy :: FoldableWithIndex i t => (r -> r -> r) -> r -> (i -> a -> r) -> t a -> r Source #

ifoldMapByOf :: IndexedFold i t a -> (r -> r -> r) -> r -> (i -> a -> r) -> t -> r Source #

itraverseBy :: TraversableWithIndex i t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (i -> a -> f b) -> t a -> f (t b) Source #

itraverseByOf :: IndexedTraversal i s t a b -> (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (i -> a -> f b) -> s -> f t Source #

makePrisms Source #

Arguments

:: Name	Type constructor name
-> DecsQ

Generate a Prism for each constructor of a data type. Isos generated when possible. Reviews are created for constructors with existentially quantified constructors and GADTs.

e.g.

data FooBarBaz a
  = Foo Int
  | Bar a
  | Baz Int Char
makePrisms ''FooBarBaz

will create

_Foo :: Prism' (FooBarBaz a) Int
_Bar :: Prism (FooBarBaz a) (FooBarBaz b) a b
_Baz :: Prism' (FooBarBaz a) (Int, Char)

makeClassyPrisms Source #

Arguments

:: Name	Type constructor name
-> DecsQ

Generate a Prism for each constructor of a data type and combine them into a single class. No Isos are created. Reviews are created for constructors with existentially quantified constructors and GADTs.

e.g.

data FooBarBaz a
  = Foo Int
  | Bar a
  | Baz Int Char
makeClassyPrisms ''FooBarBaz

will create

class AsFooBarBaz s a | s -> a where
  _FooBarBaz :: Prism' s (FooBarBaz a)
  _Foo :: Prism' s Int
  _Bar :: Prism' s a
  _Baz :: Prism' s (Int,Char)

  _Foo = _FooBarBaz . _Foo
  _Bar = _FooBarBaz . _Bar
  _Baz = _FooBarBaz . _Baz

instance AsFooBarBaz (FooBarBaz a) a

Generate an As class of prisms. Names are selected by prefixing the constructor name with an underscore. Constructors with multiple fields will construct Prisms to tuples of those fields.

In the event that the name of a data type is also the name of one of its constructors, the name of the Prism generated for the data type will be prefixed with an extra _ (if the data type name is prefix) or . (if the name is infix) to disambiguate it from the Prism for the corresponding constructor. For example, this code:

data Quux = Quux Int | Fred Bool
makeClassyPrisms ''Quux

will create:

class AsQuux s where
  __Quux :: Prism' s Quux -- Data type prism
  _Quux :: Prism' s Int   -- Constructor prism
  _Fred :: Prism' s Bool

  _Quux = __Quux . _Quux
  _Fred = __Quux . _Fred

instance AsQuux Quux

retagged :: (Profunctor p, Bifunctor p) => p a b -> p s b Source #

This is a profunctor used internally to implement Review

It plays a role similar to that of Accessor or Const do for Control.Lens.Getter

iso :: (s -> a) -> (b -> t) -> Iso s t a b Source #

Build a simple isomorphism from a pair of inverse functions.

view (iso f g) ≡ f
view (from (iso f g)) ≡ g
over (iso f g) h ≡ g . h . f
over (from (iso f g)) h ≡ f . h . g

cloneIso :: AnIso s t a b -> Iso s t a b Source #

Convert from AnIso back to any Iso.

This is useful when you need to store an isomorphism as a data type inside a container and later reconstitute it as an overloaded function.

See cloneLens or cloneTraversal for more information on why you might want to do this.

withIso :: forall s t a b rep (r :: TYPE rep). AnIso s t a b -> ((s -> a) -> (b -> t) -> r) -> r Source #

Extract the two functions, one from s -> a and one from b -> t that characterize an Iso.

au :: Functor f => AnIso s t a b -> ((b -> t) -> f s) -> f a Source #

Based on ala from Conor McBride's work on Epigram.

This version is generalized to accept any Iso, not just a newtype.

>>> au (_Wrapping Sum) foldMap [1,2,3,4]
10

You may want to think of this combinator as having the following, simpler type:

au :: AnIso s t a b -> ((b -> t) -> e -> s) -> e -> a

au = xplat . from

auf :: (Functor f, Functor g) => AnIso s t a b -> (f t -> g s) -> f b -> g a Source #

Based on ala' from Conor McBride's work on Epigram.

This version is generalized to accept any Iso, not just a newtype.

For a version you pass the name of the newtype constructor to, see alaf.

>>> auf (_Wrapping Sum) (foldMapOf both) Prelude.length ("hello","world")
10

Mnemonically, the German auf plays a similar role to à la, and the combinator is au with an extra function argument:

auf :: Iso s t a b -> ((r -> t) -> e -> s) -> (r -> b) -> e -> a

but the signature is general.

Note: The direction of the Iso required for this function changed in lens 4.18 to match up with the behavior of au. For the old behavior use xplatf or for a version that is compatible across both old and new versions of lens you can just use coerce!

xplat :: Optic (Costar ((->) s)) g s t a b -> ((s -> a) -> g b) -> g t Source #

xplat = au . from but with a nicer signature.

xplatf :: Optic (Costar f) g s t a b -> (f a -> g b) -> f s -> g t Source #

xplatf = auf . from but with a nicer signature.

>>> xplatf (_Unwrapping Sum) (foldMapOf both) Prelude.length ("hello","world")
10

xplatf :: Iso s t a b -> ((r -> a) -> e -> b) -> (r -> s) -> e -> t

under :: AnIso s t a b -> (t -> s) -> b -> a Source #

The opposite of working over a Setter is working under an isomorphism.

under ≡ over . from

under :: Iso s t a b -> (t -> s) -> b -> a

mapping :: (Functor f, Functor g) => AnIso s t a b -> Iso (f s) (g t) (f a) (g b) Source #

This can be used to lift any Iso into an arbitrary Functor.

non :: Eq a => a -> Iso' (Maybe a) a Source #

If v is an element of a type a, and a' is a sans the element v, then non v is an isomorphism from Maybe a' to a.

non ≡ non' . only

Keep in mind this is only a real isomorphism if you treat the domain as being Maybe (a sans v).

This is practically quite useful when you want to have a Map where all the entries should have non-zero values.

>>> Map.fromList [("hello",1)] & at "hello" . non 0 +~ 2
fromList [("hello",3)]

>>> Map.fromList [("hello",1)] & at "hello" . non 0 -~ 1
fromList []

>>> Map.fromList [("hello",1)] ^. at "hello" . non 0
1

>>> Map.fromList [] ^. at "hello" . non 0
0

This combinator is also particularly useful when working with nested maps.

e.g. When you want to create the nested Map when it is missing:

>>> Map.empty & at "hello" . non Map.empty . at "world" ?~ "!!!"
fromList [("hello",fromList [("world","!!!")])]

and when have deleting the last entry from the nested Map mean that we should delete its entry from the surrounding one:

>>> Map.fromList [("hello",Map.fromList [("world","!!!")])] & at "hello" . non Map.empty . at "world" .~ Nothing
fromList []

It can also be used in reverse to exclude a given value:

>>> non 0 # rem 10 4
Just 2

>>> non 0 # rem 10 5
Nothing

non' :: APrism' a () -> Iso' (Maybe a) a Source #

non' p generalizes non (p # ()) to take any unit Prism

This function generates an isomorphism between Maybe (a | isn't p a) and a.

>>> Map.singleton "hello" Map.empty & at "hello" . non' _Empty . at "world" ?~ "!!!"
fromList [("hello",fromList [("world","!!!")])]

>>> Map.fromList [("hello",Map.fromList [("world","!!!")])] & at "hello" . non' _Empty . at "world" .~ Nothing
fromList []

anon :: a -> (a -> Bool) -> Iso' (Maybe a) a Source #

anon a p generalizes non a to take any value and a predicate.

This function assumes that p a holds True and generates an isomorphism between Maybe (a | not (p a)) and a.

>>> Map.empty & at "hello" . anon Map.empty Map.null . at "world" ?~ "!!!"
fromList [("hello",fromList [("world","!!!")])]

>>> Map.fromList [("hello",Map.fromList [("world","!!!")])] & at "hello" . anon Map.empty Map.null . at "world" .~ Nothing
fromList []

enum :: Enum a => Iso' Int a Source #

This isomorphism can be used to convert to or from an instance of Enum.

>>> LT^.from enum
0

>>> 97^.enum :: Char
'a'

Note: this is only an isomorphism from the numeric range actually used and it is a bit of a pleasant fiction, since there are questionable Enum instances for Double, and Float that exist solely for [1.0 .. 4.0] sugar and the instances for those and Integer don't cover all values in their range.

curried :: Iso ((a, b) -> c) ((d, e) -> f) (a -> b -> c) (d -> e -> f) Source #

The canonical isomorphism for currying and uncurrying a function.

curried = iso curry uncurry

>>> (fst^.curried) 3 4
3

>>> view curried fst 3 4
3

uncurried :: Iso (a -> b -> c) (d -> e -> f) ((a, b) -> c) ((d, e) -> f) Source #

The canonical isomorphism for uncurrying and currying a function.

uncurried = iso uncurry curry

uncurried = from curried

>>> ((+)^.uncurried) (1,2)
3

flipped :: Iso (a -> b -> c) (a' -> b' -> c') (b -> a -> c) (b' -> a' -> c') Source #

The isomorphism for flipping a function.

>>> ((,)^.flipped) 1 2
(2,1)

reversed :: Reversing a => Iso' a a Source #

An Iso between a list, ByteString, Text fragment, etc. and its reversal.

>>> "live" ^. reversed
"evil"

>>> "live" & reversed %~ ('d':)
"lived"

involuted :: (a -> a) -> Iso' a a Source #

Given a function that is its own inverse, this gives you an Iso using it in both directions.

involuted ≡ join iso

>>> "live" ^. involuted reverse
"evil"

>>> "live" & involuted reverse %~ ('d':)
"lived"

magma :: LensLike (Mafic a b) s t a b -> Iso s u (Magma Int t b a) (Magma j u c c) Source #

This isomorphism can be used to inspect a Traversal to see how it associates the structure and it can also be used to bake the Traversal into a Magma so that you can traverse over it multiple times.

imagma :: Over (Indexed i) (Molten i a b) s t a b -> Iso s t' (Magma i t b a) (Magma j t' c c) Source #

This isomorphism can be used to inspect an IndexedTraversal to see how it associates the structure and it can also be used to bake the IndexedTraversal into a Magma so that you can traverse over it multiple times with access to the original indices.

contramapping :: Contravariant f => AnIso s t a b -> Iso (f a) (f b) (f s) (f t) Source #

Lift an Iso into a Contravariant functor.

contramapping :: Contravariant f => Iso s t a b -> Iso (f a) (f b) (f s) (f t)
contramapping :: Contravariant f => Iso' s a -> Iso' (f a) (f s)

dimapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> AnIso s' t' a' b' -> Iso (p a s') (q b t') (p s a') (q t b') Source #

Lift two Isos into both arguments of a Profunctor simultaneously.

dimapping :: Profunctor p => Iso s t a b -> Iso s' t' a' b' -> Iso (p a s') (p b t') (p s a') (p t b')
dimapping :: Profunctor p => Iso' s a -> Iso' s' a' -> Iso' (p a s') (p s a')

lmapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> Iso (p a x) (q b y) (p s x) (q t y) Source #

Lift an Iso contravariantly into the left argument of a Profunctor.

lmapping :: Profunctor p => Iso s t a b -> Iso (p a x) (p b y) (p s x) (p t y)
lmapping :: Profunctor p => Iso' s a -> Iso' (p a x) (p s x)

rmapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> Iso (p x s) (q y t) (p x a) (q y b) Source #

Lift an Iso covariantly into the right argument of a Profunctor.

rmapping :: Profunctor p => Iso s t a b -> Iso (p x s) (p y t) (p x a) (p y b)
rmapping :: Profunctor p => Iso' s a -> Iso' (p x s) (p x a)

bimapping :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> AnIso s' t' a' b' -> Iso (f s s') (g t t') (f a a') (g b b') Source #

Lift two Isos into both arguments of a Bifunctor.

bimapping :: Bifunctor p => Iso s t a b -> Iso s' t' a' b' -> Iso (p s s') (p t t') (p a a') (p b b')
bimapping :: Bifunctor p => Iso' s a -> Iso' s' a' -> Iso' (p s s') (p a a')

firsting :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> Iso (f s x) (g t y) (f a x) (g b y) Source #

Lift an Iso into the first argument of a Bifunctor.

firsting :: Bifunctor p => Iso s t a b -> Iso (p s x) (p t y) (p a x) (p b y)
firsting :: Bifunctor p => Iso' s a -> Iso' (p s x) (p a x)

seconding :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> Iso (f x s) (g y t) (f x a) (g y b) Source #

Lift an Iso into the second argument of a Bifunctor. This is essentially the same as mapping, but it takes a 'Bifunctor p' constraint instead of a 'Functor (p a)' one.

seconding :: Bifunctor p => Iso s t a b -> Iso (p x s) (p y t) (p x a) (p y b)
seconding :: Bifunctor p => Iso' s a -> Iso' (p x s) (p x a)

coerced :: forall s t a b. (Coercible s a, Coercible t b) => Iso s t a b Source #

Data types that are representationally equal are isomorphic.

This is only available on GHC 7.8+

Since: 4.13

lens :: (s -> a) -> (s -> b -> t) -> Lens s t a b Source #

Build a Lens from a getter and a setter.

lens :: Functor f => (s -> a) -> (s -> b -> t) -> (a -> f b) -> s -> f t

>>> s ^. lens getter setter
getter s

>>> s & lens getter setter .~ b
setter s b

>>> s & lens getter setter %~ f
setter s (f (getter s))

lens :: (s -> a) -> (s -> a -> s) -> Lens' s a

ilens :: (s -> (i, a)) -> (s -> b -> t) -> IndexedLens i s t a b Source #

Build an IndexedLens from a Getter and a Setter.

iplens :: (s -> a) -> (s -> b -> t) -> IndexPreservingLens s t a b Source #

Build an index-preserving Lens from a Getter and a Setter.

withLens :: forall s t a b rep (r :: TYPE rep). ALens s t a b -> ((s -> a) -> (s -> b -> t) -> r) -> r Source #

Obtain a getter and a setter from a lens, reversing lens.

choosing :: Functor f => LensLike f s t a b -> LensLike f s' t' a b -> LensLike f (Either s s') (Either t t') a b Source #

Merge two lenses, getters, setters, folds or traversals.

chosen ≡ choosing id id

choosing :: Getter s a     -> Getter s' a     -> Getter (Either s s') a
choosing :: Fold s a       -> Fold s' a       -> Fold (Either s s') a
choosing :: Lens' s a      -> Lens' s' a      -> Lens' (Either s s') a
choosing :: Traversal' s a -> Traversal' s' a -> Traversal' (Either s s') a
choosing :: Setter' s a    -> Setter' s' a    -> Setter' (Either s s') a

alongside :: LensLike (AlongsideLeft f b') s t a b -> LensLike (AlongsideRight f t) s' t' a' b' -> LensLike f (s, s') (t, t') (a, a') (b, b') Source #

alongside makes a Lens from two other lenses or a Getter from two other getters by executing them on their respective halves of a product.

>>> (Left a, Right b)^.alongside chosen chosen
(a,b)

>>> (Left a, Right b) & alongside chosen chosen .~ (c,d)
(Left c,Right d)

alongside :: Lens   s t a b -> Lens   s' t' a' b' -> Lens   (s,s') (t,t') (a,a') (b,b')
alongside :: Getter s   a   -> Getter s'    a'    -> Getter (s,s')        (a,a')

inside :: Corepresentable p => ALens s t a b -> Lens (p e s) (p e t) (p e a) (p e b) Source #

Lift a Lens so it can run under a function (or other corepresentable profunctor).

inside :: Lens s t a b -> Lens (e -> s) (e -> t) (e -> a) (e -> b)

>>> (\x -> (x-1,x+1)) ^. inside _1 $ 5
4

>>> runState (modify (1:) >> modify (2:)) ^. (inside _2) $ []
[2,1]

cloneLens :: ALens s t a b -> Lens s t a b Source #

Cloning a Lens is one way to make sure you aren't given something weaker, such as a Traversal and can be used as a way to pass around lenses that have to be monomorphic in f.

Note: This only accepts a proper Lens.

>>> let example l x = set (cloneLens l) (x^.cloneLens l + 1) x in example _2 ("hello",1,"you")
("hello",2,"you")

cloneIndexPreservingLens :: ALens s t a b -> IndexPreservingLens s t a b Source #

Clone a Lens as an IndexedPreservingLens that just passes through whatever index is on any IndexedLens, IndexedFold, IndexedGetter or IndexedTraversal it is composed with.

cloneIndexedLens :: AnIndexedLens i s t a b -> IndexedLens i s t a b Source #

Clone an IndexedLens as an IndexedLens with the same index.

overA :: Arrow ar => LensLike (Context a b) s t a b -> ar a b -> ar s t Source #

over for Arrows.

Unlike over, overA can't accept a simple Setter, but requires a full lens, or close enough.

>>> overA _1 ((+1) *** (+2)) ((1,2),6)
((2,4),6)

overA :: Arrow ar => Lens s t a b -> ar a b -> ar s t

storing :: ALens s t a b -> b -> s -> t Source #

A version of set that works on ALens.

>>> storing _2 "world" ("hello","there")
("hello","world")

devoid :: Over p f Void Void a b Source #

There is a field for every type in the Void. Very zen.

>>> [] & mapped.devoid +~ 1
[]

>>> Nothing & mapped.devoid %~ abs
Nothing

devoid :: Lens' Void a

united :: Lens' a () Source #

We can always retrieve a () from any type.

>>> "hello"^.united
()

>>> "hello" & united .~ ()
"hello"

head1 :: Traversable1 t => Lens' (t a) a Source #

A Lens focusing on the first element of a Traversable1 container.

>>> 2 :| [3, 4] & head1 +~ 10
12 :| [3,4]

>>> Identity True ^. head1
True

last1 :: Traversable1 t => Lens' (t a) a Source #

A Lens focusing on the last element of a Traversable1 container.

>>> 2 :| [3, 4] & last1 +~ 10
2 :| [3,14]

>>> Node 'a' [Node 'b' [], Node 'c' []] ^. last1
'c'

locus :: IndexedComonadStore p => Lens (p a c s) (p b c s) a b Source #

This Lens lets you view the current pos of any indexed store comonad and seek to a new position. This reduces the API for working these instances to a single Lens.

ipos w ≡ w ^. locus
iseek s w ≡ w & locus .~ s
iseeks f w ≡ w & locus %~ f

locus :: Lens' (Context' a s) a
locus :: Conjoined p => Lens' (Pretext' p a s) a
locus :: Conjoined p => Lens' (PretextT' p g a s) a

fusing :: Functor f => LensLike (Yoneda f) s t a b -> LensLike f s t a b Source #

Fuse a composition of lenses using Yoneda to provide fmap fusion.

In general, given a pair of lenses foo and bar

fusing (foo.bar) = foo.bar

however, foo and bar are either going to fmap internally or they are trivial.

fusing exploits the Yoneda lemma to merge these separate uses into a single fmap.

This is particularly effective when the choice of functor f is unknown at compile time or when the Lens foo.bar in the above description is recursive or complex enough to prevent inlining.

fusing :: Lens s t a b -> Lens s t a b

ilevels :: Applicative f => Traversing (Indexed i) f s t a b -> IndexedLensLike Int f s t (Level i a) (Level j b) Source #

This provides a breadth-first Traversal or Fold of the individual levels of any other Traversal or Fold via iterative deepening depth-first search. The levels are returned to you in a compressed format.

This is similar to levels, but retains the index of the original IndexedTraversal, so you can access it when traversing the levels later on.

>>> ["dog","cat"]^@..ilevels (traversed<.>traversed).itraversed
[((0,0),'d'),((0,1),'o'),((1,0),'c'),((0,2),'g'),((1,1),'a'),((1,2),'t')]

The resulting Traversal of the levels which is indexed by the depth of each Level.

>>> ["dog","cat"]^@..ilevels (traversed<.>traversed)<.>itraversed
[((2,(0,0)),'d'),((3,(0,1)),'o'),((3,(1,0)),'c'),((4,(0,2)),'g'),((4,(1,1)),'a'),((5,(1,2)),'t')]

ilevels :: IndexedTraversal i s t a b      -> IndexedTraversal Int s t (Level i a) (Level i b)
ilevels :: IndexedFold i s a               -> IndexedFold Int s (Level i a)

Note: Internally this is implemented by using an illegal Applicative, as it extracts information in an order that violates the Applicative laws.

children :: Plated a => a -> [a] Source #

Extract the immediate descendants of a Plated container.

children ≡ toListOf plate

rewrite :: Plated a => (a -> Maybe a) -> a -> a Source #

Rewrite by applying a rule everywhere you can. Ensures that the rule cannot be applied anywhere in the result:

propRewrite r x = all (isNothing . r) (universe (rewrite r x))

Usually transform is more appropriate, but rewrite can give better compositionality. Given two single transformations f and g, you can construct \a -> f a <|> g a which performs both rewrites until a fixed point.

rewriteOf :: ASetter a b a b -> (b -> Maybe a) -> a -> b Source #

Rewrite by applying a rule everywhere you can. Ensures that the rule cannot be applied anywhere in the result:

propRewriteOf l r x = all (isNothing . r) (universeOf l (rewriteOf l r x))

Usually transformOf is more appropriate, but rewriteOf can give better compositionality. Given two single transformations f and g, you can construct \a -> f a <|> g a which performs both rewrites until a fixed point.

rewriteOf :: Iso' a a       -> (a -> Maybe a) -> a -> a
rewriteOf :: Lens' a a      -> (a -> Maybe a) -> a -> a
rewriteOf :: Traversal' a a -> (a -> Maybe a) -> a -> a
rewriteOf :: Setter' a a    -> (a -> Maybe a) -> a -> a

rewriteOn :: Plated a => ASetter s t a a -> (a -> Maybe a) -> s -> t Source #

Rewrite recursively over part of a larger structure.

rewriteOn :: Plated a => Iso' s a       -> (a -> Maybe a) -> s -> s
rewriteOn :: Plated a => Lens' s a      -> (a -> Maybe a) -> s -> s
rewriteOn :: Plated a => Traversal' s a -> (a -> Maybe a) -> s -> s
rewriteOn :: Plated a => ASetter' s a   -> (a -> Maybe a) -> s -> s

rewriteOnOf :: ASetter s t a b -> ASetter a b a b -> (b -> Maybe a) -> s -> t Source #

Rewrite recursively over part of a larger structure using a specified Setter.

rewriteOnOf :: Iso' s a       -> Iso' a a       -> (a -> Maybe a) -> s -> s
rewriteOnOf :: Lens' s a      -> Lens' a a      -> (a -> Maybe a) -> s -> s
rewriteOnOf :: Traversal' s a -> Traversal' a a -> (a -> Maybe a) -> s -> s
rewriteOnOf :: Setter' s a    -> Setter' a a    -> (a -> Maybe a) -> s -> s

rewriteM :: (Monad m, Plated a) => (a -> m (Maybe a)) -> a -> m a Source #

Rewrite by applying a monadic rule everywhere you can. Ensures that the rule cannot be applied anywhere in the result.

rewriteMOf :: Monad m => LensLike (WrappedMonad m) a b a b -> (b -> m (Maybe a)) -> a -> m b Source #

Rewrite by applying a monadic rule everywhere you recursing with a user-specified Traversal. Ensures that the rule cannot be applied anywhere in the result.

rewriteMOn :: (Monad m, Plated a) => LensLike (WrappedMonad m) s t a a -> (a -> m (Maybe a)) -> s -> m t Source #

Rewrite by applying a monadic rule everywhere inside of a structure located by a user-specified Traversal. Ensures that the rule cannot be applied anywhere in the result.

rewriteMOnOf :: Monad m => LensLike (WrappedMonad m) s t a b -> LensLike (WrappedMonad m) a b a b -> (b -> m (Maybe a)) -> s -> m t Source #

Rewrite by applying a monadic rule everywhere inside of a structure located by a user-specified Traversal, using a user-specified Traversal for recursion. Ensures that the rule cannot be applied anywhere in the result.

universe :: Plated a => a -> [a] Source #

Retrieve all of the transitive descendants of a Plated container, including itself.

universeOf :: Getting (Endo [a]) a a -> a -> [a] Source #

Given a Fold that knows how to locate immediate children, retrieve all of the transitive descendants of a node, including itself.

universeOf :: Fold a a -> a -> [a]

universeOn :: Plated a => Getting (Endo [a]) s a -> s -> [a] Source #

Given a Fold that knows how to find Plated parts of a container retrieve them and all of their descendants, recursively.

universeOnOf :: Getting (Endo [a]) s a -> Getting (Endo [a]) a a -> s -> [a] Source #

Given a Fold that knows how to locate immediate children, retrieve all of the transitive descendants of a node, including itself that lie in a region indicated by another Fold.

toListOf l ≡ universeOnOf l ignored

cosmos :: Plated a => Fold a a Source #

Fold over all transitive descendants of a Plated container, including itself.

cosmosOf :: (Applicative f, Contravariant f) => LensLike' f a a -> LensLike' f a a Source #

Given a Fold that knows how to locate immediate children, fold all of the transitive descendants of a node, including itself.

cosmosOf :: Fold a a -> Fold a a

cosmosOn :: (Applicative f, Contravariant f, Plated a) => LensLike' f s a -> LensLike' f s a Source #

Given a Fold that knows how to find Plated parts of a container fold them and all of their descendants, recursively.

cosmosOn :: Plated a => Fold s a -> Fold s a

cosmosOnOf :: (Applicative f, Contravariant f) => LensLike' f s a -> LensLike' f a a -> LensLike' f s a Source #

Given a Fold that knows how to locate immediate children, fold all of the transitive descendants of a node, including itself that lie in a region indicated by another Fold.

cosmosOnOf :: Fold s a -> Fold a a -> Fold s a

transformOf :: ASetter a b a b -> (b -> b) -> a -> b Source #

Transform every element by recursively applying a given Setter in a bottom-up manner.

transformOf :: Traversal' a a -> (a -> a) -> a -> a
transformOf :: Setter' a a    -> (a -> a) -> a -> a

transformOn :: Plated a => ASetter s t a a -> (a -> a) -> s -> t Source #

Transform every element in the tree in a bottom-up manner over a region indicated by a Setter.

transformOn :: Plated a => Traversal' s a -> (a -> a) -> s -> s
transformOn :: Plated a => Setter' s a    -> (a -> a) -> s -> s

transformOnOf :: ASetter s t a b -> ASetter a b a b -> (b -> b) -> s -> t Source #

Transform every element in a region indicated by a Setter by recursively applying another Setter in a bottom-up manner.

transformOnOf :: Setter' s a -> Traversal' a a -> (a -> a) -> s -> s
transformOnOf :: Setter' s a -> Setter' a a    -> (a -> a) -> s -> s

transformM :: (Monad m, Plated a) => (a -> m a) -> a -> m a Source #

Transform every element in the tree, in a bottom-up manner, monadically.

transformMOf :: Monad m => LensLike (WrappedMonad m) a b a b -> (b -> m b) -> a -> m b Source #

Transform every element in a tree using a user supplied Traversal in a bottom-up manner with a monadic effect.

transformMOf :: Monad m => Traversal' a a -> (a -> m a) -> a -> m a

transformMOn :: (Monad m, Plated a) => LensLike (WrappedMonad m) s t a a -> (a -> m a) -> s -> m t Source #

Transform every element in the tree in a region indicated by a supplied Traversal, in a bottom-up manner, monadically.

transformMOn :: (Monad m, Plated a) => Traversal' s a -> (a -> m a) -> s -> m s

transformMOnOf :: Monad m => LensLike (WrappedMonad m) s t a b -> LensLike (WrappedMonad m) a b a b -> (b -> m b) -> s -> m t Source #

Transform every element in a tree that lies in a region indicated by a supplied Traversal, walking with a user supplied Traversal in a bottom-up manner with a monadic effect.

transformMOnOf :: Monad m => Traversal' s a -> Traversal' a a -> (a -> m a) -> s -> m s

contexts :: Plated a => a -> [Context a a a] Source #

Return a list of all of the editable contexts for every location in the structure, recursively.

propUniverse x = universe x == map pos (contexts x)
propId x = all (== x) [extract w | w <- contexts x]

contexts ≡ contextsOf plate

contextsOf :: ATraversal' a a -> a -> [Context a a a] Source #

Return a list of all of the editable contexts for every location in the structure, recursively, using a user-specified Traversal to walk each layer.

propUniverse l x = universeOf l x == map pos (contextsOf l x)
propId l x = all (== x) [extract w | w <- contextsOf l x]

contextsOf :: Traversal' a a -> a -> [Context a a a]

contextsOn :: Plated a => ATraversal s t a a -> s -> [Context a a t] Source #

Return a list of all of the editable contexts for every location in the structure in an areas indicated by a user supplied Traversal, recursively using plate.

contextsOn b ≡ contextsOnOf b plate

contextsOn :: Plated a => Traversal' s a -> s -> [Context a a s]

contextsOnOf :: ATraversal s t a a -> ATraversal' a a -> s -> [Context a a t] Source #

Return a list of all of the editable contexts for every location in the structure in an areas indicated by a user supplied Traversal, recursively using another user-supplied Traversal to walk each layer.

contextsOnOf :: Traversal' s a -> Traversal' a a -> s -> [Context a a s]

holes :: Plated a => a -> [Pretext (->) a a a] Source #

The one-level version of context. This extracts a list of the immediate children as editable contexts.

Given a context you can use pos to see the values, peek at what the structure would be like with an edited result, or simply extract the original structure.

propChildren x = children l x == map pos (holes l x)
propId x = all (== x) [extract w | w <- holes l x]

holes = holesOf plate

holesOn :: Conjoined p => Over p (Bazaar p a a) s t a a -> s -> [Pretext p a a t] Source #

An alias for holesOf, provided for consistency with the other combinators.

holesOn ≡ holesOf

holesOn :: Iso' s a                -> s -> [Pretext (->) a a s]
holesOn :: Lens' s a               -> s -> [Pretext (->) a a s]
holesOn :: Traversal' s a          -> s -> [Pretext (->) a a s]
holesOn :: IndexedLens' i s a      -> s -> [Pretext (Indexed i) a a s]
holesOn :: IndexedTraversal' i s a -> s -> [Pretext (Indexed i) a a s]

holesOnOf :: Conjoined p => LensLike (Bazaar p r r) s t a b -> Over p (Bazaar p r r) a b r r -> s -> [Pretext p r r t] Source #

Extract one level of holes from a container in a region specified by one Traversal, using another.

holesOnOf b l ≡ holesOf (b . l)

holesOnOf :: Iso' s a       -> Iso' a a                -> s -> [Pretext (->) a a s]
holesOnOf :: Lens' s a      -> Lens' a a               -> s -> [Pretext (->) a a s]
holesOnOf :: Traversal' s a -> Traversal' a a          -> s -> [Pretext (->) a a s]
holesOnOf :: Lens' s a      -> IndexedLens' i a a      -> s -> [Pretext (Indexed i) a a s]
holesOnOf :: Traversal' s a -> IndexedTraversal' i a a -> s -> [Pretext (Indexed i) a a s]

para :: Plated a => (a -> [r] -> r) -> a -> r Source #

Perform a fold-like computation on each value, technically a paramorphism.

para ≡ paraOf plate

paraOf :: Getting (Endo [a]) a a -> (a -> [r] -> r) -> a -> r Source #

Perform a fold-like computation on each value, technically a paramorphism.

paraOf :: Fold a a -> (a -> [r] -> r) -> a -> r

deep :: (Conjoined p, Applicative f, Plated s) => Traversing p f s s a b -> Over p f s s a b Source #

Try to apply a traversal to all transitive descendants of a Plated container, but do not recurse through matching descendants.

deep :: Plated s => Fold s a                 -> Fold s a
deep :: Plated s => IndexedFold s a          -> IndexedFold s a
deep :: Plated s => Traversal s s a b        -> Traversal s s a b
deep :: Plated s => IndexedTraversal s s a b -> IndexedTraversal s s a b

composOpFold :: Plated a => b -> (b -> b -> b) -> (a -> b) -> a -> b Source #

Fold the immediate children of a Plated container.

composOpFold z c f = foldrOf plate (c . f) z

parts :: Plated a => Lens' a [a] Source #

The original uniplate combinator, implemented in terms of Plated as a Lens.

parts ≡ partsOf plate

The resulting Lens is safer to use as it ignores 'over-application' and deals gracefully with under-application, but it is only a proper Lens if you don't change the list length!

gplate :: (Generic a, GPlated a (Rep a)) => Traversal' a a Source #

Implement plate operation for a type using its Generic instance.

Note: the behavior may be different than with uniplate in some special cases. gplate doesn't look through other types in a group of mutually recursive types.

For example consider mutually recursive even and odd natural numbers:

>>> data Even = Z | E Odd deriving (Show, Generic, Data); data Odd = O Even deriving (Show, Generic, Data)

Then uniplate, which is based on Data, finds all even numbers less or equal than four:

>>> import Data.Data.Lens (uniplate)
>>> universeOf uniplate (E (O (E (O Z))))
[E (O (E (O Z))),E (O Z),Z]

but gplate doesn't see through Odd.

>>> universeOf gplate (E (O (E (O Z))))
[E (O (E (O Z)))]

If using Data is not an option, you can still write the traversal manually. It is sometimes useful to use helper traversals

>>> :{
let oddeven :: Traversal' Odd Even
    oddeven f (O n) = O <$> f n
    evenplate :: Traversal' Even Even
    evenplate f Z     = pure Z
    evenplate f (E n) = E <$> oddeven f n
:}

>>> universeOf evenplate (E (O (E (O Z))))
[E (O (E (O Z))),E (O Z),Z]

gplate1 :: (Generic1 f, GPlated1 f (Rep1 f)) => Traversal' (f a) (f a) Source #

Implement plate operation for a type using its Generic1 instance.

prism :: (b -> t) -> (s -> Either t a) -> Prism s t a b Source #

Build a Prism.

Either t a is used instead of Maybe a to permit the types of s and t to differ.

prism' :: (b -> s) -> (s -> Maybe a) -> Prism s s a b Source #

This is usually used to build a Prism', when you have to use an operation like cast which already returns a Maybe.

withPrism :: APrism s t a b -> ((b -> t) -> (s -> Either t a) -> r) -> r Source #

Convert APrism to the pair of functions that characterize it.

clonePrism :: APrism s t a b -> Prism s t a b Source #

Clone a Prism so that you can reuse the same monomorphically typed Prism for different purposes.

See cloneLens and cloneTraversal for examples of why you might want to do this.

outside :: Representable p => APrism s t a b -> Lens (p t r) (p s r) (p b r) (p a r) Source #

Use a Prism as a kind of first-class pattern.

outside :: Prism s t a b -> Lens (t -> r) (s -> r) (b -> r) (a -> r)

aside :: APrism s t a b -> Prism (e, s) (e, t) (e, a) (e, b) Source #

Use a Prism to work over part of a structure.

without :: APrism s t a b -> APrism u v c d -> Prism (Either s u) (Either t v) (Either a c) (Either b d) Source #

Given a pair of prisms, project sums.

Viewing a Prism as a co-Lens, this combinator can be seen to be dual to alongside.

below :: Traversable f => APrism' s a -> Prism' (f s) (f a) Source #

lift a Prism through a Traversable functor, giving a Prism that matches only if all the elements of the container match the Prism.

>>> [Left 1, Right "foo", Left 4, Right "woot"]^..below _Right
[]

>>> [Right "hail hydra!", Right "foo", Right "blah", Right "woot"]^..below _Right
[["hail hydra!","foo","blah","woot"]]

isn't :: APrism s t a b -> s -> Bool Source #

Check to see if this Prism doesn't match.

>>> isn't _Left (Right 12)
True

>>> isn't _Left (Left 12)
False

>>> isn't _Empty []
False

isn't = not . is
isn't = hasn't

matching :: APrism s t a b -> s -> Either t a Source #

Retrieve the value targeted by a Prism or return the original value while allowing the type to change if it does not match.

>>> matching _Just (Just 12)
Right 12

>>> matching _Just (Nothing :: Maybe Int) :: Either (Maybe Bool) Int
Left Nothing

matching' :: LensLike (Either a) s t a b -> s -> Either t a Source #

Like matching, but also works for combinations of Lens and Prisms, and also Traversals.

>>> matching' (_2 . _Just) ('x', Just True)
Right True

>>> matching' (_2 . _Just) ('x', Nothing :: Maybe Int) :: Either (Char, Maybe Bool) Int
Left ('x',Nothing)

>>> matching' traverse "" :: Either [Int] Char
Left []

>>> matching' traverse "xyz" :: Either [Int] Char
Right 'x'

_Left :: Prism (Either a c) (Either b c) a b Source #

This Prism provides a Traversal for tweaking the Left half of an Either:

>>> over _Left (+1) (Left 2)
Left 3

>>> over _Left (+1) (Right 2)
Right 2

>>> Right 42 ^._Left :: String
""

>>> Left "hello" ^._Left
"hello"

It also can be turned around to obtain the embedding into the Left half of an Either:

>>> _Left # 5
Left 5

>>> 5^.re _Left
Left 5

_Right :: Prism (Either c a) (Either c b) a b Source #

This Prism provides a Traversal for tweaking the Right half of an Either:

>>> over _Right (+1) (Left 2)
Left 2

>>> over _Right (+1) (Right 2)
Right 3

>>> Right "hello" ^._Right
"hello"

>>> Left "hello" ^._Right :: [Double]
[]

It also can be turned around to obtain the embedding into the Right half of an Either:

>>> _Right # 5
Right 5

>>> 5^.re _Right
Right 5

_Just :: Prism (Maybe a) (Maybe b) a b Source #

This Prism provides a Traversal for tweaking the target of the value of Just in a Maybe.

>>> over _Just (+1) (Just 2)
Just 3

Unlike traverse this is a Prism, and so you can use it to inject as well:

>>> _Just # 5
Just 5

>>> 5^.re _Just
Just 5

Interestingly,

m ^? _Just ≡ m

>>> Just x ^? _Just
Just x

>>> Nothing ^? _Just
Nothing

_Nothing :: Prism' (Maybe a) () Source #

This Prism provides the Traversal of a Nothing in a Maybe.

>>> Nothing ^? _Nothing
Just ()

>>> Just () ^? _Nothing
Nothing

But you can turn it around and use it to construct Nothing as well:

>>> _Nothing # ()
Nothing

_Void :: Prism s s a Void Source #

Void is a logically uninhabited data type.

This is a Prism that will always fail to match.

_Show :: (Read a, Show a) => Prism' String a Source #

This is an improper prism for text formatting based on Read and Show.

This Prism is "improper" in the sense that it normalizes the text formatting, but round tripping is idempotent given sane Read/Show instances.

>>> _Show # 2
"2"

>>> "EQ" ^? _Show :: Maybe Ordering
Just EQ

_Show ≡ prism' show readMaybe

nearly :: a -> (a -> Bool) -> Prism' a () Source #

This Prism compares for approximate equality with a given value and a predicate for testing, an example where the value is the empty list and the predicate checks that a list is empty (same as _Empty with the AsEmpty list instance):

>>> nearly [] null # ()
[]
>>> [1,2,3,4] ^? nearly [] null
Nothing

nearly [] null :: Prism' [a] ()

To comply with the Prism laws the arguments you supply to nearly a p are somewhat constrained.

We assume p x holds iff x ≡ a. Under that assumption then this is a valid Prism.

This is useful when working with a type where you can test equality for only a subset of its values, and the prism selects such a value.

cloneTraversal :: ATraversal s t a b -> Traversal s t a b Source #

A Traversal is completely characterized by its behavior on a Bazaar.

Cloning a Traversal is one way to make sure you aren't given something weaker, such as a Fold and can be used as a way to pass around traversals that have to be monomorphic in f.

Note: This only accepts a proper Traversal (or Lens). To clone a Lens as such, use cloneLens.

Note: It is usually better to use ReifiedTraversal and runTraversal than to cloneTraversal. The former can execute at full speed, while the latter needs to round trip through the Bazaar.

>>> let foo l a = (view (getting (cloneTraversal l)) a, set (cloneTraversal l) 10 a)
>>> foo both ("hello","world")
("helloworld",(10,10))

cloneTraversal :: LensLike (Bazaar (->) a b) s t a b -> Traversal s t a b

ignored :: Applicative f => pafb -> s -> f s Source #

This is the trivial empty Traversal.

ignored :: IndexedTraversal i s s a b

ignored ≡ const pure

>>> 6 & ignored %~ absurd
6

unto :: (Profunctor p, Bifunctor p, Functor f) => (b -> t) -> Optic p f s t a b Source #

An analogue of to for review.

unto :: (b -> t) -> Review' t b

unto = un . to

un :: (Profunctor p, Bifunctor p, Functor f) => Getting a s a -> Optic' p f a s Source #

Turn a Getter around to get a Review

un = unto . view
unto = un . to

>>> un (to length) # [1,2,3]
3

re :: AReview t b -> Getter b t Source #

Turn a Prism or Iso around to build a Getter.

If you have an Iso, from is a more powerful version of this function that will return an Iso instead of a mere Getter.

>>> 5 ^.re _Left
Left 5

>>> 6 ^.re (_Left.unto succ)
Left 7

review  ≡ view  . re
reviews ≡ views . re
reuse   ≡ use   . re
reuses  ≡ uses  . re

re :: Prism s t a b -> Getter b t
re :: Iso s t a b   -> Getter b t

review :: MonadReader b m => AReview t b -> m t Source #

This can be used to turn an Iso or Prism around and view a value (or the current environment) through it the other way.

review ≡ view . re
review . unto ≡ id

>>> review _Left "mustard"
Left "mustard"

>>> review (unto succ) 5
6

Usually review is used in the (->) Monad with a Prism or Iso, in which case it may be useful to think of it as having one of these more restricted type signatures:

review :: Iso' s a   -> a -> s
review :: Prism' s a -> a -> s

However, when working with a Monad transformer stack, it is sometimes useful to be able to review the current environment, in which case it may be beneficial to think of it as having one of these slightly more liberal type signatures:

review :: MonadReader a m => Iso' s a   -> m s
review :: MonadReader a m => Prism' s a -> m s

reviews :: MonadReader b m => AReview t b -> (t -> r) -> m r Source #

This can be used to turn an Iso or Prism around and view a value (or the current environment) through it the other way, applying a function.

reviews ≡ views . re
reviews (unto f) g ≡ g . f

>>> reviews _Left isRight "mustard"
False

>>> reviews (unto succ) (*2) 3
8

Usually this function is used in the (->) Monad with a Prism or Iso, in which case it may be useful to think of it as having one of these more restricted type signatures:

reviews :: Iso' s a   -> (s -> r) -> a -> r
reviews :: Prism' s a -> (s -> r) -> a -> r

However, when working with a Monad transformer stack, it is sometimes useful to be able to review the current environment, in which case it may be beneficial to think of it as having one of these slightly more liberal type signatures:

reviews :: MonadReader a m => Iso' s a   -> (s -> r) -> m r
reviews :: MonadReader a m => Prism' s a -> (s -> r) -> m r

reuse :: MonadState b m => AReview t b -> m t Source #

This can be used to turn an Iso or Prism around and use a value (or the current environment) through it the other way.

reuse ≡ use . re
reuse . unto ≡ gets

>>> evalState (reuse _Left) 5
Left 5

>>> evalState (reuse (unto succ)) 5
6

reuse :: MonadState a m => Prism' s a -> m s
reuse :: MonadState a m => Iso' s a   -> m s

reuses :: MonadState b m => AReview t b -> (t -> r) -> m r Source #

This can be used to turn an Iso or Prism around and use the current state through it the other way, applying a function.

reuses ≡ uses . re
reuses (unto f) g ≡ gets (g . f)

>>> evalState (reuses _Left isLeft) (5 :: Int)
True

reuses :: MonadState a m => Prism' s a -> (s -> r) -> m r
reuses :: MonadState a m => Iso' s a   -> (s -> r) -> m r

reviewing :: (Bifunctor p, Functor f) => Optic Tagged Identity s t a b -> Optic' p f t b Source #

Coerce a polymorphic Prism to a Review.

reviewing :: Iso s t a b -> Review t b
reviewing :: Prism s t a b -> Review t b

sets :: (Profunctor p, Profunctor q, Settable f) => (p a b -> q s t) -> Optical p q f s t a b Source #

Build a Setter, IndexedSetter or IndexPreservingSetter depending on your choice of Profunctor.

sets :: ((a -> b) -> s -> t) -> Setter s t a b

setting :: ((a -> b) -> s -> t) -> IndexPreservingSetter s t a b Source #

Build an index-preserving Setter from a map-like function.

Your supplied function f is required to satisfy:

f id ≡ id
f g . f h ≡ f (g . h)

Equational reasoning:

setting . over ≡ id
over . setting ≡ id

Another way to view sets is that it takes a "semantic editor combinator" and transforms it into a Setter.

setting :: ((a -> b) -> s -> t) -> Setter s t a b

cloneSetter :: ASetter s t a b -> Setter s t a b Source #

Restore ASetter to a full Setter.

cloneIndexPreservingSetter :: ASetter s t a b -> IndexPreservingSetter s t a b Source #

Build an IndexPreservingSetter from any Setter.

cloneIndexedSetter :: AnIndexedSetter i s t a b -> IndexedSetter i s t a b Source #

Clone an IndexedSetter.

mapped :: Functor f => Setter (f a) (f b) a b Source #

This Setter can be used to map over all of the values in a Functor.

fmap ≡ over mapped
fmapDefault ≡ over traverse
(<$) ≡ set mapped

>>> over mapped f [a,b,c]
[f a,f b,f c]

>>> over mapped (+1) [1,2,3]
[2,3,4]

>>> set mapped x [a,b,c]
[x,x,x]

>>> [[a,b],[c]] & mapped.mapped +~ x
[[a + x,b + x],[c + x]]

>>> over (mapped._2) length [("hello","world"),("leaders","!!!")]
[("hello",5),("leaders",3)]

mapped :: Functor f => Setter (f a) (f b) a b

If you want an IndexPreservingSetter use setting fmap.

lifted :: Monad m => Setter (m a) (m b) a b Source #

This setter can be used to modify all of the values in a Monad.

You sometimes have to use this rather than mapped -- due to temporary insanity Functor was not a superclass of Monad until GHC 7.10.

liftM ≡ over lifted

>>> over lifted f [a,b,c]
[f a,f b,f c]

>>> set lifted b (Just a)
Just b

If you want an IndexPreservingSetter use setting liftM.

contramapped :: Contravariant f => Setter (f b) (f a) a b Source #

This Setter can be used to map over all of the inputs to a Contravariant.

contramap ≡ over contramapped

>>> getPredicate (over contramapped (*2) (Predicate even)) 5
True

>>> getOp (over contramapped (*5) (Op show)) 100
"500"

>>> Prelude.map ($ 1) $ over (mapped . _Unwrapping' Op . contramapped) (*12) [(*2),(+1),(^3)]
[24,13,1728]

argument :: Profunctor p => Setter (p b r) (p a r) a b Source #

This Setter can be used to map over the input of a Profunctor.

The most common Profunctor to use this with is (->).

>>> (argument %~ f) g x
g (f x)

>>> (argument %~ show) length [1,2,3]
7

>>> (argument %~ f) h x y
h (f x) y

Map over the argument of the result of a function -- i.e., its second argument:

>>> (mapped.argument %~ f) h x y
h x (f y)

argument :: Setter (b -> r) (a -> r) a b

assign :: MonadState s m => ASetter s s a b -> b -> m () Source #

Replace the target of a Lens or all of the targets of a Setter or Traversal in our monadic state with a new value, irrespective of the old.

This is an alias for (.=).

>>> execState (do assign _1 c; assign _2 d) (a,b)
(c,d)

>>> execState (both .= c) (a,b)
(c,c)

assign :: MonadState s m => Iso' s a       -> a -> m ()
assign :: MonadState s m => Lens' s a      -> a -> m ()
assign :: MonadState s m => Traversal' s a -> a -> m ()
assign :: MonadState s m => Setter' s a    -> a -> m ()

modifying :: MonadState s m => ASetter s s a b -> (a -> b) -> m () Source #

This is an alias for (%=).

scribe :: (MonadWriter t m, Monoid s) => ASetter s t a b -> b -> m () Source #

Write to a fragment of a larger Writer format.

passing :: MonadWriter w m => Setter w w u v -> m (a, u -> v) -> m a Source #

This is a generalization of pass that allows you to modify just a portion of the resulting MonadWriter.

ipassing :: MonadWriter w m => IndexedSetter i w w u v -> m (a, i -> u -> v) -> m a Source #

This is a generalization of pass that allows you to modify just a portion of the resulting MonadWriter with access to the index of an IndexedSetter.

censoring :: MonadWriter w m => Setter w w u v -> (u -> v) -> m a -> m a Source #

This is a generalization of censor that allows you to censor just a portion of the resulting MonadWriter.

icensoring :: MonadWriter w m => IndexedSetter i w w u v -> (i -> u -> v) -> m a -> m a Source #

This is a generalization of censor that allows you to censor just a portion of the resulting MonadWriter, with access to the index of an IndexedSetter.

locally :: MonadReader s m => ASetter s s a b -> (a -> b) -> m r -> m r Source #

Modify the value of the Reader environment associated with the target of a Setter, Lens, or Traversal.

locally l id a ≡ a
locally l f . locally l g ≡ locally l (f . g)

>>> (1,1) & locally _1 (+1) (uncurry (+))
3

>>> "," & locally ($) ("Hello" <>) (<> " world!")
"Hello, world!"

locally :: MonadReader s m => Iso s s a b       -> (a -> b) -> m r -> m r
locally :: MonadReader s m => Lens s s a b      -> (a -> b) -> m r -> m r
locally :: MonadReader s m => Traversal s s a b -> (a -> b) -> m r -> m r
locally :: MonadReader s m => Setter s s a b    -> (a -> b) -> m r -> m r

ilocally :: MonadReader s m => AnIndexedSetter i s s a b -> (i -> a -> b) -> m r -> m r Source #

This is a generalization of locally that allows one to make indexed local changes to a Reader environment associated with the target of a Setter, Lens, or Traversal.

locally l f ≡ ilocally l f . const
ilocally l f ≡ locally l f . Indexed

ilocally :: MonadReader s m => IndexedLens s s a b      -> (i -> a -> b) -> m r -> m r
ilocally :: MonadReader s m => IndexedTraversal s s a b -> (i -> a -> b) -> m r -> m r
ilocally :: MonadReader s m => IndexedSetter s s a b    -> (i -> a -> b) -> m r -> m r

set' :: ASetter' s a -> a -> s -> s Source #

Replace the target of a Lens or all of the targets of a Setter' or Traversal with a constant value, without changing its type.

This is a type restricted version of set, which retains the type of the original.

>>> set' mapped x [a,b,c,d]
[x,x,x,x]

>>> set' _2 "hello" (1,"world")
(1,"hello")

>>> set' mapped 0 [1,2,3,4]
[0,0,0,0]

Note: Attempting to adjust set' a Fold or Getter will fail at compile time with an relatively nice error message.

set' :: Setter' s a    -> a -> s -> s
set' :: Iso' s a       -> a -> s -> s
set' :: Lens' s a      -> a -> s -> s
set' :: Traversal' s a -> a -> s -> s

imapOf :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t Source #

Deprecated: Use iover

Map with index. (Deprecated alias for iover).

When you do not need access to the index, then mapOf is more liberal in what it can accept.

mapOf l ≡ imapOf l . const

imapOf :: IndexedSetter i s t a b    -> (i -> a -> b) -> s -> t
imapOf :: IndexedLens i s t a b      -> (i -> a -> b) -> s -> t
imapOf :: IndexedTraversal i s t a b -> (i -> a -> b) -> s -> t

iover :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t Source #

Map with index. This is an alias for imapOf.

When you do not need access to the index, then over is more liberal in what it can accept.

over l ≡ iover l . const
iover l ≡ over l . Indexed

iover :: IndexedSetter i s t a b    -> (i -> a -> b) -> s -> t
iover :: IndexedLens i s t a b      -> (i -> a -> b) -> s -> t
iover :: IndexedTraversal i s t a b -> (i -> a -> b) -> s -> t

iset :: AnIndexedSetter i s t a b -> (i -> b) -> s -> t Source #

Set with index. Equivalent to iover with the current value ignored.

When you do not need access to the index, then set is more liberal in what it can accept.

set l ≡ iset l . const

iset :: IndexedSetter i s t a b    -> (i -> b) -> s -> t
iset :: IndexedLens i s t a b      -> (i -> b) -> s -> t
iset :: IndexedTraversal i s t a b -> (i -> b) -> s -> t

imodifying :: MonadState s m => AnIndexedSetter i s s a b -> (i -> a -> b) -> m () Source #

This is an alias for (%@=).

isets :: ((i -> a -> b) -> s -> t) -> IndexedSetter i s t a b Source #

Build an IndexedSetter from an imap-like function.

Your supplied function f is required to satisfy:

f id ≡ id
f g . f h ≡ f (g . h)

Equational reasoning:

isets . iover ≡ id
iover . isets ≡ id

Another way to view isets is that it takes a "semantic editor combinator" which has been modified to carry an index and transforms it into a IndexedSetter.

assignA :: Arrow p => ASetter s t a b -> p s b -> p s t Source #

Run an arrow command and use the output to set all the targets of a Lens, Setter or Traversal to the result.

assignA can be used very similarly to (<~), except that the type of the object being modified can change; for example:

runKleisli action ((), (), ()) where
  action =      assignA _1 (Kleisli (const getVal1))
           >>> assignA _2 (Kleisli (const getVal2))
           >>> assignA _3 (Kleisli (const getVal3))
  getVal1 :: Either String Int
  getVal1 = ...
  getVal2 :: Either String Bool
  getVal2 = ...
  getVal3 :: Either String Char
  getVal3 = ...

has the type Either String (Int, Bool, Char)

assignA :: Arrow p => Iso s t a b       -> p s b -> p s t
assignA :: Arrow p => Lens s t a b      -> p s b -> p s t
assignA :: Arrow p => Traversal s t a b -> p s b -> p s t
assignA :: Arrow p => Setter s t a b    -> p s b -> p s t

mapOf :: ASetter s t a b -> (a -> b) -> s -> t Source #

Deprecated: Use over

mapOf is a deprecated alias for over.

makeLenses :: Name -> DecsQ Source #

Build lenses (and traversals) with a sensible default configuration.

e.g.

data FooBar
  = Foo { _x, _y :: Int }
  | Bar { _x :: Int }
makeLenses ''FooBar

will create

x :: Lens' FooBar Int
x f (Foo a b) = (\a' -> Foo a' b) <$> f a
x f (Bar a)   = Bar <$> f a
y :: Traversal' FooBar Int
y f (Foo a b) = (\b' -> Foo a  b') <$> f b
y _ c@(Bar _) = pure c

makeLenses = makeLensesWith lensRules

makeLensesFor :: [(String, String)] -> Name -> DecsQ Source #

Derive lenses and traversals, specifying explicit pairings of (fieldName, lensName).

If you map multiple names to the same label, and it is present in the same constructor then this will generate a Traversal.

e.g.

makeLensesFor [("_foo", "fooLens"), ("baz", "lbaz")] ''Foo
makeLensesFor [("_barX", "bar"), ("_barY", "bar")] ''Bar

makeClassy :: Name -> DecsQ Source #

Make lenses and traversals for a type, and create a class when the type has no arguments.

e.g.

data Foo = Foo { _fooX, _fooY :: Int }
makeClassy ''Foo

will create

class HasFoo t where
  foo :: Lens' t Foo
  fooX :: Lens' t Int
  fooX = foo . go where go f (Foo x y) = (\x' -> Foo x' y) <$> f x
  fooY :: Lens' t Int
  fooY = foo . go where go f (Foo x y) = (\y' -> Foo x y') <$> f y
instance HasFoo Foo where
  foo = id

makeClassy = makeLensesWith classyRules

makeClassyFor :: String -> String -> [(String, String)] -> Name -> DecsQ Source #

Derive lenses and traversals, using a named wrapper class, and specifying explicit pairings of (fieldName, traversalName).

Example usage:

makeClassyFor "HasFoo" "foo" [("_foo", "fooLens"), ("bar", "lbar")] ''Foo

makeClassy_ :: Name -> DecsQ Source #

Make lenses and traversals for a type, and create a class when the type has no arguments. Works the same as makeClassy except that (a) it expects that record field names do not begin with an underscore, (b) all record fields are made into lenses, and (c) the resulting lens is prefixed with an underscore.

makeFields :: Name -> DecsQ Source #

Generate overloaded field accessors.

e.g

data Foo a = Foo { _fooX :: Int, _fooY :: a }
newtype Bar = Bar { _barX :: Char }
makeFields ''Foo
makeFields ''Bar

will create

_fooXLens :: Lens' (Foo a) Int
_fooYLens :: Lens (Foo a) (Foo b) a b
class HasX s a | s -> a where
  x :: Lens' s a
instance HasX (Foo a) Int where
  x = _fooXLens
class HasY s a | s -> a where
  y :: Lens' s a
instance HasY (Foo a) a where
  y = _fooYLens
_barXLens :: Iso' Bar Char
instance HasX Bar Char where
  x = _barXLens

For details, see camelCaseFields.

makeFields = makeLensesWith defaultFieldRules

makeFieldsNoPrefix :: Name -> DecsQ Source #

Generate overloaded field accessors based on field names which are only prefixed with an underscore (e.g. _name), not additionally with the type name (e.g. _fooName).

This might be the desired behaviour in case the DuplicateRecordFields language extension is used in order to get rid of the necessity to prefix each field name with the type name.

As an example:

data Foo a  = Foo { _x :: Int, _y :: a }
newtype Bar = Bar { _x :: Char }
makeFieldsNoPrefix ''Foo
makeFieldsNoPrefix ''Bar

will create classes

class HasX s a | s -> a where
  x :: Lens' s a
class HasY s a | s -> a where
  y :: Lens' s a

together with instances

instance HasX (Foo a) Int
instance HasY (Foo a) a where
instance HasX Bar Char where

For details, see classUnderscoreNoPrefixFields.

makeFieldsNoPrefix = makeLensesWith classUnderscoreNoPrefixFields

makeWrapped :: Name -> DecsQ Source #

Build Wrapped instance for a given newtype

declareLenses :: DecsQ -> DecsQ Source #

Make lenses for all records in the given declaration quote. All record syntax in the input will be stripped off.

e.g.

declareLenses [d|
  data Foo = Foo { fooX, fooY :: Int }
    deriving Show
  |]

will create

data Foo = Foo Int Int deriving Show
fooX, fooY :: Lens' Foo Int

declareLensesFor :: [(String, String)] -> DecsQ -> DecsQ Source #

Similar to makeLensesFor, but takes a declaration quote.

declareClassy :: DecsQ -> DecsQ Source #

For each record in the declaration quote, make lenses and traversals for it, and create a class when the type has no arguments. All record syntax in the input will be stripped off.

e.g.

declareClassy [d|
  data Foo = Foo { fooX, fooY :: Int }
    deriving Show
  |]

will create

data Foo = Foo Int Int deriving Show
class HasFoo t where
  foo :: Lens' t Foo
instance HasFoo Foo where foo = id
fooX, fooY :: HasFoo t => Lens' t Int

declareClassyFor :: [(String, (String, String))] -> [(String, String)] -> DecsQ -> DecsQ Source #

Similar to makeClassyFor, but takes a declaration quote.

declareFields :: DecsQ -> DecsQ Source #

 declareFields = declareLensesWith defaultFieldRules

declarePrisms :: DecsQ -> DecsQ Source #

Generate a Prism for each constructor of each data type.

e.g.

declarePrisms [d|
  data Exp = Lit Int | Var String | Lambda{ bound::String, body::Exp }
  |]

will create

data Exp = Lit Int | Var String | Lambda { bound::String, body::Exp }
_Lit :: Prism' Exp Int
_Var :: Prism' Exp String
_Lambda :: Prism' Exp (String, Exp)

declareWrapped :: DecsQ -> DecsQ Source #

Build Wrapped instance for each newtype.

makeLensesWith :: LensRules -> Name -> DecsQ Source #

Build lenses with a custom configuration.

declareLensesWith :: LensRules -> DecsQ -> DecsQ Source #

Declare lenses for each records in the given declarations, using the specified LensRules. Any record syntax in the input will be stripped off.

lensRules :: LensRules Source #

Rules for making fairly simple partial lenses, ignoring the special cases for isomorphisms and traversals, and not making any classes. It uses underscoreNoPrefixNamer.

lensRulesFor Source #

Arguments

:: [(String, String)]	(Field Name, Definition Name)
-> LensRules

Construct a LensRules value for generating top-level definitions using the given map from field names to definition names.

classyRules :: LensRules Source #

Rules for making lenses and traversals that precompose another Lens.

classyRules_ :: LensRules Source #

A LensRules used by makeClassy_.

defaultFieldRules :: LensRules Source #

camelCaseFields :: LensRules Source #

Field rules for fields in the form prefixFieldname or _prefixFieldname If you want all fields to be lensed, then there is no reason to use an _ before the prefix. If any of the record fields leads with an _ then it is assume a field without an _ should not have a lens created.

Note: The prefix must be the same as the typename (with the first letter lowercased). This is a change from lens versions before lens 4.5. If you want the old behaviour, use makeLensesWith abbreviatedFields

classUnderscoreNoPrefixFields :: LensRules Source #

Field rules for fields in the form _fieldname (the leading underscore is mandatory).

Note: The primary difference to camelCaseFields is that for classUnderscoreNoPrefixFields the field names are not expected to be prefixed with the type name. This might be the desired behaviour when the DuplicateRecordFields extension is enabled.

underscoreFields :: LensRules Source #

Field rules for fields in the form _prefix_fieldname

abbreviatedFields :: LensRules Source #

Field rules fields in the form prefixFieldname or _prefixFieldname If you want all fields to be lensed, then there is no reason to use an _ before the prefix. If any of the record fields leads with an _ then it is assume a field without an _ should not have a lens created.

Note that prefix may be any string of characters that are not uppercase letters. (In particular, it may be arbitrary string of lowercase letters and numbers) This is the behavior that defaultFieldRules had in lens 4.4 and earlier.

lensField :: Lens' LensRules FieldNamer Source #

Lens' to access the convention for naming fields in our LensRules.

lensClass :: Lens' LensRules ClassyNamer Source #

Lens' to access the option for naming "classy" lenses.

simpleLenses :: Lens' LensRules Bool Source #

Generate "simple" optics even when type-changing optics are possible. (e.g. Lens' instead of Lens)

createClass :: Lens' LensRules Bool Source #

Create the class if the constructor is Simple and the lensClass rule matches.

generateSignatures :: Lens' LensRules Bool Source #

Indicate whether or not to supply the signatures for the generated lenses.

Disabling this can be useful if you want to provide a more restricted type signature or if you want to supply hand-written haddocks.

generateUpdateableOptics :: Lens' LensRules Bool Source #

Generate "updateable" optics when True. When False, Folds will be generated instead of Traversals and Getters will be generated instead of Lenses. This mode is intended to be used for types with invariants which must be maintained by "smart" constructors.

generateLazyPatterns :: Lens' LensRules Bool Source #

Generate optics using lazy pattern matches. This can allow fields of an undefined value to be initialized with lenses:

data Foo = Foo {_x :: Int, _y :: Bool}
  deriving Show

makeLensesWith (lensRules & generateLazyPatterns .~ True) ''Foo

> undefined & x .~ 8 & y .~ True
Foo {_x = 8, _y = True}

The downside of this flag is that it can lead to space-leaks and code-size/compile-time increases when generated for large records. By default this flag is turned off, and strict optics are generated.

When using lazy optics the strict optic can be recovered by composing with $!:

strictOptic = ($!) . lazyOptic

generateRecordSyntax :: Lens' LensRules Bool Source #

underscoreNoPrefixNamer :: FieldNamer Source #

A FieldNamer that strips the _ off of the field name, lowercases the name, and skips the field if it doesn't start with an '_'.

lookingupNamer :: [(String, String)] -> FieldNamer Source #

Create a FieldNamer from explicit pairings of (fieldName, lensName).

mappingNamer Source #

Arguments

:: (String -> [String])	A function that maps a `fieldName` to `lensName`s.
-> FieldNamer

Create a FieldNamer from a mapping function. If the function returns [], it creates no lens for the field.

camelCaseNamer :: FieldNamer Source #

A FieldNamer for camelCaseFields.

classUnderscoreNoPrefixNamer :: FieldNamer Source #

A FieldNamer for classUnderscoreNoPrefixFields.

underscoreNamer :: FieldNamer Source #

A FieldNamer for underscoreFields.

abbreviatedNamer :: FieldNamer Source #

A FieldNamer for abbreviatedFields.

traversal :: ((a -> f b) -> s -> f t) -> LensLike f s t a b Source #

Build a Traversal by providing a function which specifies the elements you wish to focus.

The caller provides a function of type:

Applicative f => (a -> f b) -> s -> f t

Which is a higher order function which accepts a "focusing function" and applies it to all desired focuses within s, then constructs a t using the Applicative instance of f.

Only elements which are "focused" using the focusing function will be targeted by the resulting traversal.

For example, we can explicitly write a traversal which targets the first and third elements of a tuple like this:

firstAndThird :: Traversal (a, x, a) (b, x, b) a b
firstAndThird = traversal go
  where
    go :: Applicative f => (a -> f b) -> (a, x, a) -> f (b, x, b)
    go focus (a, x, a') = liftA3 (,,) (focus a) (pure x) (focus a')

>>> (1,"two",3) & firstAndThird *~ 10
(10,"two",30)

>>> over firstAndThird length ("one",2,"three")
(3,2,5)

We can re-use existing Traversals when writing new ones by passing our focusing function along to them. This example re-uses traverse to focus all elements in a list which is embedded in a tuple. This traversal could also be written simply as _2 . traverse.

selectNested :: Traversal (x, [a]) (x, [b]) a b
selectNested = traversal go
  where
    go :: Applicative f => (a -> f b) -> (x, [a]) -> f (x, [b])
    go focus (x, as) = liftA2 (,) (pure x) (traverse focus as)

>>> selectNested .~ "hello" $ (1,[2,3,4,5])
(1,["hello","hello","hello","hello"])

>>> (1,[2,3,4,5]) & selectNested *~ 3
(1,[6,9,12,15])

Note that the traversal function actually just returns the same function you pass to it. The function it accepts is in fact a valid traversal all on its own! The use of traversal does nothing except verify that the function it is passed matches the signature of a valid traversal. One could remove the traversal combinator from either of the last two examples and use the definition of go directly with no change in behaviour.

This function exists for consistency with the lens, prism and iso constructors as well as to serve as a touchpoint for beginners who wish to construct their own traversals but are uncertain how to do so.

traverseOf :: LensLike f s t a b -> (a -> f b) -> s -> f t Source #

Map each element of a structure targeted by a Lens or Traversal, evaluate these actions from left to right, and collect the results.

This function is only provided for consistency, id is strictly more general.

>>> traverseOf each print (1,2,3)
1
2
3
((),(),())

traverseOf ≡ id
itraverseOf l ≡ traverseOf l . Indexed
itraverseOf itraversed ≡ itraverse

This yields the obvious law:

traverse ≡ traverseOf traverse

traverseOf :: Functor f     => Iso s t a b        -> (a -> f b) -> s -> f t
traverseOf :: Functor f     => Lens s t a b       -> (a -> f b) -> s -> f t
traverseOf :: Apply f       => Traversal1 s t a b -> (a -> f b) -> s -> f t
traverseOf :: Applicative f => Traversal s t a b  -> (a -> f b) -> s -> f t

forOf :: LensLike f s t a b -> s -> (a -> f b) -> f t Source #

A version of traverseOf with the arguments flipped, such that:

>>> forOf each (1,2,3) print
1
2
3
((),(),())

This function is only provided for consistency, flip is strictly more general.

forOf ≡ flip
forOf ≡ flip . traverseOf

for ≡ forOf traverse
ifor l s ≡ for l s . Indexed

forOf :: Functor f => Iso s t a b -> s -> (a -> f b) -> f t
forOf :: Functor f => Lens s t a b -> s -> (a -> f b) -> f t
forOf :: Applicative f => Traversal s t a b -> s -> (a -> f b) -> f t

sequenceAOf :: LensLike f s t (f b) b -> s -> f t Source #

Evaluate each action in the structure from left to right, and collect the results.

>>> sequenceAOf both ([1,2],[3,4])
[(1,3),(1,4),(2,3),(2,4)]

sequenceA ≡ sequenceAOf traverse ≡ traverse id
sequenceAOf l ≡ traverseOf l id ≡ l id

sequenceAOf :: Functor f => Iso s t (f b) b       -> s -> f t
sequenceAOf :: Functor f => Lens s t (f b) b      -> s -> f t
sequenceAOf :: Applicative f => Traversal s t (f b) b -> s -> f t

mapMOf :: LensLike (WrappedMonad m) s t a b -> (a -> m b) -> s -> m t Source #

Map each element of a structure targeted by a Lens to a monadic action, evaluate these actions from left to right, and collect the results.

>>> mapMOf both (\x -> [x, x + 1]) (1,3)
[(1,3),(1,4),(2,3),(2,4)]

mapM ≡ mapMOf traverse
imapMOf l ≡ forM l . Indexed

mapMOf :: Monad m => Iso s t a b       -> (a -> m b) -> s -> m t
mapMOf :: Monad m => Lens s t a b      -> (a -> m b) -> s -> m t
mapMOf :: Monad m => Traversal s t a b -> (a -> m b) -> s -> m t

forMOf :: LensLike (WrappedMonad m) s t a b -> s -> (a -> m b) -> m t Source #

forMOf is a flipped version of mapMOf, consistent with the definition of forM.

>>> forMOf both (1,3) $ \x -> [x, x + 1]
[(1,3),(1,4),(2,3),(2,4)]

forM ≡ forMOf traverse
forMOf l ≡ flip (mapMOf l)
iforMOf l s ≡ forM l s . Indexed

forMOf :: Monad m => Iso s t a b       -> s -> (a -> m b) -> m t
forMOf :: Monad m => Lens s t a b      -> s -> (a -> m b) -> m t
forMOf :: Monad m => Traversal s t a b -> s -> (a -> m b) -> m t

sequenceOf :: LensLike (WrappedMonad m) s t (m b) b -> s -> m t Source #

Sequence the (monadic) effects targeted by a Lens in a container from left to right.

>>> sequenceOf each ([1,2],[3,4],[5,6])
[(1,3,5),(1,3,6),(1,4,5),(1,4,6),(2,3,5),(2,3,6),(2,4,5),(2,4,6)]

sequence ≡ sequenceOf traverse
sequenceOf l ≡ mapMOf l id
sequenceOf l ≡ unwrapMonad . l WrapMonad

sequenceOf :: Monad m => Iso s t (m b) b       -> s -> m t
sequenceOf :: Monad m => Lens s t (m b) b      -> s -> m t
sequenceOf :: Monad m => Traversal s t (m b) b -> s -> m t

transposeOf :: LensLike ZipList s t [a] a -> s -> [t] Source #

This generalizes transpose to an arbitrary Traversal.

Note: transpose handles ragged inputs more intelligently, but for non-ragged inputs:

>>> transposeOf traverse [[1,2,3],[4,5,6]]
[[1,4],[2,5],[3,6]]

transpose ≡ transposeOf traverse

Since every Lens is a Traversal, we can use this as a form of monadic strength as well:

transposeOf _2 :: (b, [a]) -> [(b, a)]

mapAccumLOf :: LensLike (State acc) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t) Source #

This generalizes mapAccumL to an arbitrary Traversal.

mapAccumL ≡ mapAccumLOf traverse

mapAccumLOf accumulates State from left to right.

mapAccumLOf :: Iso s t a b       -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
mapAccumLOf :: Lens s t a b      -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
mapAccumLOf :: Traversal s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)

mapAccumLOf :: LensLike (State acc) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
mapAccumLOf l f acc0 s = swap (runState (l (a -> state (acc -> swap (f acc a))) s) acc0)

mapAccumROf :: LensLike (Backwards (State acc)) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t) Source #

This generalizes mapAccumR to an arbitrary Traversal.

mapAccumR ≡ mapAccumROf traverse

mapAccumROf accumulates State from right to left.

mapAccumROf :: Iso s t a b       -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
mapAccumROf :: Lens s t a b      -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
mapAccumROf :: Traversal s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)

mapAccumROf :: LensLike (Backwards (State acc)) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)

scanr1Of :: LensLike (Backwards (State (Maybe a))) s t a a -> (a -> a -> a) -> s -> t Source #

This permits the use of scanr1 over an arbitrary Traversal or Lens.

scanr1 ≡ scanr1Of traverse

scanr1Of :: Iso s t a a       -> (a -> a -> a) -> s -> t
scanr1Of :: Lens s t a a      -> (a -> a -> a) -> s -> t
scanr1Of :: Traversal s t a a -> (a -> a -> a) -> s -> t

scanl1Of :: LensLike (State (Maybe a)) s t a a -> (a -> a -> a) -> s -> t Source #

This permits the use of scanl1 over an arbitrary Traversal or Lens.

scanl1 ≡ scanl1Of traverse

scanl1Of :: Iso s t a a       -> (a -> a -> a) -> s -> t
scanl1Of :: Lens s t a a      -> (a -> a -> a) -> s -> t
scanl1Of :: Traversal s t a a -> (a -> a -> a) -> s -> t

failover :: Alternative m => LensLike ((,) Any) s t a b -> (a -> b) -> s -> m t Source #

Try to map a function over this Traversal, failing if the Traversal has no targets.

>>> failover (element 3) (*2) [1,2] :: Maybe [Int]
Nothing

>>> failover _Left (*2) (Right 4) :: Maybe (Either Int Int)
Nothing

>>> failover _Right (*2) (Right 4) :: Maybe (Either Int Int)
Just (Right 8)

failover :: Alternative m => Traversal s t a b -> (a -> b) -> s -> m t

ifailover :: Alternative m => Over (Indexed i) ((,) Any) s t a b -> (i -> a -> b) -> s -> m t Source #

Try to map a function which uses the index over this IndexedTraversal, failing if the IndexedTraversal has no targets.

ifailover :: Alternative m => IndexedTraversal i s t a b -> (i -> a -> b) -> s -> m t

cloneIndexPreservingTraversal :: ATraversal s t a b -> IndexPreservingTraversal s t a b Source #

Clone a Traversal yielding an IndexPreservingTraversal that passes through whatever index it is composed with.

cloneIndexedTraversal :: AnIndexedTraversal i s t a b -> IndexedTraversal i s t a b Source #

Clone an IndexedTraversal yielding an IndexedTraversal with the same index.

cloneTraversal1 :: ATraversal1 s t a b -> Traversal1 s t a b Source #

A Traversal1 is completely characterized by its behavior on a Bazaar1.

cloneIndexPreservingTraversal1 :: ATraversal1 s t a b -> IndexPreservingTraversal1 s t a b Source #

Clone a Traversal1 yielding an IndexPreservingTraversal1 that passes through whatever index it is composed with.

cloneIndexedTraversal1 :: AnIndexedTraversal1 i s t a b -> IndexedTraversal1 i s t a b Source #

Clone an IndexedTraversal1 yielding an IndexedTraversal1 with the same index.

partsOf :: Functor f => Traversing (->) f s t a a -> LensLike f s t [a] [a] Source #

partsOf turns a Traversal into a Lens that resembles an early version of the uniplate (or biplate) type.

Note: You should really try to maintain the invariant of the number of children in the list.

>>> (a,b,c) & partsOf each .~ [x,y,z]
(x,y,z)

Any extras will be lost. If you do not supply enough, then the remainder will come from the original structure.

>>> (a,b,c) & partsOf each .~ [w,x,y,z]
(w,x,y)

>>> (a,b,c) & partsOf each .~ [x,y]
(x,y,c)

>>> ('b', 'a', 'd', 'c') & partsOf each %~ sort
('a','b','c','d')

So technically, this is only a Lens if you do not change the number of results it returns.

When applied to a Fold the result is merely a Getter.

partsOf :: Iso' s a       -> Lens' s [a]
partsOf :: Lens' s a      -> Lens' s [a]
partsOf :: Traversal' s a -> Lens' s [a]
partsOf :: Fold s a       -> Getter s [a]
partsOf :: Getter s a     -> Getter s [a]

partsOf' :: ATraversal s t a a -> Lens s t [a] [a] Source #

A type-restricted version of partsOf that can only be used with a Traversal.

unsafePartsOf :: Functor f => Traversing (->) f s t a b -> LensLike f s t [a] [b] Source #

unsafePartsOf turns a Traversal into a uniplate (or biplate) family.

If you do not need the types of s and t to be different, it is recommended that you use partsOf.

It is generally safer to traverse with the Bazaar rather than use this combinator. However, it is sometimes convenient.

This is unsafe because if you don't supply at least as many b's as you were given a's, then the reconstruction of t will result in an error!

When applied to a Fold the result is merely a Getter (and becomes safe).

unsafePartsOf :: Iso s t a b       -> Lens s t [a] [b]
unsafePartsOf :: Lens s t a b      -> Lens s t [a] [b]
unsafePartsOf :: Traversal s t a b -> Lens s t [a] [b]
unsafePartsOf :: Fold s a          -> Getter s [a]
unsafePartsOf :: Getter s a        -> Getter s [a]

unsafePartsOf' :: ATraversal s t a b -> Lens s t [a] [b] Source #

holesOf :: Conjoined p => Over p (Bazaar p a a) s t a a -> s -> [Pretext p a a t] Source #

The one-level version of contextsOf. This extracts a list of the immediate children according to a given Traversal as editable contexts.

Given a context you can use pos to see the values, peek at what the structure would be like with an edited result, or simply extract the original structure.

propChildren l x = toListOf l x == map pos (holesOf l x)
propId l x = all (== x) [extract w | w <- holesOf l x]

holesOf :: Iso' s a                -> s -> [Pretext' (->) a s]
holesOf :: Lens' s a               -> s -> [Pretext' (->) a s]
holesOf :: Traversal' s a          -> s -> [Pretext' (->) a s]
holesOf :: IndexedLens' i s a      -> s -> [Pretext' (Indexed i) a s]
holesOf :: IndexedTraversal' i s a -> s -> [Pretext' (Indexed i) a s]

holes1Of :: Conjoined p => Over p (Bazaar1 p a a) s t a a -> s -> NonEmpty (Pretext p a a t) Source #

The non-empty version of holesOf. This extract a non-empty list of immediate children according to a given Traversal1 as editable contexts.

>>> let head1 f s = runPretext (NonEmpty.head $ holes1Of traversed1 s) f
>>> ('a' :| "bc") ^. head1
'a'

>>> ('a' :| "bc") & head1 %~ toUpper
'A' :| "bc"

holes1Of :: Iso' s a                 -> s -> NonEmpty (Pretext' (->) a s)
holes1Of :: Lens' s a                -> s -> NonEmpty (Pretext' (->) a s)
holes1Of :: Traversal1' s a          -> s -> NonEmpty (Pretext' (->) a s)
holes1Of :: IndexedLens' i s a       -> s -> NonEmpty (Pretext' (Indexed i) a s)
holes1Of :: IndexedTraversal1' i s a -> s -> NonEmpty (Pretext' (Indexed i) a s)

singular :: (HasCallStack, Conjoined p, Functor f) => Traversing p f s t a a -> Over p f s t a a Source #

This converts a Traversal that you "know" will target one or more elements to a Lens. It can also be used to transform a non-empty Fold into a Getter.

The resulting Lens or Getter will be partial if the supplied Traversal returns no results.

>>> [1,2,3] ^. singular _head
1

>>> Left (ErrorCall "singular: empty traversal") <- try (evaluate ([] ^. singular _head)) :: IO (Either ErrorCall ())

>>> Left 4 ^. singular _Left
4

>>> [1..10] ^. singular (ix 7)
8

>>> [] & singular traverse .~ 0
[]

singular :: Traversal s t a a          -> Lens s t a a
singular :: Fold s a                   -> Getter s a
singular :: IndexedTraversal i s t a a -> IndexedLens i s t a a
singular :: IndexedFold i s a          -> IndexedGetter i s a

unsafeSingular :: (HasCallStack, Conjoined p, Functor f) => Traversing p f s t a b -> Over p f s t a b Source #

This converts a Traversal that you "know" will target only one element to a Lens. It can also be used to transform a Fold into a Getter.

The resulting Lens or Getter will be partial if the Traversal targets nothing or more than one element.

>>> Left (ErrorCall "unsafeSingular: empty traversal") <- try (evaluate ([] & unsafeSingular traverse .~ 0)) :: IO (Either ErrorCall [Integer])

unsafeSingular :: Traversal s t a b          -> Lens s t a b
unsafeSingular :: Fold s a                   -> Getter s a
unsafeSingular :: IndexedTraversal i s t a b -> IndexedLens i s t a b
unsafeSingular :: IndexedFold i s a          -> IndexedGetter i s a

both :: Bitraversable r => Traversal (r a a) (r b b) a b Source #

Traverse both parts of a Bitraversable container with matching types.

Usually that type will be a pair. Use each to traverse the elements of arbitrary homogeneous tuples.

>>> (1,2) & both *~ 10
(10,20)

>>> over both length ("hello","world")
(5,5)

>>> ("hello","world")^.both
"helloworld"

both :: Traversal (a, a)       (b, b)       a b
both :: Traversal (Either a a) (Either b b) a b

both1 :: Bitraversable1 r => Traversal1 (r a a) (r b b) a b Source #

Traverse both parts of a Bitraversable1 container with matching types.

Usually that type will be a pair.

both1 :: Traversal1 (a, a)       (b, b)       a b
both1 :: Traversal1 (Either a a) (Either b b) a b

beside :: (Representable q, Applicative (Rep q), Applicative f, Bitraversable r) => Optical p q f s t a b -> Optical p q f s' t' a b -> Optical p q f (r s s') (r t t') a b Source #

Apply a different Traversal or Fold to each side of a Bitraversable container.

beside :: Traversal s t a b                -> Traversal s' t' a b                -> Traversal (r s s') (r t t') a b
beside :: IndexedTraversal i s t a b       -> IndexedTraversal i s' t' a b       -> IndexedTraversal i (r s s') (r t t') a b
beside :: IndexPreservingTraversal s t a b -> IndexPreservingTraversal s' t' a b -> IndexPreservingTraversal (r s s') (r t t') a b

beside :: Traversal s t a b                -> Traversal s' t' a b                -> Traversal (s,s') (t,t') a b
beside :: Lens s t a b                     -> Lens s' t' a b                     -> Traversal (s,s') (t,t') a b
beside :: Fold s a                         -> Fold s' a                          -> Fold (s,s') a
beside :: Getter s a                       -> Getter s' a                        -> Fold (s,s') a

beside :: IndexedTraversal i s t a b       -> IndexedTraversal i s' t' a b       -> IndexedTraversal i (s,s') (t,t') a b
beside :: IndexedLens i s t a b            -> IndexedLens i s' t' a b            -> IndexedTraversal i (s,s') (t,t') a b
beside :: IndexedFold i s a                -> IndexedFold i s' a                 -> IndexedFold i (s,s') a
beside :: IndexedGetter i s a              -> IndexedGetter i s' a               -> IndexedFold i (s,s') a

beside :: IndexPreservingTraversal s t a b -> IndexPreservingTraversal s' t' a b -> IndexPreservingTraversal (s,s') (t,t') a b
beside :: IndexPreservingLens s t a b      -> IndexPreservingLens s' t' a b      -> IndexPreservingTraversal (s,s') (t,t') a b
beside :: IndexPreservingFold s a          -> IndexPreservingFold s' a           -> IndexPreservingFold (s,s') a
beside :: IndexPreservingGetter s a        -> IndexPreservingGetter s' a         -> IndexPreservingFold (s,s') a

>>> ("hello",["world","!!!"])^..beside id traverse
["hello","world","!!!"]

taking :: (Conjoined p, Applicative f) => Int -> Traversing p f s t a a -> Over p f s t a a Source #

Visit the first n targets of a Traversal, Fold, Getter or Lens.

>>> [("hello","world"),("!!!","!!!")]^.. taking 2 (traverse.both)
["hello","world"]

>>> timingOut $ [1..] ^.. taking 3 traverse
[1,2,3]

>>> over (taking 5 traverse) succ "hello world"
"ifmmp world"

taking :: Int -> Traversal' s a                   -> Traversal' s a
taking :: Int -> Lens' s a                        -> Traversal' s a
taking :: Int -> Iso' s a                         -> Traversal' s a
taking :: Int -> Prism' s a                       -> Traversal' s a
taking :: Int -> Getter s a                       -> Fold s a
taking :: Int -> Fold s a                         -> Fold s a
taking :: Int -> IndexedTraversal' i s a          -> IndexedTraversal' i s a
taking :: Int -> IndexedLens' i s a               -> IndexedTraversal' i s a
taking :: Int -> IndexedGetter i s a              -> IndexedFold i s a
taking :: Int -> IndexedFold i s a                -> IndexedFold i s a

dropping :: (Conjoined p, Applicative f) => Int -> Over p (Indexing f) s t a a -> Over p f s t a a Source #

Visit all but the first n targets of a Traversal, Fold, Getter or Lens.

>>> ("hello","world") ^? dropping 1 both
Just "world"

Dropping works on infinite traversals as well:

>>> [1..] ^? dropping 1 folded
Just 2

dropping :: Int -> Traversal' s a                   -> Traversal' s a
dropping :: Int -> Lens' s a                        -> Traversal' s a
dropping :: Int -> Iso' s a                         -> Traversal' s a
dropping :: Int -> Prism' s a                       -> Traversal' s a
dropping :: Int -> Getter s a                       -> Fold s a
dropping :: Int -> Fold s a                         -> Fold s a
dropping :: Int -> IndexedTraversal' i s a          -> IndexedTraversal' i s a
dropping :: Int -> IndexedLens' i s a               -> IndexedTraversal' i s a
dropping :: Int -> IndexedGetter i s a              -> IndexedFold i s a
dropping :: Int -> IndexedFold i s a                -> IndexedFold i s a

failing :: (Conjoined p, Applicative f) => Traversing p f s t a b -> Over p f s t a b -> Over p f s t a b infixl 5 Source #

Try the first Traversal (or Fold), falling back on the second Traversal (or Fold) if it returns no entries.

This is only a valid Traversal if the second Traversal is disjoint from the result of the first or returns exactly the same results. These conditions are trivially met when given a Lens, Iso, Getter, Prism or "affine" Traversal -- one that has 0 or 1 target.

Mutatis mutandis for Fold.

>>> [0,1,2,3] ^? failing (ix 1) (ix 2)
Just 1

>>> [0,1,2,3] ^? failing (ix 42) (ix 2)
Just 2

failing :: Traversal s t a b -> Traversal s t a b -> Traversal s t a b
failing :: Prism s t a b     -> Prism s t a b     -> Traversal s t a b
failing :: Fold s a          -> Fold s a          -> Fold s a

These cases are also supported, trivially, but are boring, because the left hand side always succeeds.

failing :: Lens s t a b      -> Traversal s t a b -> Traversal s t a b
failing :: Iso s t a b       -> Traversal s t a b -> Traversal s t a b
failing :: Equality s t a b  -> Traversal s t a b -> Traversal s t a b
failing :: Getter s a        -> Fold s a          -> Fold s a

If both of the inputs are indexed, the result is also indexed, so you can apply this to a pair of indexed traversals or indexed folds, obtaining an indexed traversal or indexed fold.

failing :: IndexedTraversal i s t a b -> IndexedTraversal i s t a b -> IndexedTraversal i s t a b
failing :: IndexedFold i s a          -> IndexedFold i s a          -> IndexedFold i s a

These cases are also supported, trivially, but are boring, because the left hand side always succeeds.

failing :: IndexedLens i s t a b      -> IndexedTraversal i s t a b -> IndexedTraversal i s t a b
failing :: IndexedGetter i s a        -> IndexedGetter i s a        -> IndexedFold i s a

deepOf :: (Conjoined p, Applicative f) => LensLike f s t s t -> Traversing p f s t a b -> Over p f s t a b Source #

Try the second traversal. If it returns no entries, try again with all entries from the first traversal, recursively.

deepOf :: Fold s s          -> Fold s a                   -> Fold s a
deepOf :: Traversal' s s    -> Traversal' s a             -> Traversal' s a
deepOf :: Traversal s t s t -> Traversal s t a b          -> Traversal s t a b
deepOf :: Fold s s          -> IndexedFold i s a          -> IndexedFold i s a
deepOf :: Traversal s t s t -> IndexedTraversal i s t a b -> IndexedTraversal i s t a b

traversed :: Traversable f => IndexedTraversal Int (f a) (f b) a b Source #

Traverse any Traversable container. This is an IndexedTraversal that is indexed by ordinal position.

traversed1 :: Traversable1 f => IndexedTraversal1 Int (f a) (f b) a b Source #

Traverse any Traversable1 container. This is an IndexedTraversal1 that is indexed by ordinal position.

traversed64 :: Traversable f => IndexedTraversal Int64 (f a) (f b) a b Source #

Traverse any Traversable container. This is an IndexedTraversal that is indexed by ordinal position.

elementOf :: Applicative f => LensLike (Indexing f) s t a a -> Int -> IndexedLensLike Int f s t a a Source #

Traverse the nth elementOf a Traversal, Lens or Iso if it exists.

>>> [[1],[3,4]] & elementOf (traverse.traverse) 1 .~ 5
[[1],[5,4]]

>>> [[1],[3,4]] ^? elementOf (folded.folded) 1
Just 3

>>> timingOut $ ['a'..] ^?! elementOf folded 5
'f'

>>> timingOut $ take 10 $ elementOf traverse 3 .~ 16 $ [0..]
[0,1,2,16,4,5,6,7,8,9]

elementOf :: Traversal' s a -> Int -> IndexedTraversal' Int s a
elementOf :: Fold s a       -> Int -> IndexedFold Int s a

element :: Traversable t => Int -> IndexedTraversal' Int (t a) a Source #

Traverse the nth element of a Traversable container.

element ≡ elementOf traverse

elementsOf :: Applicative f => LensLike (Indexing f) s t a a -> (Int -> Bool) -> IndexedLensLike Int f s t a a Source #

Traverse (or fold) selected elements of a Traversal (or Fold) where their ordinal positions match a predicate.

elementsOf :: Traversal' s a -> (Int -> Bool) -> IndexedTraversal' Int s a
elementsOf :: Fold s a       -> (Int -> Bool) -> IndexedFold Int s a

ipartsOf :: forall i p f s t a. (Indexable [i] p, Functor f) => Traversing (Indexed i) f s t a a -> Over p f s t [a] [a] Source #

An indexed version of partsOf that receives the entire list of indices as its index.

ipartsOf' :: forall i p f s t a. (Indexable [i] p, Functor f) => Over (Indexed i) (Bazaar' (Indexed i) a) s t a a -> Over p f s t [a] [a] Source #

A type-restricted version of ipartsOf that can only be used with an IndexedTraversal.

iunsafePartsOf :: forall i p f s t a b. (Indexable [i] p, Functor f) => Traversing (Indexed i) f s t a b -> Over p f s t [a] [b] Source #

An indexed version of unsafePartsOf that receives the entire list of indices as its index.

iunsafePartsOf' :: forall i s t a b. Over (Indexed i) (Bazaar (Indexed i) a b) s t a b -> IndexedLens [i] s t [a] [b] Source #

itraverseOf :: (Indexed i a (f b) -> s -> f t) -> (i -> a -> f b) -> s -> f t Source #

Traversal with an index.

NB: When you don't need access to the index then you can just apply your IndexedTraversal directly as a function!

itraverseOf ≡ withIndex
traverseOf l = itraverseOf l . const = id

itraverseOf :: Functor f     => IndexedLens i s t a b       -> (i -> a -> f b) -> s -> f t
itraverseOf :: Applicative f => IndexedTraversal i s t a b  -> (i -> a -> f b) -> s -> f t
itraverseOf :: Apply f       => IndexedTraversal1 i s t a b -> (i -> a -> f b) -> s -> f t

iforOf :: (Indexed i a (f b) -> s -> f t) -> s -> (i -> a -> f b) -> f t Source #

Traverse with an index (and the arguments flipped).

forOf l a ≡ iforOf l a . const
iforOf ≡ flip . itraverseOf

iforOf :: Functor f     => IndexedLens i s t a b       -> s -> (i -> a -> f b) -> f t
iforOf :: Applicative f => IndexedTraversal i s t a b  -> s -> (i -> a -> f b) -> f t
iforOf :: Apply f       => IndexedTraversal1 i s t a b -> s -> (i -> a -> f b) -> f t

imapMOf :: Over (Indexed i) (WrappedMonad m) s t a b -> (i -> a -> m b) -> s -> m t Source #

Map each element of a structure targeted by a Lens to a monadic action, evaluate these actions from left to right, and collect the results, with access its position.

When you don't need access to the index mapMOf is more liberal in what it can accept.

mapMOf l ≡ imapMOf l . const

imapMOf :: Monad m => IndexedLens       i s t a b -> (i -> a -> m b) -> s -> m t
imapMOf :: Monad m => IndexedTraversal  i s t a b -> (i -> a -> m b) -> s -> m t
imapMOf :: Bind  m => IndexedTraversal1 i s t a b -> (i -> a -> m b) -> s -> m t

iforMOf :: (Indexed i a (WrappedMonad m b) -> s -> WrappedMonad m t) -> s -> (i -> a -> m b) -> m t Source #

Map each element of a structure targeted by a Lens to a monadic action, evaluate these actions from left to right, and collect the results, with access its position (and the arguments flipped).

forMOf l a ≡ iforMOf l a . const
iforMOf ≡ flip . imapMOf

iforMOf :: Monad m => IndexedLens i s t a b      -> s -> (i -> a -> m b) -> m t
iforMOf :: Monad m => IndexedTraversal i s t a b -> s -> (i -> a -> m b) -> m t

imapAccumROf :: Over (Indexed i) (Backwards (State acc)) s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t) Source #

Generalizes mapAccumR to an arbitrary IndexedTraversal with access to the index.

imapAccumROf accumulates state from right to left.

mapAccumROf l ≡ imapAccumROf l . const

imapAccumROf :: IndexedLens i s t a b      -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
imapAccumROf :: IndexedTraversal i s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)

imapAccumLOf :: Over (Indexed i) (State acc) s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t) Source #

Generalizes mapAccumL to an arbitrary IndexedTraversal with access to the index.

imapAccumLOf accumulates state from left to right.

mapAccumLOf l ≡ imapAccumLOf l . const

imapAccumLOf :: IndexedLens i s t a b      -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
imapAccumLOf :: IndexedTraversal i s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)

traverseByOf :: Traversal s t a b -> (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (a -> f b) -> s -> f t Source #

Traverse a container using a specified Applicative.

This is like traverseBy where the Traversable instance can be specified by any Traversal

traverseByOf traverse ≡ traverseBy

sequenceByOf :: Traversal s t (f b) b -> (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> s -> f t Source #

Sequence a container using a specified Applicative.

This is like traverseBy where the Traversable instance can be specified by any Traversal

sequenceByOf traverse ≡ sequenceBy

loci :: Traversal (Bazaar (->) a c s) (Bazaar (->) b c s) a b Source #

This Traversal allows you to traverse the individual stores in a Bazaar.

iloci :: IndexedTraversal i (Bazaar (Indexed i) a c s) (Bazaar (Indexed i) b c s) a b Source #

This IndexedTraversal allows you to traverse the individual stores in a Bazaar with access to their indices.

confusing :: Applicative f => LensLike (Curried (Yoneda f) (Yoneda f)) s t a b -> LensLike f s t a b Source #

Fuse a Traversal by reassociating all of the (<*>) operations to the left and fusing all of the fmap calls into one. This is particularly useful when constructing a Traversal using operations from GHC.Generics.

Given a pair of Traversals foo and bar,

confusing (foo.bar) = foo.bar

However, foo and bar are each going to use the Applicative they are given.

confusing exploits the Yoneda lemma to merge their separate uses of fmap into a single fmap. and it further exploits an interesting property of the right Kan lift (or Curried) to left associate all of the uses of (<*>) to make it possible to fuse together more fmaps.

This is particularly effective when the choice of functor f is unknown at compile time or when the Traversal foo.bar in the above description is recursive or complex enough to prevent inlining.

fusing is a version of this combinator suitable for fusing lenses.

confusing :: Traversal s t a b -> Traversal s t a b

_1' :: Field1 s t a b => Lens s t a b Source #

Strict version of _1

_2' :: Field2 s t a b => Lens s t a b Source #

Strict version of _2

_3' :: Field3 s t a b => Lens s t a b Source #

Strict version of _3

_4' :: Field4 s t a b => Lens s t a b Source #

Strict version of _4

_5' :: Field5 s t a b => Lens s t a b Source #

Strict version of _5

_6' :: Field6 s t a b => Lens s t a b Source #

Strict version of _6

_7' :: Field7 s t a b => Lens s t a b Source #

Strict version of _7

_8' :: Field8 s t a b => Lens s t a b Source #

Strict version of _8

_9' :: Field9 s t a b => Lens s t a b Source #

Strict version of _9

_10' :: Field10 s t a b => Lens s t a b Source #

Strict version of _10

_11' :: Field11 s t a b => Lens s t a b Source #

Strict version of _11

_12' :: Field12 s t a b => Lens s t a b Source #

Strict version of _12

_13' :: Field13 s t a b => Lens s t a b Source #

Strict version of _13

_14' :: Field14 s t a b => Lens s t a b Source #

Strict version of _14

_15' :: Field15 s t a b => Lens s t a b Source #

Strict version of _15

_16' :: Field16 s t a b => Lens s t a b Source #

Strict version of _16

_17' :: Field17 s t a b => Lens s t a b Source #

Strict version of _17

_18' :: Field18 s t a b => Lens s t a b Source #

Strict version of _18

_19' :: Field19 s t a b => Lens s t a b Source #

Strict version of _19

_Unwrapped' :: Wrapped s => Iso' (Unwrapped s) s Source #

_Wrapping' :: Wrapped s => (Unwrapped s -> s) -> Iso' s (Unwrapped s) Source #

This is a convenient version of _Wrapped with an argument that's ignored.

The user supplied function is ignored, merely its type is used.

_Unwrapping' :: Wrapped s => (Unwrapped s -> s) -> Iso' (Unwrapped s) s Source #

This is a convenient version of _Wrapped with an argument that's ignored.

The user supplied function is ignored, merely its type is used.

_Wrapped :: Rewrapping s t => Iso s t (Unwrapped s) (Unwrapped t) Source #

Work under a newtype wrapper.

>>> Const "hello" & _Wrapped %~ Prelude.length & getConst
5

_Wrapped   ≡ from _Unwrapped
_Unwrapped ≡ from _Wrapped

_Unwrapped :: Rewrapping s t => Iso (Unwrapped t) (Unwrapped s) t s Source #

_Wrapping :: Rewrapping s t => (Unwrapped s -> s) -> Iso s t (Unwrapped s) (Unwrapped t) Source #

This is a convenient version of _Wrapped with an argument that's ignored.

The user supplied function is ignored, merely its types are used.

_Unwrapping :: Rewrapping s t => (Unwrapped s -> s) -> Iso (Unwrapped t) (Unwrapped s) t s Source #

This is a convenient version of _Unwrapped with an argument that's ignored.

The user supplied function is ignored, merely its types are used.

op :: Wrapped s => (Unwrapped s -> s) -> s -> Unwrapped s Source #

Given the constructor for a Wrapped type, return a deconstructor that is its inverse.

Assuming the Wrapped instance is legal, these laws hold:

op f . f ≡ id
f . op f ≡ id

>>> op Identity (Identity 4)
4

>>> op Const (Const "hello")
"hello"

ala :: (Functor f, Rewrapping s t) => (Unwrapped s -> s) -> ((Unwrapped t -> t) -> f s) -> f (Unwrapped s) Source #

This combinator is based on ala from Conor McBride's work on Epigram.

As with _Wrapping, the user supplied function for the newtype is ignored.

>>> ala Sum foldMap [1,2,3,4]
10

>>> ala All foldMap [True,True]
True

>>> ala All foldMap [True,False]
False

>>> ala Any foldMap [False,False]
False

>>> ala Any foldMap [True,False]
True

>>> ala Product foldMap [1,2,3,4]
24

You may want to think of this combinator as having the following, simpler, type.

ala :: Rewrapping s t => (Unwrapped s -> s) -> ((Unwrapped t -> t) -> e -> s) -> e -> Unwrapped s

alaf :: (Functor f, Functor g, Rewrapping s t) => (Unwrapped s -> s) -> (f t -> g s) -> f (Unwrapped t) -> g (Unwrapped s) Source #

This combinator is based on ala' from Conor McBride's work on Epigram.

As with _Wrapping, the user supplied function for the newtype is ignored.

alaf :: Rewrapping s t => (Unwrapped s -> s) -> ((r -> t) -> e -> s) -> (r -> Unwrapped t) -> e -> Unwrapped s

>>> alaf Sum foldMap Prelude.length ["hello","world"]
10

_GWrapped' :: (Generic s, D1 d (C1 c (S1 s' (Rec0 a))) ~ Rep s, Unwrapped s ~ GUnwrapped (Rep s)) => Iso' s (Unwrapped s) Source #

Implement the _Wrapped operation for a type using its Generic instance.