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
Description
Synopsis
- class ( Sieve p ( Rep p), Strong p) => Representable p where
- 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 :: * -> *
- cotabulate :: ( Corep p d -> c) -> p d c
- 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
- 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
.
Methods
Instances
( Monad m, Functor m) => Representable ( Kleisli m) Source # | |
Representable ((->) :: Type -> Type -> Type ) Source # | |
Representable ( Forget r :: Type -> Type -> Type ) Source # | |
Functor f => Representable ( Star f) Source # | |
( Representable p, Representable q) => Representable ( Procompose p q) Source # |
The composition of two
|
Defined in Data.Profunctor.Composition 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
.
Methods
cotabulate :: ( Corep p d -> c) -> p d c Source #
Laws:
cotabulate
.
cosieve
≡id
cosieve
.
cotabulate
≡id
Instances
Corepresentable ( Tagged :: Type -> Type -> Type ) Source # | |
Corepresentable ((->) :: Type -> Type -> Type ) Source # | |
Defined in Data.Profunctor.Rep Methods cotabulate :: ( Corep (->) d -> c) -> d -> c Source # |
|
Functor w => Corepresentable ( Cokleisli w) Source # | |
Functor f => Corepresentable ( Costar f) Source # | |
( Corepresentable p, Corepresentable q) => Corepresentable ( Procompose p q) Source # | |
Defined in Data.Profunctor.Composition 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
Prep
-|Star
:: [Hask, Hask] -> Prof
This gives rise to a monad in
Prof
,
(
, and
a comonad in
Star
.
Prep
)
[Hask,Hask]
(
Prep
.
Star
)
Prep
has a polymorphic kind since
5.6
.
Instances
( Monad ( Rep p), Representable p) => Monad ( Prep p) Source # | |
Profunctor p => Functor ( Prep p) Source # | |
( Applicative ( Rep p), Representable p) => Applicative ( Prep p) Source # | |
prepCounit :: Prep ( Star f) a -> f a Source #
Coprep -| Costar
Prep
has a polymorphic kind since
5.6
.
coprepCounit :: f a -> Coprep ( Costar f) a Source #