profunctors-3.2: Haskell 98 Profunctors

Portabilityportable
Stabilityprovisional
MaintainerEdward Kmett <ekmett@gmail.com>
Safe HaskellTrustworthy

Data.Profunctor

Contents

Description

For a good explanation of profunctors in Haskell see Dan Piponi's article:

http://blog.sigfpe.com/2011/07/profunctors-in-haskell.html

For more information on strength and costrength, see:

http://comonad.com/reader/2008/deriving-strength-from-laziness/

Synopsis

Profunctors

class Profunctor p whereSource

Formally, the class Profunctor represents a profunctor from Hask -> Hask.

Intuitively it is a bifunctor where the first argument is contravariant and the second argument is covariant.

You can define a Profunctor by either defining dimap or by defining both lmap and rmap.

If you supply dimap, you should ensure that: 

dimap id id ≡ id

If you supply lmap and rmap, ensure: 

 lmap id ≡ id
 rmap id ≡ id

If you supply both, you should also ensure: 

dimap f g ≡ lmap f . rmap g

These ensure by parametricity: 

 dimap (f . g) (h . i) ≡ dimap g h . dimap f i
 lmap (f . g) ≡ lmap g . lmap f
 rmap (f . g) ≡ rmap f . rmap g

Methods

dimap :: (a -> b) -> (c -> d) -> p b c -> p a dSource

Map over both arguments at the same time. 

dimap f g ≡ lmap f . rmap g

lmap :: (a -> b) -> p b c -> p a cSource

Map the first argument contravariantly. 

lmap f ≡ dimap f id

rmap :: (b -> c) -> p a b -> p a cSource

Map the second argument covariantly. 

rmap ≡ dimap id

Instances

Profunctorial Strength

class Profunctor p => Strong p whereSource

Generalizing upstar of a strong Functor

Minimal complete definition: first' or second'

Note: Every Functor in Haskell is strong.

Methods

first' :: p a b -> p (a, c) (b, c)Source

second' :: p a b -> p (c, a) (c, b)Source

Instances

class Profunctor p => Choice p whereSource

The generalization of DownStar of a "costrong" Functor

Minimal complete definition: left' or right'

Note: We use traverse and extract as approximate costrength as needed.

Methods

left' :: p a b -> p (Either a c) (Either b c)Source

right' :: p a b -> p (Either c a) (Either c b)Source

Instances

Choice (->) 
(Profunctor (Kleisli m), Monad m) => Choice (Kleisli m) 
(Profunctor (Cokleisli w), Comonad w) => Choice (Cokleisli w)

extract approximates costrength

Choice (Tagged *) 
(Profunctor (WrappedArrow p), ArrowChoice p) => Choice (WrappedArrow p) 
(Profunctor (DownStar w), Traversable w) => Choice (DownStar w)

sequence approximates costrength

Common Profunctors

newtype UpStar f d c Source

Lift a Functor into a Profunctor (forwards).

Constructors

UpStar 

Fields

runUpStar :: d -> f c
 

Instances

newtype DownStar f d c Source

Lift a Functor into a Profunctor (backwards).

Constructors

DownStar 

Fields

runDownStar :: f d -> c
 

Instances

Functor f => Profunctor (DownStar f) 
(Profunctor (DownStar w), Traversable w) => Choice (DownStar w)

sequence approximates costrength

Functor (DownStar f a) 

newtype WrappedArrow p a b Source

Wrap an arrow for use as a Profunctor.

Constructors

WrapArrow 

Fields

unwrapArrow :: p a b
 

Instances