Copyright	(C) 2011-2015 Edward Kmett,
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	Type-Families
Safe Haskell	Safe
Language	Haskell2010

Data.Profunctor.Rep

Contents

Representable Profunctors
Corepresentable Profunctors
Prep -| Star
Coprep -| Costar

Description

Synopsis

Representable Profunctors

class (Sieve p (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

Instances

Representable (->)
(Monad m, Functor m) => Representable (Kleisli m)
Representable (Forget r)
Functor f => Representable (Star f)
(Representable p, Representable q) => Representable (Procompose p q)	The composition of two `Representable` `Profunctor`s 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 sieve 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 (Cosieve p (Corep p), Costrong 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

Instances

Corepresentable (->)
Functor w => Corepresentable (Cokleisli w)
Corepresentable (Tagged *)
Functor f => Corepresentable (Costar 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 cosieve 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)

unfirstCorep :: Corepresentable p => p (a, d) (b, d) -> p a b

Default definition for unfirst given that p is Corepresentable.

unsecondCorep :: Corepresentable p => p (d, a) (d, b) -> p a b

Default definition for unsecond given that p is Corepresentable.

closedCorep :: Corepresentable p => p a b -> p (x -> a) (x -> b)

Default definition for closed given that p is Corepresentable

Prep -| Star

data Prep p a where

Prep -| Star :: [Hask, Hask] -> Prof

This gives rise to a monad in Prof, ('Star'.'Prep'), and a comonad in [Hask,Hask] ('Prep'.'Star')

Constructors

Prep :: x -> p x a -> Prep p a

Instances

(Monad (Rep p), Representable p) => Monad (Prep p)
Profunctor p => Functor (Prep p)
(Applicative (Rep p), Representable p) => Applicative (Prep p)

prepAdj :: (forall a. Prep p a -> g a) -> p :-> Star g

unprepAdj :: (p :-> Star g) -> Prep p a -> g a

prepUnit :: p :-> Star (Prep p)

prepCounit :: Prep (Star f) a -> f a

Coprep -| Costar

newtype Coprep p a

Constructors

Coprep
Fields runCoprep :: forall r. p a r -> r

Instances

Profunctor p => Functor (Coprep p)

coprepAdj :: (forall a. f a -> Coprep p a) -> p :-> Costar f

Coprep -| Costar :: [Hask, Hask]^op -> Prof

Like all adjunctions this gives rise to a monad and a comonad.

This gives rise to a monad on Prof ('Costar'.'Coprep') and a comonad on [Hask, Hask]^op given by ('Coprep'.'Costar') which is a monad in [Hask,Hask]

uncoprepAdj :: (p :-> Costar f) -> f a -> Coprep p a

coprepUnit :: p :-> Costar (Coprep p)

coprepCounit :: f a -> Coprep (Costar f) a