Data.Profunctor.Ran

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