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 :: k -> k1 -> Type) (q :: k -> k2 -> Type) (a :: k1) (b :: k2) = Ran {
- runRan :: forall (x :: k). p x a -> q x b
}
decomposeRan :: forall {k1} {k2} {k3} (q :: k1 -> k2 -> Type) p (a :: k1) (b :: k3). Procompose (Ran q p) q a b -> p a b
precomposeRan :: forall {k} (q :: Type -> Type -> Type) (p :: Type -> k -> Type). Profunctor q => Procompose q (Ran p (->)) :-> Ran p q
curryRan :: forall {k1} {k2} {k3} (p :: k1 -> k2 -> Type) (q :: k3 -> k1 -> Type) (r :: k3 -> k2 -> Type). (Procompose p q :-> r) -> p :-> Ran q r
uncurryRan :: forall {k1} {k2} {k3} (p :: k1 -> k2 -> Type) (q :: k3 -> k1 -> Type) (r :: k3 -> k2 -> Type). (p :-> Ran q r) -> Procompose p q :-> r
newtype Codensity (p :: k -> k1 -> Type) (a :: k1) (b :: k1) = Codensity {
- runCodensity :: forall (x :: k). p x a -> p x b
}
decomposeCodensity :: forall {k2} {k1} p (a :: k2) (b :: k1). Procompose (Codensity p) p a b -> p a b

Documentation

newtype Ran (p :: k -> k1 -> Type) (q :: k -> k2 -> Type) (a :: k1) (b :: k2) Source #

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 :: k). p x a -> q x b

Instances

Instances details

ProfunctorFunctor (Ran p :: (Type -> Type -> Type) -> k -> Type -> Type) Source #
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 Source #
p ~ q => Category (Ran p q :: k2 -> k2 -> Type) Source #	`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 :: k2). Ran p q a a # (.) :: forall (b :: k2) (c :: k2) (a :: k2). 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) Source #
Instance details Defined in Data.Profunctor.Ran Methods proextract :: forall (p0 :: Type -> Type -> Type). Profunctor p0 => Ran p p0 :-> p0 Source # produplicate :: forall (p0 :: Type -> Type -> Type). Profunctor p0 => Ran p p0 :-> Ran p (Ran p p0) Source #
(Profunctor p, Profunctor q) => Profunctor (Ran p q) Source #
Instance details Defined in Data.Profunctor.Ran Methods dimap :: (a -> b) -> (c -> d) -> Ran p q b c -> Ran p q a d Source # lmap :: (a -> b) -> Ran p q b c -> Ran p q a c Source # rmap :: (b -> c) -> Ran p q a b -> Ran p q a c Source # (#.) :: forall a b c q0. Coercible c b => q0 b c -> Ran p q a b -> Ran p q a c Source # (.#) :: forall a b c q0. Coercible b a => Ran p q b c -> q0 a b -> Ran p q a c Source #
Profunctor q => Functor (Ran p q a) Source #
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 :: forall {k1} {k2} {k3} (q :: k1 -> k2 -> Type) p (a :: k1) (b :: k3). 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.

precomposeRan :: forall {k} (q :: Type -> Type -> Type) (p :: Type -> k -> Type). Profunctor q => Procompose q (Ran p (->)) :-> Ran p q Source #

curryRan :: forall {k1} {k2} {k3} (p :: k1 -> k2 -> Type) (q :: k3 -> k1 -> Type) (r :: k3 -> k2 -> Type). (Procompose p q :-> r) -> p :-> Ran q r Source #

uncurryRan :: forall {k1} {k2} {k3} (p :: k1 -> k2 -> Type) (q :: k3 -> k1 -> Type) (r :: k3 -> k2 -> Type). (p :-> Ran q r) -> Procompose p q :-> r Source #

newtype 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
Fields runCodensity :: forall (x :: k). p x a -> p x b

Instances

Instances details

Category (Codensity p :: k2 -> k2 -> Type) Source #
Instance details Defined in Data.Profunctor.Ran Methods id :: forall (a :: k2). Codensity p a a # (.) :: forall (b :: k2) (c :: k2) (a :: k2). Codensity p b c -> Codensity p a b -> Codensity p a c #
Profunctor p => Profunctor (Codensity p) Source #
Instance details Defined in Data.Profunctor.Ran Methods dimap :: (a -> b) -> (c -> d) -> Codensity p b c -> Codensity p a d Source # lmap :: (a -> b) -> Codensity p b c -> Codensity p a c Source # rmap :: (b -> c) -> Codensity p a b -> Codensity p a c Source # (#.) :: forall a b c q. Coercible c b => q b c -> Codensity p a b -> Codensity p a c Source # (.#) :: forall a b c q. Coercible b a => Codensity p b c -> q a b -> Codensity p a c Source #
Profunctor p => Functor (Codensity p a) Source #
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 :: forall {k2} {k1} p (a :: k2) (b :: k1). Procompose (Codensity p) p a b -> p a b Source #