Control.Functor.Adjunction

Documentation

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

An Adjunction formed by the Functor f and Functor g.

Methods

unit :: a -> g (f a)

counit :: f (g a) -> a

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

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

Instances

Adjunction Identity Identity

Adjunction ((,) e) ((->) e)

Adjunction (Coreader e) (Reader e)

(Adjunction f1 g1, Adjunction f2 g2) => Adjunction (CompF f2 f1) (CompF g1 g2)

newtype ACompF f g a

Adjunction-oriented composition, yields monads and comonads from adjunctions

Constructors

ACompF (CompF f g a)

Instances

Composition ACompF

MonadState e (ACompF ((->) e) ((,) e))

ComonadContext e (ACompF ((,) e) ((->) e))

Functor f => HFunctor (ACompF f)

Adjunction f g => Monad (ACompF g f)

(Functor f, Functor g) => Functor (ACompF f g)

Adjunction f g => Applicative (ACompF g f)

(Full f, Full g) => Full (ACompF f g)

(ExpFunctor f, ExpFunctor g) => ExpFunctor (ACompF f g)

Adjunction f g => Copointed (ACompF f g)

Adjunction f g => Pointed (ACompF g f)

Adjunction f g => Comonad (ACompF f g)

Every Right Adjoint is Representable

repAdjunction :: Adjunction f g => (f () -> a) -> g a

unrepAdjunction :: Adjunction f g => g a -> f () -> a