Portability | non-portable (functional-dependencies) |
---|---|
Stability | experimental |
Maintainer | Edward Kmett <ekmett@gmail.com> |
- 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 whereSource
An Adjunction
formed by the Functor
f and Functor
g.
leftAdjunct :: (f a -> b) -> a -> g bSource
rightAdjunct :: (a -> g b) -> f a -> bSource
Adjunction Identity Identity | |
Adjunction ((,) e) ((->) e) | |
Adjunction (Coreader e) (Reader e) | |
(Adjunction f1 g1, Adjunction f2 g2) => Adjunction (CompF f2 f1) (CompF g1 g2) |
Adjunction-oriented composition, yields monads and comonads from adjunctions
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 aSource
unrepAdjunction :: Adjunction f g => g a -> f () -> aSource