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 |
- newtype Ran p q a b = Ran {
- runRan :: forall x. p x a -> q x b
- decomposeRan :: Procompose (Ran q p) q :-> p
- 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 = Codensity {
- runCodensity :: forall x. p x a -> p x b
- decomposeCodensity :: Procompose (Codensity p) p a b -> p a b
Documentation
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.
Category * p => ProfunctorComonad (Ran p) # | |
ProfunctorFunctor (Ran p) # | |
(~) (* -> * -> *) p q => Category * (Ran p q) # |
|
(Profunctor p, Profunctor q) => Profunctor (Ran p q) # | |
Profunctor q => Functor (Ran p q a) # | |
decomposeRan :: Procompose (Ran q p) q :-> p #
The 2-morphism that defines a right Kan extension.
Note: When q
is left adjoint to
then Ran
q (->)decomposeRan
is the counit
of the adjunction.
precomposeRan :: Profunctor q => Procompose q (Ran p (->)) :-> Ran p q #
uncurryRan :: (p :-> Ran q r) -> Procompose p q :-> r #
This represents the right Kan extension of a Profunctor
p
along itself. This provides a generalization of the "difference list" trick to profunctors.
Codensity | |
|
Profunctor p => Profunctor (Codensity p) # | |
Category * (Codensity p) # | |
Profunctor p => Functor (Codensity p a) # | |
decomposeCodensity :: Procompose (Codensity p) p a b -> p a b #