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 :: * -> *
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 :: * -> *
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.

Minimal complete definition

tabulate

Associated Types

type Rep p :: * -> * Source #

Methods

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

Laws:

tabulate  .  sieve  ≡ id 
sieve  .  tabulate  ≡ id

Instances

Representable (->) Source #

Associated Types

type Rep ((->) :: * -> * -> *) :: * -> * Source #

Methods

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

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

Associated Types

type Rep (Kleisli m :: * -> * -> *) :: * -> * Source #

Methods

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

Representable (Forget r) Source #

Associated Types

type Rep (Forget r :: * -> * -> *) :: * -> * Source #

Methods

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

Functor f => Representable (Star f) Source #

Associated Types

type Rep (Star f :: * -> * -> *) :: * -> * 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.

Associated Types

type Rep (Procompose p q :: * -> * -> *) :: * -> * 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.

Minimal complete definition

cotabulate

Associated Types

type Corep p :: * -> * Source #

Methods

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

Laws:

cotabulate  .  cosieve  ≡ id 
cosieve  .  cotabulate  ≡ id

Instances

Corepresentable (->) Source #

Associated Types

type Corep ((->) :: * -> * -> *) :: * -> * Source #

Methods

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

Functor w => Corepresentable (Cokleisli w) Source #

Associated Types

type Corep (Cokleisli w :: * -> * -> *) :: * -> * Source #

Methods

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

Corepresentable (Tagged *) Source #

Associated Types

type Corep (Tagged * :: * -> * -> *) :: * -> * Source #

Methods

cotabulate :: (Corep (Tagged *) d -> c) -> Tagged * d c Source #

Functor f => Corepresentable (Costar f) Source #

Associated Types

type Corep (Costar f :: * -> * -> *) :: * -> * Source #

Methods

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

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

Associated Types

type Corep (Procompose p q :: * -> * -> *) :: * -> * 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')

Constructors

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

Instances

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

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 #

fail :: String -> Prep p a #

Profunctor p => Functor (Prep p) Source #

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) Source #

Methods

pure :: a -> Prep p a #

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

(*>) :: 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 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 #

Constructors

Coprep

Fields

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

Instances

Profunctor p => Functor (Coprep p) Source #

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 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 #