Moduleprofunctors-5.6.3Haskell2010

Data.Profunctor.Rep

2 types
2 classes
15 values

Packageprofunctors-5.6.3
Exports19
LanguageHaskell2010
LicenceBSD-3-Clause
SourceRep.hs

Representable Profunctors

4 declarations

classclass (Sieve p (Rep p), Strong p) => Representable (p :: Type -> Type -> Type) 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 family Rep (p :: Type -> Type -> Type) :: Type -> Type

Methods

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

Laws:

tabulate . sieve ≡ id
sieve . tabulate ≡ id

Instances5Representable

(Monad m, Functor m) => Representable (Kleisli m)Defined in profunctors-5.6.3 · Data.Profunctor.Rep
Functor f => Representable (Star f)Defined in profunctors-5.6.3 · Data.Profunctor.Rep
Representable (->)Defined in profunctors-5.6.3 · Data.Profunctor.Rep
Representable (Forget r)Defined in profunctors-5.6.3 · Data.Profunctor.Rep
(Representable p, Representable q) => Representable (Procompose p q)Defined in profunctors-5.6.3 · Data.Profunctor.Composition
The composition of two Representable Profunctors is Representable by the composition of their representations.

valuetabulated :: (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)

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

Default definition for first' given that p is Representable.

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

Default definition for second' given that p is Representable.

Corepresentable Profunctors

5 declarations

classclass (Cosieve p (Corep p), Costrong p) => Corepresentable (p :: Type -> Type -> Type) 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 family Corep (p :: Type -> Type -> Type) :: Type -> Type

Methods

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

Laws:

cotabulate . cosieve ≡ id
cosieve . cotabulate ≡ id

Instances5Corepresentable

Corepresentable TaggedDefined in profunctors-5.6.3 · Data.Profunctor.Rep
Functor f => Corepresentable (Costar f)Defined in profunctors-5.6.3 · Data.Profunctor.Rep
Functor w => Corepresentable (Cokleisli w)Defined in profunctors-5.6.3 · Data.Profunctor.Rep
Corepresentable (->)Defined in profunctors-5.6.3 · Data.Profunctor.Rep
(Corepresentable p, Corepresentable q) => Corepresentable (Procompose p q)Defined in profunctors-5.6.3 · Data.Profunctor.Composition

valuecotabulated :: (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)

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

Default definition for unfirst given that p is Corepresentable.

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

Default definition for unsecond given that p is Corepresentable.

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

Default definition for closed given that p is Corepresentable

Prep -| Star

5 declarations

datadata Prep (p :: Type -> k -> Type) (a :: k) 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

Instances3Monad, Functor, Applicative

(Monad (Rep p), Representable p) => Monad (Prep p)Defined in profunctors-5.6.3 · Data.Profunctor.Rep
Profunctor p => Functor (Prep p)Defined in profunctors-5.6.3 · Data.Profunctor.Rep
(Applicative (Rep p), Representable p) => Applicative (Prep p)Defined in profunctors-5.6.3 · Data.Profunctor.Rep

valueprepAdj :: (forall (a :: k1). Prep p a -> g a) -> p :-> Star g

valueunprepAdj :: p :-> Star g -> Prep p a -> g a

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

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

Coprep -| Costar

5 declarations

newtypenewtype Coprep (p :: k -> Type -> Type) (a :: k)

Prep has a polymorphic kind since 5.6.

Constructors

Coprep
- runCoprep :: forall r. p a r -> r

Instances1Functor

Profunctor p => Functor (Coprep p)Defined in profunctors-5.6.3 · Data.Profunctor.Rep

valuecoprepAdj :: (forall (a :: k). 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]

valueuncoprepAdj :: p :-> Costar f -> f a -> Coprep p a

valuecoprepUnit :: p a b -> Costar (Coprep p) a b

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