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 #

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

Instances details

(Monad m, Functor m) => Representable (Kleisli m) #
Instance details 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) #
Instance details Defined in Data.Profunctor.Rep Associated Types type Rep (->) :: Type -> Type # Methods tabulate :: (d -> Rep (->) c) -> d -> c #
Representable (Forget r :: Type -> Type -> Type) #
Instance details 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) #
Instance details 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` `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 # 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

Instances details

Corepresentable (Tagged :: Type -> Type -> Type) #
Instance details 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) #
Instance details Defined in Data.Profunctor.Rep Associated Types type Corep (->) :: Type -> Type # Methods cotabulate :: (Corep (->) d -> c) -> d -> c #
Functor w => Corepresentable (Cokleisli w) #
Instance details 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) #
Instance details 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) #
Instance details 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

Instances details

(Monad (Rep p), Representable p) => Monad (Prep p) #
Instance details 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) #
Instance details 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) #
Instance details 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

Instances details

Profunctor p => Functor (Coprep p) #
Instance details 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 #