Data.Profunctor

class Profunctor p  where

A Profunctor is a Functor from the pair category (Type^op, Type) to Type.

In other words, a Profunctor is a type constructor of two type arguments, which is contravariant in its first argument and covariant in its second argument.

The dimap function can be used to map functions over both arguments simultaneously.

A straightforward example of a profunctor is the function arrow (->).

Laws:

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

Members

• dimap :: forall d c b a. (a -> b) -> (c -> d) -> p b c -> p a d

Instances

• Profunctor Function

lmap :: forall p c b a. Profunctor p => (a -> b) -> p b c -> p a c

Map a function over the (contravariant) first type argument only.

rmap :: forall p c b a. Profunctor p => (b -> c) -> p a b -> p a c

Map a function over the (covariant) second type argument only.

arr :: forall p b a. Category p => Profunctor p => (a -> b) -> p a b

Lift a pure function into any Profunctor which is also a Category.

unwrapIso :: forall a t p. Profunctor p => Newtype t a => p t t -> p a a

wrapIso :: forall a t p. Profunctor p => Newtype t a => (t -> a) -> p a a -> p t t