profunctors-5.6.2: Profunctors

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

- 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

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.

`Ran` has a polymorphic kind since `5.6`.

Constructors

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

#### Instances

Instances details

ProfunctorFunctor (Ran p :: (Type -> Type -> Type) -> k -> Type -> Type) # |
Instance details Defined in Data.Profunctor.Ran Methods promap :: forall (p0 :: Type -> Type -> Type) (q :: Type -> Type -> Type). Profunctor p0 => (p0 :-> q) -> Ran p p0 :-> Ran p q #
p ~ q => Category (Ran p q :: k2 -> k2 -> Type) # | ``Ran` p p` forms a `Monad` in the `Profunctor` 2-category, which is isomorphic to a Haskell `Category` instance.
Instance details Defined in Data.Profunctor.Ran Methods id :: forall (a :: k). Ran p q a a (.) :: forall (b :: k) (c :: k) (a :: k). Ran p q b c -> Ran p q a b -> Ran p q a c
Category p => ProfunctorComonad (Ran p :: (Type -> Type -> Type) -> Type -> Type -> Type) # |
Instance details Defined in Data.Profunctor.Ran Methods proextract :: forall (p0 :: Type -> Type -> Type). Profunctor p0 => Ran p p0 :-> p0 # produplicate :: forall (p0 :: Type -> Type -> Type). Profunctor p0 => Ran p p0 :-> Ran p (Ran p p0) #
(Profunctor p, Profunctor q) => Profunctor (Ran p q) # |
Instance details Defined in Data.Profunctor.Ran 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 # (#.) :: forall a b c q0. Coercible c b => q0 b c -> Ran p q a b -> Ran p q a c # (.#) :: forall a b c q0. Coercible b a => Ran p q b c -> q0 a b -> Ran p q a c #
Profunctor q => Functor (Ran p q a) # |
Instance details Defined in Data.Profunctor.Ran Methods fmap :: (a0 -> b) -> Ran p q a a0 -> Ran p q a b # (<$) :: a0 -> Ran p q a b -> Ran p q a a0 #

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.

`Codensity` has a polymorphic kind since `5.6`.

Constructors

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

#### Instances

Instances details

Category (Codensity p :: k2 -> k2 -> Type) # |
Instance details Defined in Data.Profunctor.Ran Methods id :: forall (a :: k). Codensity p a a (.) :: forall (b :: k) (c :: k) (a :: k). Codensity p b c -> Codensity p a b -> Codensity p a c
Profunctor p => Profunctor (Codensity p) # |
Instance details Defined in Data.Profunctor.Ran 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 # (#.) :: forall a b c q. Coercible c b => q b c -> Codensity p a b -> Codensity p a c # (.#) :: forall a b c q. Coercible b a => Codensity p b c -> q a b -> Codensity p a c #
Profunctor p => Functor (Codensity p a) # |
Instance details Defined in Data.Profunctor.Ran Methods fmap :: (a0 -> b) -> Codensity p a a0 -> Codensity p a b # (<$) :: a0 -> Codensity p a b -> Codensity p a a0 #

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