Copyright	(c) Edward Kmett 2011-2014
License	BSD3
Maintainer	ekmett@gmail.com
Stability	experimental
Safe Haskell	None
Language	Haskell98

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 #

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 :: * #

Methods

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

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

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

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

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

Instances

Instances details

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

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

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 #