Data.Profunctor.Rep

Representable Profunctors

class (Sieve p (Rep p), Strong p) => Representable p where

A Profunctor p is Representable if there exists a Functor f such that p d c is isomorphic to d -> f c.

Associated Types

type Rep p :: * -> *

Methods

tabulate :: (d -> Rep p c) -> p d c

Laws:

tabulate . sieve ≡ id
sieve . tabulate ≡ id

Instances

(Monad m, Functor m) => Representable (Kleisli m)

Defined in Data.Profunctor.Rep

Associated Types

type Rep (Kleisli m) :: Type -> Type

Methods

tabulate :: (d -> Rep (Kleisli m) c) -> Kleisli m d c

Representable ((->) :: Type -> Type -> Type)

Defined in Data.Profunctor.Rep

Associated Types

type Rep (->) :: Type -> Type

Methods

tabulate :: (d -> Rep (->) c) -> d -> c

Representable (Forget r :: Type -> Type -> Type)

Defined in Data.Profunctor.Rep

Associated Types

type Rep (Forget r) :: Type -> Type

Methods

tabulate :: (d -> Rep (Forget r) c) -> Forget r d c

Functor f => Representable (Star f)

Defined in Data.Profunctor.Rep

Associated Types

type Rep (Star f) :: Type -> Type

Methods

tabulate :: (d -> Rep (Star f) c) -> Star f d c

(Representable p, Representable q) => Representable (Procompose p q)

The composition of two Representable Profunctors is Representable by the composition of their representations.

Defined in Data.Profunctor.Composition

Associated Types

type Rep (Procompose p q) :: Type -> Type

Methods

tabulate :: (d -> Rep (Procompose p q) c) -> Procompose p q d c

tabulated :: (Representable p, Representable q) => Iso (d -> Rep p c) (d' -> Rep q c') (p d c) (q d' c')

tabulate and sieve form two halves of an isomorphism.

This can be used with the combinators from the lens package.

tabulated :: Representable p => Iso' (d -> Rep p c) (p d c)

firstRep :: Representable p => p a b -> p (a, c) (b, c)

Default definition for first' given that p is Representable.

secondRep :: Representable p => p a b -> p (c, a) (c, b)

Default definition for second' given that p is Representable.

Corepresentable Profunctors

class (Cosieve p (Corep p), Costrong p) => Corepresentable p where

A Profunctor p is Corepresentable if there exists a Functor f such that p d c is isomorphic to f d -> c.

Associated Types

type Corep p :: * -> *

Methods

cotabulate :: (Corep p d -> c) -> p d c

Laws:

cotabulate . cosieve ≡ id
cosieve . cotabulate ≡ id

Instances

Corepresentable (Tagged :: Type -> Type -> Type)

Defined in Data.Profunctor.Rep

Associated Types

type Corep Tagged :: Type -> Type

Methods

cotabulate :: (Corep Tagged d -> c) -> Tagged d c

Corepresentable ((->) :: Type -> Type -> Type)

Defined in Data.Profunctor.Rep

Associated Types

type Corep (->) :: Type -> Type

Methods

cotabulate :: (Corep (->) d -> c) -> d -> c

Functor w => Corepresentable (Cokleisli w)

Defined in Data.Profunctor.Rep

Associated Types

type Corep (Cokleisli w) :: Type -> Type

Methods

cotabulate :: (Corep (Cokleisli w) d -> c) -> Cokleisli w d c

Functor f => Corepresentable (Costar f)

Defined in Data.Profunctor.Rep

Associated Types

type Corep (Costar f) :: Type -> Type

Methods

cotabulate :: (Corep (Costar f) d -> c) -> Costar f d c

(Corepresentable p, Corepresentable q) => Corepresentable (Procompose p q)

Defined in Data.Profunctor.Composition

Associated Types

type Corep (Procompose p q) :: Type -> Type

Methods

cotabulate :: (Corep (Procompose p q) d -> c) -> Procompose p q d c

cotabulated :: (Corepresentable p, Corepresentable q) => Iso (Corep p d -> c) (Corep q d' -> c') (p d c) (q d' c')

cotabulate and cosieve form two halves of an isomorphism.

This can be used with the combinators from the lens package.

cotabulated :: Corep f p => Iso' (f d -> c) (p d c)

unfirstCorep :: Corepresentable p => p (a, d) (b, d) -> p a b

Default definition for unfirst given that p is Corepresentable.

unsecondCorep :: Corepresentable p => p (d, a) (d, b) -> p a b

Default definition for unsecond given that p is Corepresentable.

closedCorep :: Corepresentable p => p a b -> p (x -> a) (x -> b)

Default definition for closed given that p is Corepresentable

Prep -| Star

data Prep p a where

Prep -| Star :: [Hask, Hask] -> Prof

This gives rise to a monad in Prof, (Star.Prep), and a comonad in [Hask,Hask] (Prep.Star)

Prep has a polymorphic kind since 5.6.

Constructors

Prep :: x -> p x a -> Prep p a

Instances

(Monad (Rep p), Representable p) => Monad (Prep p)

Defined in Data.Profunctor.Rep

Methods

(>>=) :: Prep p a -> (a -> Prep p b) -> Prep p b

(>>) :: Prep p a -> Prep p b -> Prep p b

return :: a -> Prep p a

Profunctor p => Functor (Prep p)

Defined in Data.Profunctor.Rep

Methods

fmap :: (a -> b) -> Prep p a -> Prep p b

(<$) :: a -> Prep p b -> Prep p a

(Applicative (Rep p), Representable p) => Applicative (Prep p)

Defined in Data.Profunctor.Rep

Methods

pure :: a -> Prep p a

(<*>) :: Prep p (a -> b) -> Prep p a -> Prep p b

liftA2 :: (a -> b -> c) -> Prep p a -> Prep p b -> Prep p c

(*>) :: Prep p a -> Prep p b -> Prep p b

(<*) :: Prep p a -> Prep p b -> Prep p a

prepAdj :: (forall a. Prep p a -> g a) -> p :-> Star g

unprepAdj :: (p :-> Star g) -> Prep p a -> g a

prepUnit :: p :-> Star (Prep p)

prepCounit :: Prep (Star f) a -> f a

Coprep -| Costar

newtype Coprep p a

Prep has a polymorphic kind since 5.6.

Constructors

Coprep

Fields

• runCoprep :: forall r. p a r -> r

Instances

Profunctor p => Functor (Coprep p)

Defined in Data.Profunctor.Rep

Methods

fmap :: (a -> b) -> Coprep p a -> Coprep p b

(<$) :: a -> Coprep p b -> Coprep p a

coprepAdj :: (forall a. f a -> Coprep p a) -> p :-> Costar f

Coprep -| Costar :: [Hask, Hask]^op -> Prof

Like all adjunctions this gives rise to a monad and a comonad.

This gives rise to a monad on Prof (Costar.Coprep) and a comonad on [Hask, Hask]^op given by (Coprep.Costar) which is a monad in [Hask,Hask]

uncoprepAdj :: (p :-> Costar f) -> f a -> Coprep p a

coprepUnit :: p :-> Costar (Coprep p)

coprepCounit :: f a -> Coprep (Costar f) a