category-extras-0.53.6: Various modules and constructs inspired by category theory Contents Index

Control.Functor.Adjunction Portability non-portable (functional-dependencies) Stability experimental Maintainer Edward Kmett <ekmett@gmail.com>

Contents Every Right Adjoint is Representable

Description

Synopsis

class (Representable g (f ()), Functor f) => Adjunction f g | f -> g, g -> f where unit :: a -> g (f a) counit :: f (g a) -> a leftAdjunct :: (f a -> b) -> a -> g b rightAdjunct :: (a -> g b) -> f a -> b newtype ACompF f g a = ACompF (CompF f g a) repAdjunction :: Adjunction f g => (f () -> a) -> g a unrepAdjunction :: Adjunction f g => g a -> (f () -> a)

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 (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 ComonadContext e (ACompF ((,) e) ((->) e)) MonadState e (ACompF ((->) e) ((,) e)) Functor f => HFunctor (ACompF f) Adjunction f g => Monad (ACompF g f) (Functor f, Functor g) => Functor (ACompF f g) (Full f, Full g) => Full (ACompF f g) (ExpFunctor f, ExpFunctor g) => ExpFunctor (ACompF f g) Adjunction f g => Pointed (ACompF g f) Adjunction f g => Copointed (ACompF f g) Adjunction f g => Comonad (ACompF f g) Adjunction f g => Applicative (ACompF g f)

Every Right Adjoint is Representable

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

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

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