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 :: Type -> Type -> Type) where
- type Rep (p :: Type -> Type -> Type) :: Type -> Type
- tabulate :: (d -> Rep p c) -> p d c
tabulated :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type) d c d' c'. (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 :: Type -> Type -> Type) where
- type Corep (p :: Type -> Type -> Type) :: Type -> Type
- cotabulate :: (Corep p d -> c) -> p d c
cotabulated :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type) d c d' c'. (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 :: Type -> k -> Type) (a :: k) where
- Prep :: forall {k} x (p :: Type -> k -> Type) (a :: k). x -> p x a -> Prep p a
prepAdj :: forall {k1} (p :: Type -> k1 -> Type) g. (forall (a :: k1). Prep p a -> g a) -> p :-> Star g
unprepAdj :: forall {k} (p :: Type -> k -> Type) g (a :: k). (p :-> Star g) -> Prep p a -> g a
prepUnit :: forall {k} p a (b :: k). p a b -> Star (Prep p) a b
prepCounit :: forall {k} f (a :: k). Prep (Star f) a -> f a
newtype Coprep (p :: k -> Type -> Type) (a :: k) = Coprep {
- runCoprep :: forall r. p a r -> r
}
coprepAdj :: forall {k} f (p :: k -> Type -> Type). (forall (a :: k). f a -> Coprep p a) -> p :-> Costar f
uncoprepAdj :: forall {k} (p :: k -> Type -> Type) f (a :: k). (p :-> Costar f) -> f a -> Coprep p a
coprepUnit :: forall {k} p (a :: k) b. p a b -> Costar (Coprep p) a b
coprepCounit :: forall {k} f (a :: k). f a -> Coprep (Costar f) a

Representable Profunctors

class (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 Rep (p :: Type -> Type -> Type) :: Type -> Type 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)
Instance details Defined in Data.Profunctor.Rep type Rep (Kleisli m) = m

Methods

tabulate :: (d -> Rep (Kleisli m) c) -> Kleisli m 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 -> Type)
Instance details Defined in Data.Profunctor.Rep type Rep (Forget r :: Type -> Type -> Type) = Const r :: Type -> Type

Methods

tabulate :: (d -> Rep (Forget r :: Type -> Type -> Type) 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)
Instance details Defined in Data.Profunctor.Rep type Rep (Star f) = f

Methods

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

Representable (->) Source #

Instance details

Defined in Data.Profunctor.Rep

Associated Types

type Rep (->)
Instance details Defined in Data.Profunctor.Rep type Rep (->) = Identity

Methods

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

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

The composition of two Representable Profunctors is Representable by the composition of their representations.

Instance details

Defined in Data.Profunctor.Composition

Associated Types

type Rep (Procompose p q)
Instance details Defined in Data.Profunctor.Composition type Rep (Procompose p q) = Compose (Rep q) (Rep p)

Methods

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

tabulated :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type) d c d' c'. (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 :: 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 Corep (p :: Type -> Type -> Type) :: Type -> Type 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 -> Type)
Instance details Defined in Data.Profunctor.Rep type Corep (Tagged :: Type -> Type -> Type) = Proxy :: Type -> Type

Methods

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

Functor w => Corepresentable (Cokleisli w) Source #

Instance details

Defined in Data.Profunctor.Rep

Associated Types

type Corep (Cokleisli w)
Instance details Defined in Data.Profunctor.Rep type Corep (Cokleisli w) = w

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)
Instance details Defined in Data.Profunctor.Rep type Corep (Costar f) = f

Methods

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

Corepresentable (->) Source #

Instance details

Defined in Data.Profunctor.Rep

Associated Types

type Corep (->)
Instance details Defined in Data.Profunctor.Rep type Corep (->) = Identity

Methods

cotabulate :: (Corep (->) d -> c) -> 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)
Instance details Defined in Data.Profunctor.Composition type Corep (Procompose p q) = Compose (Corep p) (Corep q)

Methods

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

cotabulated :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type) d c d' c'. (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 :: 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 :: forall {k} x (p :: Type -> k -> Type) (a :: k). x -> p x a -> Prep p a

Instances

Instances details

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

prepAdj :: forall {k1} (p :: Type -> k1 -> Type) g. (forall (a :: k1). Prep p a -> g a) -> p :-> Star g Source #

unprepAdj :: forall {k} (p :: Type -> k -> Type) g (a :: k). (p :-> Star g) -> Prep p a -> g a Source #

prepUnit :: forall {k} p a (b :: k). p a b -> Star (Prep p) a b Source #

prepCounit :: forall {k} f (a :: k). Prep (Star f) a -> f a Source #

Coprep -| Costar

newtype Coprep (p :: k -> Type -> Type) (a :: k) 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 # (<$) :: a -> Coprep p b -> Coprep p a #

coprepAdj :: forall {k} f (p :: k -> Type -> Type). (forall (a :: k). 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 :: forall {k} (p :: k -> Type -> Type) f (a :: k). (p :-> Costar f) -> f a -> Coprep p a Source #

coprepUnit :: forall {k} p (a :: k) b. p a b -> Costar (Coprep p) a b Source #

coprepCounit :: forall {k} f (a :: k). f a -> Coprep (Costar f) a Source #