Data.Functor.Corepresentable

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

Values

type family Value f

Contravariant Keyed

class Contravariant f => Valued f where

Dual to Keyed.

Methods

contramapWithValue :: (b -> Either a (Value f)) -> f a -> f b

Instances

Valued Predicate

Contravariant (Op r) => Valued (Op r)

(Contravariant (Product f g), Valued f, Valued g) => Valued (Product f g)

Contravariant Indexed

class Coindexed f where

Dual to Indexed.

Methods

coindex :: f a -> a -> Value f

Instances

Coindexed Predicate

Coindexed (Op r)

(Coindexed f, Coindexed g) => Coindexed (Coproduct f g)

(Coindexed f, Coindexed g) => Coindexed (Product f g)

Representable Contravariant Functors

class (Coindexed f, Valued f) => Corepresentable f where

A Functor f is Corepresentable if corep and coindex witness an isomorphism to (_ -> Value f).

 tabulate . index = id
 index . tabulate = id
 tabulate . return f = return f

Methods

corep :: (a -> Value f) -> f a

 contramap f (corep g) = corep (g . f)

Instances

Corepresentable Predicate

(Coindexed (Op r), Valued (Op r)) => Corepresentable (Op r)

(Coindexed (Product f g), Valued (Product f g), Corepresentable f, Corepresentable g) => Corepresentable (Product f g)

Default definitions

contramapDefault :: Corepresentable f => (a -> b) -> f b -> f a

contramapWithValueDefault :: Corepresentable f => (b -> Either a (Value f)) -> f a -> f b