Description

Synopsis

# Documentation

class (Contravariant f, Representable g) => Adjunction f g | f -> g, g -> f where #

An adjunction from Hask^op to Hask

Op (f a) b ~ Hask a (g b)
rightAdjunct unit = id
leftAdjunct counit = id


Any adjunction from Hask to Hask^op would indirectly permit unsafePerformIO, and therefore does not exist.

Methods

unit :: a -> g (f a) #

counit :: a -> f (g a) #

leftAdjunct :: (b -> f a) -> a -> g b #

rightAdjunct :: (a -> g b) -> b -> f a #

Instances

 # This gives rise to the Cont Bool Monad Methodsunit :: a -> Predicate (Predicate a) #counit :: a -> Predicate (Predicate a) #leftAdjunct :: (b -> Predicate a) -> a -> Predicate b #rightAdjunct :: (a -> Predicate b) -> b -> Predicate a # Adjunction (Op r) (Op r) # This Adjunction gives rise to the Cont Monad Methodsunit :: a -> Op r (Op r a) #counit :: a -> Op r (Op r a) #leftAdjunct :: (b -> Op r a) -> a -> Op r b #rightAdjunct :: (a -> Op r b) -> b -> Op r a #

adjuncted :: (Adjunction f g, Profunctor p, Functor h) => p (a -> g b) (h (c -> g d)) -> p (b -> f a) (h (d -> f c)) #

leftAdjunct and rightAdjunct form two halves of an isomorphism.

This can be used with the combinators from the lens package.

adjuncted :: Adjunction f g => Iso' (b -> f a) (a -> g b)

contrarepAdjunction :: Adjunction f g => (a -> f ()) -> g a #

Represent a Contravariant functor that has a left adjoint

coindexAdjunction :: Adjunction f g => g a -> a -> f () #