- class (Contravariant f, Contravariant g) => Adjunction f g | f -> g, g -> f where
- unit :: a -> g (f a)
- counit :: a -> f (g a)
- leftAdjunct :: (b -> f a) -> a -> g b
- rightAdjunct :: (a -> g b) -> b -> f a
- data Representation f x = Representation {}
- repAdjunction :: Adjunction f g => Representation g (f ())
- repFlippedAdjunction :: Adjunction f g => Representation f (g ())
Documentation
class (Contravariant f, Contravariant g) => Adjunction f g | f -> g, g -> f whereSource
An adjunction from Hask^op to Hask
Op (f a) b ~ Hask a (g b)
rightAdjunct unit = id leftAdjunct counit = id
leftAdjunct :: (b -> f a) -> a -> g bSource
rightAdjunct :: (a -> g b) -> b -> f aSource
Adjunction Predicate Predicate | This gives rise to the Cont Bool monad |
Adjunction (Op r) (Op r) | This adjunction gives rise to the Cont monad |
repAdjunction :: Adjunction f g => Representation g (f ())Source
Represent a contravariant functor that has a left adjoint
repFlippedAdjunction :: Adjunction f g => Representation f (g ())Source