Portability | GADTs |
---|---|
Stability | provisional |
Maintainer | Edward Kmett <ekmett@gmail.com> |
Safe Haskell | Trustworthy |
- data Procompose p q d c where
- Procompose :: p d a -> q a c -> Procompose p q d c
- idl :: (Profunctor p, Profunctor q, Functor f) => p (q d c) (f (r d' c')) -> p (Procompose (->) q d c) (f (Procompose (->) r d' c'))
- idr :: (Profunctor p, Profunctor q, Functor f) => p (q d c) (f (r d' c')) -> p (Procompose q (->) d c) (f (Procompose r (->) d' c'))
- upstars :: (Profunctor p, Functor f, Functor h) => p (UpStar (Compose f g) d c) (h (UpStar (Compose f' g') d' c')) -> p (Procompose (UpStar f) (UpStar g) d c) (h (Procompose (UpStar f') (UpStar g') d' c'))
- kleislis :: (Profunctor p, Monad f, Functor h) => p (Kleisli (Compose f g) d c) (h (Kleisli (Compose f' g') d' c')) -> p (Procompose (Kleisli f) (Kleisli g) d c) (h (Procompose (Kleisli f') (Kleisli g') d' c'))
- downstars :: (Profunctor p, Functor g, Functor h) => p (DownStar (Compose g f) d c) (h (DownStar (Compose g' f') d' c')) -> p (Procompose (DownStar f) (DownStar g) d c) (h (Procompose (DownStar f') (DownStar g') d' c'))
- cokleislis :: (Profunctor p, Functor g, Functor h) => p (Cokleisli (Compose g f) d c) (h (Cokleisli (Compose g' f') d' c')) -> p (Procompose (Cokleisli f) (Cokleisli g) d c) (h (Procompose (Cokleisli f') (Cokleisli g') d' c'))
Profunctor Composition
data Procompose p q d c whereSource
is the Procompose
p qProfunctor
composition of the profunctors p
and q
.
For a good explanation of profunctor composition in Haskell see Dan Piponi's article:
Procompose :: p d a -> q a c -> Procompose p q d c |
(Profunctor p, Profunctor q) => Profunctor (Procompose p q) | |
(Functor (Corep (Procompose p q)), Profunctor (Procompose p q), Corepresentable p, Corepresentable q) => Corepresentable (Procompose p q) | |
(Functor (Rep (Procompose p q)), Profunctor (Procompose p q), Representable p, Representable q) => Representable (Procompose p q) | The composition of two representable profunctors is representable by the composition of their representations. |
Profunctor q => Functor (Procompose p q a) |
Lax identity
idl :: (Profunctor p, Profunctor q, Functor f) => p (q d c) (f (r d' c')) -> p (Procompose (->) q d c) (f (Procompose (->) r d' c'))Source
(->)
functions as a lax identity for profunctor composition.
This provides an Iso
for the lens
package that witnesses the
isomorphism between
and Procompose
(->) q d cq d c
, which
is the left identity law.
idl
::Profunctor
q => Iso' (Procompose
(->) q d c) (q d c)
idr :: (Profunctor p, Profunctor q, Functor f) => p (q d c) (f (r d' c')) -> p (Procompose q (->) d c) (f (Procompose r (->) d' c'))Source
(->)
functions as a lax identity for profunctor composition.
This provides an Iso
for the lens
package that witnesses the
isomorphism between
and Procompose
q (->) d cq d c
, which
is the right identity law.
idr
::Profunctor
q => Iso' (Procompose
q (->) d c) (q d c)
Generalized Composition
upstars :: (Profunctor p, Functor f, Functor h) => p (UpStar (Compose f g) d c) (h (UpStar (Compose f' g') d' c')) -> p (Procompose (UpStar f) (UpStar g) d c) (h (Procompose (UpStar f') (UpStar g') d' c'))Source
kleislis :: (Profunctor p, Monad f, Functor h) => p (Kleisli (Compose f g) d c) (h (Kleisli (Compose f' g') d' c')) -> p (Procompose (Kleisli f) (Kleisli g) d c) (h (Procompose (Kleisli f') (Kleisli g') d' c'))Source
downstars :: (Profunctor p, Functor g, Functor h) => p (DownStar (Compose g f) d c) (h (DownStar (Compose g' f') d' c')) -> p (Procompose (DownStar f) (DownStar g) d c) (h (Procompose (DownStar f') (DownStar g') d' c'))Source
cokleislis :: (Profunctor p, Functor g, Functor h) => p (Cokleisli (Compose g f) d c) (h (Cokleisli (Compose g' f') d' c')) -> p (Procompose (Cokleisli f) (Cokleisli g) d c) (h (Procompose (Cokleisli f') (Cokleisli g') d' c'))Source
This is a variant on downstars
that uses Cokleisli
instead of DownStar
.
cokleislis
::Functor
f => Iso' (Procompose
(Cokleisli
f) (Cokleisli
g) d c) (Cokleisli
(Compose
g f) d c)