Generic implementations of Logical methods.

As discussed in the documentation for the Logical class, method implementations are not particularly interesting and can be easily automated. This module provides such automated implementations using Generic.

This module expects that you already have a logical representation for your type, and there's already a Logic type instance. The logical type must not change the order of constructors as well as the order of fields in each constructor, but the names do not matter. Additionally, each field in the original type must be wrapped in a Term in the logical representation.

For example, consider the following type definition:

data Tree a
  = Leaf a
  | Node (Tree a) (Tree a)
  deriving (Generic)

data LogicTree a
  = LogicLeaf (Term a)
  | LogicNode (Term (Tree a)) (Term (Tree a))
  deriving (Generic)

From there, using the generic implementations is trivial:

instance (Logical a) => Logical (Tree a) where
  type Logic (Tree a) = LogicTree a
  unify = genericUnify
  subst = genericSubst
  inject = genericInject
  extract = genericExtract