Moduleadjunctions-4.4.4Haskell2010

Data.Functor.Contravariant.Adjunction

Synopsis

classclass (Contravariant f, Representable g) => Adjunction (f :: Type -> Type) (g :: Type -> Type) | 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.

Instances2Adjunction

Adjunction Predicate PredicateDefined in adjunctions-4.4.4 · Data.Functor.Contravariant.Adjunction
This gives rise to the Cont Bool Monad
Adjunction (Op r) (Op r)Defined in adjunctions-4.4.4 · Data.Functor.Contravariant.Adjunction
This Adjunction gives rise to the Cont Monad

valueadjuncted

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)

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

Represent a Contravariant functor that has a left adjoint

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