Data.Functor.Contravariant.Adjunction
- 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
- class (Contravariant f, Contravariant g) => DualAdjunction f g | f -> g, g -> f where
- unitOp :: g (f a) -> a
- counitOp :: f (g a) -> a
- leftAdjunctOp :: (f a -> b) -> g b -> a
- rightAdjunctOp :: (g b -> a) -> f a -> b
- 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
Instances
| Adjunction Predicate Predicate | This gives rise to the Cont Bool monad |
| Adjunction (Op r) (Op r) | This adjunction gives rise to the Cont monad |
class (Contravariant f, Contravariant g) => DualAdjunction f g | f -> g, g -> f whereSource
An adjunction from Hask to Hask^op
Hask (f a) b ~ Op a (g b)
rightAdjunct unit = id leftAdjunct counit = id
Methods
counitOp :: f (g a) -> aSource
leftAdjunctOp :: (f a -> b) -> g b -> aSource
rightAdjunctOp :: (g b -> a) -> f a -> bSource
data Representation f x Source
A representation of a contravariant functor
Constructors
| Representation | |
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