Portability | portable |
---|---|
Stability | provisional |
Maintainer | Edward Kmett <ekmett@gmail.com> |
Safe Haskell | None |
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/
- class Profunctor p where
- class Profunctor p => Lenticular p where
- lenticular :: p a b -> p a (a, b)
- class Profunctor p => Prismatic p where
- newtype UpStar f d c = UpStar {
- runUpStar :: d -> f c
- newtype DownStar f d c = DownStar {
- runDownStar :: f d -> c
- newtype WrappedArrow p a b = WrapArrow {
- unwrapArrow :: p a b
Profunctors
class Profunctor p whereSource
Formally, 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 ilmap
(f.
g) ≡lmap
g.
lmap
frmap
(f.
g) ≡rmap
f.
rmap
g
Profunctor (->) | |
Monad m => Profunctor (Kleisli m) | |
Functor w => Profunctor (Cokleisli w) | |
Profunctor (Tagged *) | |
Arrow p => Profunctor (WrappedArrow p) | |
Functor f => Profunctor (DownStar f) | |
Functor f => Profunctor (UpStar f) |
Profunctorial Strength
class Profunctor p => Lenticular p whereSource
lenticular :: p a b -> p a (a, b)Source
Lenticular (->) | |
(Profunctor (Kleisli m), Monad m) => Lenticular (Kleisli m) | |
(Profunctor (WrappedArrow p), Arrow p) => Lenticular (WrappedArrow p) | |
(Profunctor (UpStar m), Functor m) => Lenticular (UpStar m) |
class Profunctor p => Prismatic p whereSource
The generalization of DownStar
of a "Costrong" Functor
Note: Here we use Traversable
as an approximate costrength.
Prismatic (->) | |
(Profunctor (Kleisli m), Monad m) => Prismatic (Kleisli m) | |
(Profunctor (Cokleisli w), Traversable w) => Prismatic (Cokleisli w) |
|
Prismatic (Tagged *) | |
(Profunctor (WrappedArrow p), ArrowChoice p) => Prismatic (WrappedArrow p) | |
(Profunctor (DownStar w), Traversable w) => Prismatic (DownStar w) |
|
Common Profunctors
Lift a Functor
into a Profunctor
(forwards)
(Profunctor (UpStar m), Functor m) => Lenticular (UpStar m) | |
Functor f => Profunctor (UpStar f) | |
Functor f => Functor (UpStar f a) |
Lift a Functor
into a Profunctor
(backwards)
DownStar | |
|
(Profunctor (DownStar w), Traversable w) => Prismatic (DownStar w) |
|
Functor f => Profunctor (DownStar f) | |
Functor (DownStar f a) |
newtype WrappedArrow p a b Source
Wrap an arrow for use as a Profunctor
WrapArrow | |
|
(Category (WrappedArrow p), Arrow p) => Arrow (WrappedArrow p) | |
(Arrow (WrappedArrow p), ArrowZero p) => ArrowZero (WrappedArrow p) | |
(Arrow (WrappedArrow p), ArrowChoice p) => ArrowChoice (WrappedArrow p) | |
(Arrow (WrappedArrow p), ArrowApply p) => ArrowApply (WrappedArrow p) | |
(Arrow (WrappedArrow p), ArrowLoop p) => ArrowLoop (WrappedArrow p) | |
Category p => Category (WrappedArrow p) | |
(Profunctor (WrappedArrow p), ArrowChoice p) => Prismatic (WrappedArrow p) | |
(Profunctor (WrappedArrow p), Arrow p) => Lenticular (WrappedArrow p) | |
Arrow p => Profunctor (WrappedArrow p) |