Copyright	(C) 2011-2015 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	Type-Families
Safe Haskell	Safe
Language	Haskell2010

Data.Profunctor.Rep

Contents

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

Description

Synopsis

class ( Sieve p ( Rep p), Strong p) => Representable p where
- type Rep p :: * -> *
- tabulate :: (d -> Rep p c) -> p d c
tabulated :: ( Representable p, Representable q) => Iso (d -> Rep p c) (d' -> Rep q c') (p d c) (q d' c')
firstRep :: Representable p => p a b -> p (a, c) (b, c)
secondRep :: Representable p => p a b -> p (c, a) (c, b)
class ( Cosieve p ( Corep p), Costrong p) => Corepresentable p where
- type Corep p :: * -> *
- cotabulate :: ( Corep p d -> c) -> p d c
cotabulated :: ( Corepresentable p, Corepresentable q) => Iso ( Corep p d -> c) ( Corep q d' -> c') (p d c) (q d' c')
unfirstCorep :: Corepresentable p => p (a, d) (b, d) -> p a b
unsecondCorep :: Corepresentable p => p (d, a) (d, b) -> p a b
closedCorep :: Corepresentable p => p a b -> p (x -> a) (x -> b)
data Prep p a where
- Prep :: x -> p x a -> 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
newtype Coprep p a = Coprep {
- runCoprep :: forall r. p a r -> r
}
coprepAdj :: ( forall a. f a -> Coprep p a) -> p :-> Costar f
uncoprepAdj :: (p :-> Costar f) -> f a -> Coprep p a
coprepUnit :: p :-> Costar ( Coprep p)
coprepCounit :: f a -> Coprep ( Costar f) a

Representable Profunctors

class ( Sieve p ( Rep p), Strong p) => Representable p 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 Rep p :: * -> * Source #

Methods

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

Laws:

tabulate . sieve ≡ id
sieve . tabulate ≡ id

Instances

Instances details

( Monad m, Functor m) => Representable ( Kleisli m) Source #
Instance details Defined in Data.Profunctor.Rep Associated Types type Rep ( Kleisli m) :: Type -> Type Source # Methods tabulate :: (d -> Rep ( Kleisli m) c) -> Kleisli m d c Source #
Representable ((->) :: Type -> Type -> Type ) Source #
Instance details Defined in Data.Profunctor.Rep Associated Types type Rep (->) :: Type -> Type Source # Methods tabulate :: (d -> Rep (->) c) -> d -> c Source #
Representable ( Forget r :: Type -> Type -> Type ) Source #
Instance details Defined in Data.Profunctor.Rep Associated Types type Rep ( Forget r) :: Type -> Type Source # Methods tabulate :: (d -> Rep ( Forget r) c) -> Forget r d c Source #
Functor f => Representable ( Star f) Source #
Instance details Defined in Data.Profunctor.Rep Associated Types type Rep ( Star f) :: Type -> Type Source # Methods tabulate :: (d -> Rep ( Star f) c) -> Star f d c Source #
( Representable p, Representable q) => Representable ( Procompose p q) Source #	The composition of two `Representable` `Profunctor` s is `Representable` by the composition of their representations.
Instance details Defined in Data.Profunctor.Composition Associated Types type Rep ( Procompose p q) :: Type -> Type Source # Methods tabulate :: (d -> Rep ( Procompose p q) c) -> Procompose p q d c Source #

tabulated :: ( 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)

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

Default definition for first' given that p is Representable .

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

Default definition for second' given that p is Representable .

Corepresentable Profunctors

class ( Cosieve p ( Corep p), Costrong p) => Corepresentable p 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 Corep p :: * -> * Source #

Methods

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

Laws:

cotabulate . cosieve ≡ id
cosieve . cotabulate ≡ id

Instances

Instances details

Corepresentable ( Tagged :: Type -> Type -> Type ) Source #
Instance details Defined in Data.Profunctor.Rep Associated Types type Corep Tagged :: Type -> Type Source # Methods cotabulate :: ( Corep Tagged d -> c) -> Tagged d c Source #
Corepresentable ((->) :: Type -> Type -> Type ) Source #
Instance details Defined in Data.Profunctor.Rep Associated Types type Corep (->) :: Type -> Type Source # Methods cotabulate :: ( Corep (->) d -> c) -> d -> c Source #
Functor w => Corepresentable ( Cokleisli w) Source #
Instance details Defined in Data.Profunctor.Rep Associated Types type Corep ( Cokleisli w) :: Type -> Type Source # Methods cotabulate :: ( Corep ( Cokleisli w) d -> c) -> Cokleisli w d c Source #
Functor f => Corepresentable ( Costar f) Source #
Instance details Defined in Data.Profunctor.Rep Associated Types type Corep ( Costar f) :: Type -> Type Source # Methods cotabulate :: ( Corep ( Costar f) d -> c) -> Costar f d c Source #
( Corepresentable p, Corepresentable q) => Corepresentable ( Procompose p q) Source #
Instance details Defined in Data.Profunctor.Composition Associated Types type Corep ( Procompose p q) :: Type -> Type Source # Methods cotabulate :: ( Corep ( Procompose p q) d -> c) -> Procompose p q d c Source #

cotabulated :: ( 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)

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

Default definition for unfirst given that p is Corepresentable .

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

Default definition for unsecond given that p is Corepresentable .

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

Default definition for closed given that p is Corepresentable

Prep -| Star

data Prep p a 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

Instances

Instances details

( Monad ( Rep p), Representable p) => Monad ( Prep p) Source #
Instance details Defined in Data.Profunctor.Rep Methods (>>=) :: Prep p a -> (a -> Prep p b) -> Prep p b Source # (>>) :: Prep p a -> Prep p b -> Prep p b Source # return :: a -> Prep p a Source #
Profunctor p => Functor ( Prep p) Source #
Instance details Defined in Data.Profunctor.Rep Methods fmap :: (a -> b) -> Prep p a -> Prep p b Source # (<$) :: a -> Prep p b -> Prep p a Source #
( Applicative ( Rep p), Representable p) => Applicative ( Prep p) Source #
Instance details Defined in Data.Profunctor.Rep Methods pure :: a -> Prep p a Source # (<>) :: Prep p (a -> b) -> Prep p a -> Prep p b Source # liftA2 :: (a -> b -> c) -> Prep p a -> Prep p b -> Prep p c Source # (>) :: Prep p a -> Prep p b -> Prep p b Source # (<*) :: Prep p a -> Prep p b -> Prep p a Source #

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

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

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

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

Coprep -| Costar

newtype Coprep p a Source #

Prep has a polymorphic kind since 5.6 .

Constructors

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

Instances

Instances details

Profunctor p => Functor ( Coprep p) Source #
Instance details Defined in Data.Profunctor.Rep Methods fmap :: (a -> b) -> Coprep p a -> Coprep p b Source # (<$) :: a -> Coprep p b -> Coprep p a Source #

coprepAdj :: ( forall a. 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]

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

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

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