Moduleprofunctors-5.6.3Haskell2010

Data.Profunctor.Rep

Contents

Representable Profunctors
Corepresentable Profunctors
Prep -| Star
Coprep -| Costar

Synopsis

class Representable
value tabulated
value firstRep
value secondRep
class Corepresentable
value cotabulated
value unfirstCorep
value unsecondCorep
value closedCorep
data Prep
value prepAdj
value unprepAdj
value prepUnit
value prepCounit
newtype Coprep
value coprepAdj
value uncoprepAdj
value coprepUnit
value coprepCounit

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

Representable Profunctors

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

Source#

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')

Source#

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)

Source#

Default definition for first' given that p is Representable.

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

Source#

Default definition for second' given that p is Representable.

Corepresentable Profunctors

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

Source#

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')

Source#

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

Source#

Default definition for unfirst given that p is Corepresentable.

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

Source#

Default definition for unsecond given that p is Corepresentable.

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

Source#

Default definition for closed given that p is Corepresentable

Prep -| Star

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

Source#

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 :: k2). 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

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

Source#

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 :: k1). f a -> Coprep p a) -> p :-> Costar f

Source#

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