adjunctions-4.4: Adjunctions and representable functors

Copyright(c) Edward Kmett 2011-2014
LicenseBSD3
Maintainerekmett@gmail.com
Stabilityexperimental
Safe HaskellNone
LanguageHaskell98

Data.Functor.Contravariant.Rep

Contents

Description

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

Synopsis

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

Representable Predicate Source # 

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 *) Source # 

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 (Proxy *) Source # 

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 (Op r) Source # 

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 f, Representable g) => Representable ((:*:) * f g) Source # 

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 # 

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 #