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

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)

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)

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)

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)

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)

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