Copyright	(c) Edward Kmett 2011-2014
License	BSD3
Maintainer	ekmett@gmail.com
Stability	experimental
Safe Haskell	None
Language	Haskell2010

Data.Functor.Contravariant.Rep

Contents

Representable Contravariant Functors
Default definitions

Description

Representable contravariant endofunctors over the category of Haskell types are isomorphic to (_ -> r) and resemble mappings to a fixed range.

Synopsis

class Contravariant f => Representable f where
- type Rep f :: *
- tabulate :: (a -> Rep f) -> f a
- index :: f a -> a -> Rep f
- contramapWithRep :: (b -> Either a ( Rep f)) -> f a -> f b
tabulated :: ( Representable f, Representable g, Profunctor p, Functor h) => p (f a) (h (g b)) -> p (a -> Rep f) (h (b -> Rep g))
contramapRep :: Representable f => (a -> b) -> f b -> f a

Representable Contravariant Functors

class Contravariant f => Representable f where Source #

A Contravariant functor f is Representable if tabulate and index witness an isomorphism to (_ -> Rep f) .

tabulate . index ≡ id
index . tabulate ≡ id

Minimal complete definition

tabulate , index

Associated Types

type Rep f :: * Source #

Methods

tabulate :: (a -> Rep f) -> f a Source #

contramap f (tabulate g) = tabulate (g . f)

index :: f a -> a -> Rep f Source #

contramapWithRep :: (b -> Either a ( Rep f)) -> f a -> f b Source #

contramapWithRep f p ≡ tabulate $ either (index p) id . f

Instances

Instances details

Representable Predicate Source #
Instance details Defined in Data.Functor.Contravariant.Rep Associated Types type Rep Predicate Source # Methods tabulate :: (a -> Rep Predicate ) -> Predicate a Source # index :: Predicate a -> a -> Rep Predicate Source # contramapWithRep :: (b -> Either a ( Rep Predicate )) -> Predicate a -> Predicate b Source #
Representable ( U1 :: Type -> Type ) Source #
Instance details Defined in Data.Functor.Contravariant.Rep Associated Types type Rep U1 Source # Methods tabulate :: (a -> Rep U1 ) -> U1 a Source # index :: U1 a -> a -> Rep U1 Source # contramapWithRep :: (b -> Either a ( Rep U1 )) -> U1 a -> U1 b Source #
Representable ( Op r) Source #
Instance details Defined in Data.Functor.Contravariant.Rep Associated Types type Rep ( Op r) Source # Methods tabulate :: (a -> Rep ( Op r)) -> Op r a Source # index :: Op r a -> a -> Rep ( Op r) Source # contramapWithRep :: (b -> Either a ( Rep ( Op r))) -> Op r a -> Op r b Source #
Representable ( Proxy :: Type -> Type ) Source #
Instance details Defined in Data.Functor.Contravariant.Rep Associated Types type Rep Proxy Source # Methods tabulate :: (a -> Rep Proxy ) -> Proxy a Source # index :: Proxy a -> a -> Rep Proxy Source # contramapWithRep :: (b -> Either a ( Rep Proxy )) -> Proxy a -> Proxy b Source #
( Representable f, Representable g) => Representable (f :*: g) Source #
Instance details Defined in Data.Functor.Contravariant.Rep Associated Types type Rep (f :: g) Source # Methods tabulate :: (a -> Rep (f :: g)) -> (f :: g) a Source # index :: (f :: g) a -> a -> Rep (f :: g) Source # contramapWithRep :: (b -> Either a ( Rep (f :: g))) -> (f :: g) a -> (f :: g) b Source #
( Representable f, Representable g) => Representable ( Product f g) Source #
Instance details Defined in Data.Functor.Contravariant.Rep Associated Types type Rep ( Product f g) Source # Methods tabulate :: (a -> Rep ( Product f g)) -> Product f g a Source # index :: Product f g a -> a -> Rep ( Product f g) Source # contramapWithRep :: (b -> Either a ( Rep ( Product f g))) -> Product f g a -> Product f g b Source #

tabulated :: ( Representable f, Representable g, Profunctor p, Functor h) => p (f a) (h (g b)) -> p (a -> Rep f) (h (b -> Rep g)) Source #

tabulate and index form two halves of an isomorphism.

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

tabulated :: Representable f => Iso' (a -> Rep f) (f a)

Default definitions

contramapRep :: Representable f => (a -> b) -> f b -> f a Source #