Copyright	(C) 2013-2015 Edward Kmett and Dan Doel
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	Rank2Types, TFs
Safe Haskell	Safe
Language	Haskell2010

Data.Profunctor.Ran

Description

Synopsis

Documentation

newtype Ran p q a b #

This represents the right Kan extension of a Profunctor q along a Profunctor p in a limited version of the 2-category of Profunctors where the only object is the category Hask, 1-morphisms are profunctors composed and compose with Profunctor composition, and 2-morphisms are just natural transformations.

Constructors

Ran
Fields runRan :: forall x. p x a -> q x b

Instances

Category * p => ProfunctorComonad (Ran p) #
Methods proextract :: Profunctor p => Ran p p :-> p # produplicate :: Profunctor p => Ran p p :-> Ran p (Ran p p) #
ProfunctorFunctor (Ran p) #
Methods promap :: Profunctor p => (p :-> q) -> Ran p p :-> Ran p q #
(~) (* -> * -> ) p q => Category (Ran p q) #	`Ran p p` forms a `Monad` in the `Profunctor` 2-category, which is isomorphic to a Haskell `Category` instance.
Methods id :: cat a a # (.) :: cat b c -> cat a b -> cat a c #
(Profunctor p, Profunctor q) => Profunctor (Ran p q) #
Methods dimap :: (a -> b) -> (c -> d) -> Ran p q b c -> Ran p q a d # lmap :: (a -> b) -> Ran p q b c -> Ran p q a c # rmap :: (b -> c) -> Ran p q a b -> Ran p q a c # (#.) :: Coercible * c b => (b -> c) -> Ran p q a b -> Ran p q a c # (.#) :: Coercible * b a => Ran p q b c -> (a -> b) -> Ran p q a c #
Profunctor q => Functor (Ran p q a) #
Methods fmap :: (a -> b) -> Ran p q a a -> Ran p q a b # (<$) :: a -> Ran p q a b -> Ran p q a a #

decomposeRan :: Procompose (Ran q p) q :-> p #

The 2-morphism that defines a right Kan extension.

Note: When q is left adjoint to Ran q (->) then decomposeRan is the counit of the adjunction.

precomposeRan :: Profunctor q => Procompose q (Ran p (->)) :-> Ran p q #

curryRan :: (Procompose p q :-> r) -> p :-> Ran q r #

uncurryRan :: (p :-> Ran q r) -> Procompose p q :-> r #

newtype Codensity p a b #

This represents the right Kan extension of a Profunctor p along itself. This provides a generalization of the "difference list" trick to profunctors.

Constructors

Codensity
Fields runCodensity :: forall x. p x a -> p x b

Instances

Profunctor p => Profunctor (Codensity p) #
Methods dimap :: (a -> b) -> (c -> d) -> Codensity p b c -> Codensity p a d # lmap :: (a -> b) -> Codensity p b c -> Codensity p a c # rmap :: (b -> c) -> Codensity p a b -> Codensity p a c # (#.) :: Coercible * c b => (b -> c) -> Codensity p a b -> Codensity p a c # (.#) :: Coercible * b a => Codensity p b c -> (a -> b) -> Codensity p a c #
Category * (Codensity p) #
Methods id :: cat a a # (.) :: cat b c -> cat a b -> cat a c #
Profunctor p => Functor (Codensity p a) #
Methods fmap :: (a -> b) -> Codensity p a a -> Codensity p a b # (<$) :: a -> Codensity p a b -> Codensity p a a #

decomposeCodensity :: Procompose (Codensity p) p a b -> p a b #