Data.Functor.Invariant

class Invariant :: (Type -> Type) -> Constraintclass Invariant f  where

A type of functor that can be used to adapt the type of a wrapped function where the parameterised type occurs in both the positive and negative position, for example, F (a -> a).

An Invariant instance should satisfy the following laws:

• Identity: imap id id = id
• Composition: imap g1 g2 <<< imap f1 f2 = imap (g1 <<< f1) (f2 <<< g2)

Members

• imap :: forall a b. (a -> b) -> (b -> a) -> f a -> f b

Instances

• Invariant (Function a)
• Invariant Array
• Invariant Additive
• Invariant Conj
• Invariant Disj
• Invariant Dual
• Invariant (Endo Function)
• Invariant Multiplicative
• (Invariant f) => Invariant (Alternate f)

imapF :: forall f a b. Functor f => (a -> b) -> (b -> a) -> f a -> f b

As all Functors are also trivially Invariant, this function can be used as the imap implementation for any types that has an existing Functor instance.