Data.Profunctor.Rep

Representable Profunctors

class (Functor (Rep p), Strong p) => Representable p where

A Profunctor p is Representable if there exists a Functor f such that p d c is isomorphic to d -> f c.

Associated Types

type Rep p :: * -> *

Methods

tabulate :: (d -> Rep p c) -> p d c

rep :: p d c -> d -> Rep p c

Instances

Representable (->)

(Monad m, Functor m) => Representable (Kleisli m)

Representable (Forget r)

Functor f => Representable (UpStar f)

(Representable p, Representable q) => Representable (Procompose p q)

The composition of two Representable Profunctors is Representable by the composition of their representations.

tabulated :: (Representable p, Representable q) => Iso (d -> Rep p c) (d' -> Rep q c') (p d c) (q d' c')

tabulate and rep form two halves of an isomorphism.

This can be used with the combinators from the lens package.

tabulated :: Representable p => Iso' (d -> Rep p c) (p d c)

firstRep :: Representable p => p a b -> p (a, c) (b, c)

Default definition for first' given that p is Representable.

secondRep :: Representable p => p a b -> p (c, a) (c, b)

Default definition for second' given that p is Representable.

Corepresentable Profunctors

class (Functor (Corep p), Profunctor p) => Corepresentable p where

A Profunctor p is Corepresentable if there exists a Functor f such that p d c is isomorphic to f d -> c.

Associated Types

type Corep p :: * -> *

Methods

cotabulate :: (Corep p d -> c) -> p d c

corep :: p d c -> Corep p d -> c

Instances

Corepresentable (->)

Functor w => Corepresentable (Cokleisli w)

Corepresentable (Tagged *)

Functor f => Corepresentable (DownStar f)

(Corepresentable p, Corepresentable q) => Corepresentable (Procompose p q)

cotabulated :: (Corepresentable p, Corepresentable q) => Iso (Corep p d -> c) (Corep q d' -> c') (p d c) (q d' c')

cotabulate and corep form two halves of an isomorphism.

This can be used with the combinators from the lens package.

cotabulated :: Corep f p => Iso' (f d -> c) (p d c)