Portability | rank 2 types |
---|---|
Stability | experimental |
Maintainer | Edward Kmett <ekmett@gmail.com> |
Safe Haskell | None |
- newtype Ran g h a = Ran {
- runRan :: forall b. (a -> g b) -> h b
- toRan :: (Composition compose, Functor k) => (forall a. compose k g a -> h a) -> k b -> Ran g h b
- fromRan :: Composition compose => (forall a. k a -> Ran g h a) -> compose k g b -> h b
- composeRan :: Composition compose => Ran f (Ran g h) a -> Ran (compose f g) h a
- decomposeRan :: (Composition compose, Functor f) => Ran (compose f g) h a -> Ran f (Ran g h) a
- adjointToRan :: Adjunction f g => f a -> Ran g Identity a
- ranToAdjoint :: Adjunction f g => Ran g Identity a -> f a
- ranToComposedAdjoint :: (Composition compose, Adjunction f g) => Ran g h a -> compose h f a
- composedAdjointToRan :: (Composition compose, Adjunction f g, Functor h) => compose h f a -> Ran g h a
- data Lan g h a where
- toLan :: (Composition compose, Functor f) => (forall a. h a -> compose f g a) -> Lan g h b -> f b
- fromLan :: Composition compose => (forall a. Lan g h a -> f a) -> h b -> compose f g b
- adjointToLan :: Adjunction f g => g a -> Lan f Identity a
- lanToAdjoint :: Adjunction f g => Lan f Identity a -> g a
- lanToComposedAdjoint :: (Composition compose, Functor h, Adjunction f g) => Lan f h a -> compose h g a
- composedAdjointToLan :: Composition compose => Adjunction f g => compose h g a -> Lan f h a
- composeLan :: (Composition compose, Functor f) => Lan f (Lan g h) a -> Lan (compose f g) h a
- decomposeLan :: Composition compose => Lan (compose f g) h a -> Lan f (Lan g h) a
Documentation
toRan :: (Composition compose, Functor k) => (forall a. compose k g a -> h a) -> k b -> Ran g h bSource
fromRan :: Composition compose => (forall a. k a -> Ran g h a) -> compose k g b -> h bSource
composeRan :: Composition compose => Ran f (Ran g h) a -> Ran (compose f g) h aSource
decomposeRan :: (Composition compose, Functor f) => Ran (compose f g) h a -> Ran f (Ran g h) aSource
adjointToRan :: Adjunction f g => f a -> Ran g Identity aSource
ranToAdjoint :: Adjunction f g => Ran g Identity a -> f aSource
ranToComposedAdjoint :: (Composition compose, Adjunction f g) => Ran g h a -> compose h f aSource
composedAdjointToRan :: (Composition compose, Adjunction f g, Functor h) => compose h f a -> Ran g h aSource
toLan :: (Composition compose, Functor f) => (forall a. h a -> compose f g a) -> Lan g h b -> f bSource
fromLan :: Composition compose => (forall a. Lan g h a -> f a) -> h b -> compose f g bSource
adjointToLan :: Adjunction f g => g a -> Lan f Identity aSource
lanToAdjoint :: Adjunction f g => Lan f Identity a -> g aSource
lanToComposedAdjoint :: (Composition compose, Functor h, Adjunction f g) => Lan f h a -> compose h g aSource
lanToComposedAdjoint
and composedAdjointToLan
witness the natural isomorphism between Lan f h
and Compose h g
given f -| g
composedAdjointToLan :: Composition compose => Adjunction f g => compose h g a -> Lan f h aSource
composeLan :: (Composition compose, Functor f) => Lan f (Lan g h) a -> Lan (compose f g) h aSource
composeLan
and decomposeLan
witness the natural isomorphism from Lan f (Lan g h)
and Lan (f
o
g) h
decomposeLan :: Composition compose => Lan (compose f g) h a -> Lan f (Lan g h) aSource