| Copyright | (C) 2011-2013 Edward Kmett |
|---|---|
| License | BSD-style (see the file LICENSE) |
| Maintainer | Edward Kmett <ekmett@gmail.com> |
| Stability | provisional |
| Portability | MPTCs |
| Safe Haskell | Trustworthy |
| Language | Haskell98 |
Data.Functor.Contravariant.Adjunction
Description
- class (Contravariant f, Representable 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
- adjuncted :: (Adjunction f g, Profunctor p, Functor h) => p (a -> g b) (h (c -> g d)) -> p (b -> f a) (h (d -> f c))
- contrarepAdjunction :: Adjunction f g => (a -> f ()) -> g a
- coindexAdjunction :: Adjunction f g => g a -> a -> f ()
Documentation
class (Contravariant f, Representable g) => Adjunction f g | f -> g, g -> f where Source
An adjunction from Hask^op to Hask
Op(f a) b ~Haska (g b)
rightAdjunctunit=idleftAdjunctcounit=id
Any adjunction from Hask to Hask^op would indirectly
permit unsafePerformIO, and therefore does not exist.
Minimal complete definition
Nothing
Instances
| Adjunction Predicate Predicate Source | This gives rise to the |
| Adjunction (Op r) (Op r) Source | This |
adjuncted :: (Adjunction f g, Profunctor p, Functor h) => p (a -> g b) (h (c -> g d)) -> p (b -> f a) (h (d -> f c)) Source
leftAdjunct and rightAdjunct form two halves of an isomorphism.
This can be used with the combinators from the lens package.
adjuncted::Adjunctionf g =>Iso'(b -> f a) (a -> g b)
contrarepAdjunction :: Adjunction f g => (a -> f ()) -> g a Source
Represent a Contravariant functor that has a left adjoint
coindexAdjunction :: Adjunction f g => g a -> a -> f () Source