Data.Functor.Contravariant.Rep

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

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

Representable Predicate

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 *)

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 (Proxy *)

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 (Op r)

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

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)

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