Moduleprofunctors-5.6.3Haskell2010

Data.Profunctor.Ran

Synopsis

newtype Ran
value decomposeRan
value precomposeRan
value curryRan
value uncurryRan
newtype Codensity
value decomposeCodensity

Packageprofunctors-5.6.3
Exports7
LanguageHaskell2010
LicenceBSD-3-Clause
SourceRan.hs

newtypenewtype Ran (p :: k -> k1 -> Type) (q :: k -> k2 -> Type) (a :: k1) (b :: k2)

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
- runRan :: forall (x :: k1). p x a -> q x b

Instances5ProfunctorFunctor, Category, ProfunctorComonad, Profunctor, Functor

ProfunctorFunctor (Ran p)Defined in profunctors-5.6.3 · Data.Profunctor.Ran
p ~ q => Category (Ran p q)Defined in profunctors-5.6.3 · Data.Profunctor.Ran
Ran p p forms a Monad in the Profunctor 2-category, which is isomorphic to a Haskell Category instance.
Category p => ProfunctorComonad (Ran p)Defined in profunctors-5.6.3 · Data.Profunctor.Ran
(Profunctor p, Profunctor q) => Profunctor (Ran p q)Defined in profunctors-5.6.3 · Data.Profunctor.Ran
Profunctor q => Functor (Ran p q a)Defined in profunctors-5.6.3 · Data.Profunctor.Ran

valuedecomposeRan :: Procompose (Ran q p) q a b -> p a b

Source#

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.

valueprecomposeRan :: Profunctor q => Procompose q (Ran p (->)) :-> Ran p q

valuecurryRan :: Procompose p q :-> r -> p :-> Ran q r

valueuncurryRan :: p :-> Ran q r -> Procompose p q :-> r

newtypenewtype Codensity (p :: k -> k1 -> Type) (a :: k1) (b :: k1)

Source#

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
- runCodensity :: forall (x :: k1). p x a -> p x b

Instances3Category, Profunctor, Functor

Category (Codensity p)Defined in profunctors-5.6.3 · Data.Profunctor.Ran
Profunctor p => Profunctor (Codensity p)Defined in profunctors-5.6.3 · Data.Profunctor.Ran
Profunctor p => Functor (Codensity p a)Defined in profunctors-5.6.3 · Data.Profunctor.Ran

valuedecomposeCodensity :: Procompose (Codensity p) p a b -> p a b