Safe Haskell | Safe |
---|---|
Language | Haskell2010 |
Synopsis
- type Optic p s t a b = p a b -> p s t
- type Optic' p s a = Optic p s s a a
- between :: (c -> d) -> (a -> b) -> (b -> c) -> a -> d
- type IndexedOptic p i s t a b = p (i, a) b -> p (i, s) t
- type IndexedOptic' p i s a = IndexedOptic p i s s a a
- type CoindexedOptic p k s t a b = p a (k -> b) -> p s (k -> t)
- type CoindexedOptic' p k t b = CoindexedOptic p k t t b b
- type Equality s t a b = forall p. Optic p s t a b
- type Equality' s a = Equality s s a a
- type As a = Equality' a a
- type Iso s t a b = forall p. Profunctor p => Optic p s t a b
- type Iso' s a = Iso s s a a
- type Lens s t a b = forall p. Strong p => Optic p s t a b
- type Lens' s a = Lens s s a a
- type Ixlens i s t a b = forall p. Strong p => IndexedOptic p i s t a b
- type Ixlens' i s a = Ixlens i s s a a
- type Colens s t a b = forall p. Costrong p => Optic p s t a b
- type Colens' s a = Colens s s a a
- type Cxlens k s t a b = forall p. Costrong p => CoindexedOptic p k s t a b
- type Cxlens' k s a = Cxlens k s s a a
- type Prism s t a b = forall p. Choice p => Optic p s t a b
- type Prism' s a = Prism s s a a
- type Cxprism k s t a b = forall p. Choice p => CoindexedOptic p k s t a b
- type Cxprism' k s a = Cxprism k s s a a
- type Coprism s t a b = forall p. Cochoice p => Optic p s t a b
- type Coprism' t b = Coprism t t b b
- type Ixprism i s t a b = forall p. Cochoice p => IndexedOptic p i s t a b
- type Ixprism' i s a = Coprism s s a a
- type Grate s t a b = forall p. Closed p => Optic p s t a b
- type Grate' s a = Grate s s a a
- type Cxgrate k s t a b = forall p. Closed p => CoindexedOptic p k s t a b
- type Cxgrate' k s a = Cxgrate k s s a a
- type Traversal s t a b = forall p. (Choice p, Representable p, Applicative (Rep p)) => Optic p s t a b
- type Traversal' s a = Traversal s s a a
- type Ixtraversal i s t a b = forall p. (Choice p, Representable p, Applicative (Rep p)) => IndexedOptic p i s t a b
- type Ixtraversal' i s a = Ixtraversal i s s a a
- type Traversal0 s t a b = forall p. (Strong p, Choice p) => Optic p s t a b
- type Traversal0' s a = Traversal0 s s a a
- type Ixtraversal0 i s t a b = forall p. (Strong p, Choice p) => IndexedOptic p i s t a b
- type Ixtraversal0' i s a = Ixtraversal0 i s s a a
- type Traversal1 s t a b = forall p. (Choice p, Representable p, Apply (Rep p)) => Optic p s t a b
- type Traversal1' s a = Traversal1 s s a a
- type Cotraversal1 s t a b = forall p. (Closed p, Corepresentable p, Apply (Corep p)) => Optic p s t a b
- type Cotraversal1' s a = Cotraversal1 s s a a
- type Cxtraversal1 k s t a b = forall p. (Closed p, Corepresentable p, Apply (Corep p)) => CoindexedOptic p k s t a b
- type Cxtraversal1' k s a = Cxtraversal1 k s s a a
- type Fold0 s a = forall p. (Choice p, Representable p, Applicative (Rep p), forall x. Contravariant (p x)) => Optic' p s a
- type Ixfold0 i s a = forall p. (Choice p, Strong p, forall x. Contravariant (p x)) => IndexedOptic' p i s a
- type Fold s a = forall p. (Choice p, Representable p, Applicative (Rep p), forall x. Contravariant (p x)) => Optic' p s a
- type Ixfold i s a = forall p. (Choice p, Representable p, Applicative (Rep p), forall x. Contravariant (p x)) => IndexedOptic' p i s a
- type Fold1 s a = forall p. (Choice p, Representable p, Apply (Rep p), forall x. Contravariant (p x)) => Optic p s s a a
- type Cofold1 t b = forall p. (Cochoice p, Corepresentable p, Apply (Corep p), Bifunctor p) => Optic p t t b b
- type PrimView s t a b = forall p. (Profunctor p, forall x. Contravariant (p x)) => Optic p s t a b
- type View s a = forall p. (Strong p, forall x. Contravariant (p x)) => Optic' p s a
- type Ixview i s a = forall p. (Strong p, forall x. Contravariant (p x)) => IndexedOptic' p i s a
- type PrimReview s t a b = forall p. (Profunctor p, Bifunctor p) => Optic p s t a b
- type Review t b = forall p. (Costrong p, Bifunctor p) => Optic' p t b
- type Cxview k t b = forall p. (Costrong p, Bifunctor p) => CoindexedOptic' p k t b
- type Setter s t a b = forall p. (Closed p, Choice p, Representable p, Applicative (Rep p), Distributive (Rep p)) => Optic p s t a b
- type Setter' s a = Setter s s a a
- type Ixsetter i s t a b = forall p. (Closed p, Choice p, Representable p, Applicative (Rep p), Distributive (Rep p)) => IndexedOptic p i s t a b
- type Resetter s t a b = forall p. (Closed p, Cochoice p, Corepresentable p, Apply (Corep p), Traversable (Corep p)) => Optic p s t a b
- type Resetter' s a = Resetter s s a a
- type Cxsetter k s t a b = forall p. (Closed p, Cochoice p, Corepresentable p, Apply (Corep p), Traversable (Corep p)) => CoindexedOptic p k s t a b
- type ARepn f s t a b = Optic (Star f) s t a b
- type ARepn' f s a = ARepn f s s a a
- type AIxrepn f i s t a b = IndexedOptic (Star f) i s t a b
- type AIxrepn' f i s a = AIxrepn f i s s a a
- type ACorepn f s t a b = Optic (Costar f) s t a b
- type ACorepn' f t b = ACorepn f t t b b
- type ACxrepn f k s t a b = CoindexedOptic (Costar f) k s t a b
- type ACxrepn' f k t b = ACxrepn f k t t b b
- newtype Re p s t a b = Re {
- runRe :: p b a -> p t s
- re :: Optic (Re p a b) s t a b -> Optic p b a t s
- class (Sieve p (Rep p), Strong p) => Representable (p :: Type -> Type -> Type) where
- class (Cosieve p (Corep p), Costrong p) => Corepresentable (p :: Type -> Type -> Type) where
- class (Profunctor p, Functor f) => Sieve (p :: Type -> Type -> Type) (f :: Type -> Type) | p -> f where
- sieve :: p a b -> a -> f b
- class (Profunctor p, Functor f) => Cosieve (p :: Type -> Type -> Type) (f :: Type -> Type) | p -> f where
- cosieve :: p a b -> f a -> b
- class Profunctor p => Choice (p :: Type -> Type -> Type) where
- class Profunctor p => Cochoice (p :: Type -> Type -> Type) where
- class Profunctor p => Closed (p :: Type -> Type -> Type) where
- closed :: p a b -> p (x -> a) (x -> b)
- class Profunctor p => Strong (p :: Type -> Type -> Type) where
- class Profunctor p => Costrong (p :: Type -> Type -> Type) where
- type (:->) (p :: Type -> Type -> Type) (q :: Type -> Type -> Type) = forall a b. p a b -> q a b
- newtype Star (f :: Type -> Type) d c = Star {
- runStar :: d -> f c
- newtype Costar (f :: Type -> Type) d c = Costar {
- runCostar :: f d -> c
- newtype WrappedArrow (p :: Type -> Type -> Type) a b = WrapArrow {
- unwrapArrow :: p a b
- newtype Forget r a b = Forget {
- runForget :: a -> r
- class Profunctor (p :: Type -> Type -> Type) where
Optics
between :: (c -> d) -> (a -> b) -> (b -> c) -> a -> d Source #
Can be used to rewrite
\g -> f . g . h
to
between f h
type IndexedOptic p i s t a b = p (i, a) b -> p (i, s) t Source #
type IndexedOptic' p i s a = IndexedOptic p i s s a a Source #
type CoindexedOptic p k s t a b = p a (k -> b) -> p s (k -> t) Source #
type CoindexedOptic' p k t b = CoindexedOptic p k t t b b Source #
Equality
Isos
type Iso s t a b = forall p. Profunctor p => Optic p s t a b Source #
Lenses & Colenses
type Lens s t a b = forall p. Strong p => Optic p s t a b Source #
Lenses access one piece of a product.
\( \mathsf{Lens}\;S\;A = \exists C, S \cong C \times A \)
type Ixlens i s t a b = forall p. Strong p => IndexedOptic p i s t a b Source #
type Cxlens k s t a b = forall p. Costrong p => CoindexedOptic p k s t a b Source #
Prisms & Coprisms
type Prism s t a b = forall p. Choice p => Optic p s t a b Source #
Prisms access one piece of a sum.
\( \mathsf{Prism}\;S\;A = \exists D, S \cong D + A \)
type Cxprism k s t a b = forall p. Choice p => CoindexedOptic p k s t a b Source #
type Ixprism i s t a b = forall p. Cochoice p => IndexedOptic p i s t a b Source #
Grates
type Grate s t a b = forall p. Closed p => Optic p s t a b Source #
Grates access the codomain of a function.
\( \mathsf{Grate}\;S\;A = \exists I, S \cong I \to A \)
type Cxgrate k s t a b = forall p. Closed p => CoindexedOptic p k s t a b Source #
Traversals
type Traversal s t a b = forall p. (Choice p, Representable p, Applicative (Rep p)) => Optic p s t a b Source #
A Traversal
processes 0 or more parts of the whole, with Applicative
interactions.
\( \mathsf{Traversal}\;S\;A = \exists F : \mathsf{Traversable}, S \equiv F\,A \)
type Traversal' s a = Traversal s s a a Source #
type Ixtraversal i s t a b = forall p. (Choice p, Representable p, Applicative (Rep p)) => IndexedOptic p i s t a b Source #
type Ixtraversal' i s a = Ixtraversal i s s a a Source #
Affine traversals & cotraversals
type Traversal0 s t a b = forall p. (Strong p, Choice p) => Optic p s t a b Source #
A Traversal0
processes at most one part of the whole, with no interactions.
\( \mathsf{Traversal0}\;S\;A = \exists C, D, S \cong D + C \times A \)
type Traversal0' s a = Traversal0 s s a a Source #
type Ixtraversal0 i s t a b = forall p. (Strong p, Choice p) => IndexedOptic p i s t a b Source #
type Ixtraversal0' i s a = Ixtraversal0 i s s a a Source #
Non-empty traversals & cotraversals
type Traversal1 s t a b = forall p. (Choice p, Representable p, Apply (Rep p)) => Optic p s t a b Source #
A Traversal1
processes 1 or more parts of the whole, with Apply
interactions.
\( \mathsf{Traversal1}\;S\;A = \exists F : \mathsf{Traversable1}, S \equiv F\,A \)
type Traversal1' s a = Traversal1 s s a a Source #
type Cotraversal1 s t a b = forall p. (Closed p, Corepresentable p, Apply (Corep p)) => Optic p s t a b Source #
type Cotraversal1' s a = Cotraversal1 s s a a Source #
type Cxtraversal1 k s t a b = forall p. (Closed p, Corepresentable p, Apply (Corep p)) => CoindexedOptic p k s t a b Source #
type Cxtraversal1' k s a = Cxtraversal1 k s s a a Source #
Affine folds, general & non-empty folds, & cofolds
type Fold0 s a = forall p. (Choice p, Representable p, Applicative (Rep p), forall x. Contravariant (p x)) => Optic' p s a Source #
A Fold0
combines at most one element, with no interactions.
type Ixfold0 i s a = forall p. (Choice p, Strong p, forall x. Contravariant (p x)) => IndexedOptic' p i s a Source #
type Fold s a = forall p. (Choice p, Representable p, Applicative (Rep p), forall x. Contravariant (p x)) => Optic' p s a Source #
type Ixfold i s a = forall p. (Choice p, Representable p, Applicative (Rep p), forall x. Contravariant (p x)) => IndexedOptic' p i s a Source #
type Fold1 s a = forall p. (Choice p, Representable p, Apply (Rep p), forall x. Contravariant (p x)) => Optic p s s a a Source #
type Cofold1 t b = forall p. (Cochoice p, Corepresentable p, Apply (Corep p), Bifunctor p) => Optic p t t b b Source #
Views & Reviews
type PrimView s t a b = forall p. (Profunctor p, forall x. Contravariant (p x)) => Optic p s t a b Source #
type Ixview i s a = forall p. (Strong p, forall x. Contravariant (p x)) => IndexedOptic' p i s a Source #
type PrimReview s t a b = forall p. (Profunctor p, Bifunctor p) => Optic p s t a b Source #
Setters & Resetters
type Setter s t a b = forall p. (Closed p, Choice p, Representable p, Applicative (Rep p), Distributive (Rep p)) => Optic p s t a b Source #
A Setter
modifies part of a structure.
\( \mathsf{Setter}\;S\;A = \exists F : \mathsf{Functor}, S \equiv F\,A \)
type Ixsetter i s t a b = forall p. (Closed p, Choice p, Representable p, Applicative (Rep p), Distributive (Rep p)) => IndexedOptic p i s t a b Source #
type Resetter s t a b = forall p. (Closed p, Cochoice p, Corepresentable p, Apply (Corep p), Traversable (Corep p)) => Optic p s t a b Source #
type Cxsetter k s t a b = forall p. (Closed p, Cochoice p, Corepresentable p, Apply (Corep p), Traversable (Corep p)) => CoindexedOptic p k s t a b Source #
Common represenable and corepresentable carriers
type AIxrepn f i s t a b = IndexedOptic (Star f) i s t a b Source #
type ACxrepn f k s t a b = CoindexedOptic (Costar f) k s t a b Source #
Re
The Re
type and its instances witness the symmetry between the parameters of a Profunctor
.
Instances
(Profunctor p, forall x. Contravariant (p x)) => Bifunctor (Re p s t) Source # | |
Cochoice p => Choice (Re p s t) Source # | |
Choice p => Cochoice (Re p s t) Source # | |
Costrong p => Strong (Re p s t) Source # | |
Strong p => Costrong (Re p s t) Source # | |
Profunctor p => Profunctor (Re p s t) Source # | |
Defined in Data.Profunctor.Optic.Type | |
Bifunctor p => Contravariant (Re p s t a) Source # | |
class (Sieve p (Rep p), Strong p) => Representable (p :: Type -> Type -> Type) where #
A Profunctor
p
is Representable
if there exists a Functor
f
such that
p d c
is isomorphic to d -> f c
.
Instances
(Monad m, Functor m) => Representable (Kleisli m) | |
Functor f => Representable (Star f) | |
Representable (Forget r) | |
Representable (Fold0Rep r) Source # | |
Representable ((->) :: Type -> Type -> Type) | |
Representable (LensRep a b) Source # | |
Representable (Traversal0Rep a b) Source # | |
Defined in Data.Profunctor.Optic.Traversal0 type Rep (Traversal0Rep a b) :: Type -> Type # tabulate :: (d -> Rep (Traversal0Rep a b) c) -> Traversal0Rep a b d c # |
class (Cosieve p (Corep p), Costrong p) => Corepresentable (p :: Type -> Type -> Type) where #
A Profunctor
p
is Corepresentable
if there exists a Functor
f
such that
p d c
is isomorphic to f d -> c
.
cotabulate :: (Corep p d -> c) -> p d c #
Laws:
cotabulate
.
cosieve
≡id
cosieve
.
cotabulate
≡id
Instances
Functor f => Corepresentable (Costar f) | |
Corepresentable (Tagged :: Type -> Type -> Type) | |
Corepresentable ((->) :: Type -> Type -> Type) | |
Defined in Data.Profunctor.Rep cotabulate :: (Corep (->) d -> c) -> d -> c # | |
Functor w => Corepresentable (Cokleisli w) | |
Corepresentable (GrateRep a b) Source # | |
class (Profunctor p, Functor f) => Sieve (p :: Type -> Type -> Type) (f :: Type -> Type) | p -> f where #
A Profunctor
p
is a Sieve
on f
if it is a subprofunctor of
.Star
f
That is to say it is a subset of Hom(-,f=)
closed under lmap
and rmap
.
Alternately, you can view it as a sieve in the comma category Hask/f
.
Instances
(Monad m, Functor m) => Sieve (Kleisli m) m | |
Defined in Data.Profunctor.Sieve | |
Functor f => Sieve (Star f) f | |
Defined in Data.Profunctor.Sieve | |
Sieve (Fold0Rep r) (Pre r) Source # | |
Defined in Data.Profunctor.Optic.Fold0 | |
Sieve (Forget r) (Const r :: Type -> Type) | |
Defined in Data.Profunctor.Sieve | |
Sieve ((->) :: Type -> Type -> Type) Identity | |
Defined in Data.Profunctor.Sieve | |
Sieve (IsoRep a b) (Index a b) Source # | |
Defined in Data.Profunctor.Optic.Iso | |
Sieve (LensRep a b) (Index a b) Source # | |
Defined in Data.Profunctor.Optic.Lens |
class (Profunctor p, Functor f) => Cosieve (p :: Type -> Type -> Type) (f :: Type -> Type) | p -> f where #
A Profunctor
p
is a Cosieve
on f
if it is a subprofunctor of
.Costar
f
That is to say it is a subset of Hom(f-,=)
closed under lmap
and rmap
.
Alternately, you can view it as a cosieve in the comma category f/Hask
.
Instances
Functor f => Cosieve (Costar f) f | |
Defined in Data.Profunctor.Sieve | |
Cosieve (Tagged :: Type -> Type -> Type) (Proxy :: Type -> Type) | |
Defined in Data.Profunctor.Sieve | |
Cosieve ((->) :: Type -> Type -> Type) Identity | |
Defined in Data.Profunctor.Sieve | |
Functor w => Cosieve (Cokleisli w) w | |
Defined in Data.Profunctor.Sieve | |
Cosieve (IsoRep a b) (Coindex a b) Source # | |
Defined in Data.Profunctor.Optic.Iso | |
Cosieve (GrateRep a b) (Coindex a b) Source # | |
Defined in Data.Profunctor.Optic.Grate |
class Profunctor p => Choice (p :: Type -> Type -> Type) where #
The generalization of Costar
of Functor
that is strong with respect
to Either
.
Note: This is also a notion of strength, except with regards to another monoidal structure that we can choose to equip Hask with: the cocartesian coproduct.
left' :: p a b -> p (Either a c) (Either b c) #
Laws:
left'
≡dimap
swapE swapE.
right'
where swapE ::Either
a b ->Either
b a swapE =either
Right
Left
rmap
Left
≡lmap
Left
.
left'
lmap
(right
f).
left'
≡rmap
(right
f).
left'
left'
.
left'
≡dimap
assocE unassocE.
left'
where assocE ::Either
(Either
a b) c ->Either
a (Either
b c) assocE (Left
(Left
a)) =Left
a assocE (Left
(Right
b)) =Right
(Left
b) assocE (Right
c) =Right
(Right
c) unassocE ::Either
a (Either
b c) ->Either
(Either
a b) c unassocE (Left
a) =Left
(Left
a) unassocE (Right
(Left
b) =Left
(Right
b) unassocE (Right
(Right
c)) =Right
c)
right' :: p a b -> p (Either c a) (Either c b) #
Laws:
right'
≡dimap
swapE swapE.
left'
where swapE ::Either
a b ->Either
b a swapE =either
Right
Left
rmap
Right
≡lmap
Right
.
right'
lmap
(left
f).
right'
≡rmap
(left
f).
right'
right'
.
right'
≡dimap
unassocE assocE.
right'
where assocE ::Either
(Either
a b) c ->Either
a (Either
b c) assocE (Left
(Left
a)) =Left
a assocE (Left
(Right
b)) =Right
(Left
b) assocE (Right
c) =Right
(Right
c) unassocE ::Either
a (Either
b c) ->Either
(Either
a b) c unassocE (Left
a) =Left
(Left
a) unassocE (Right
(Left
b) =Left
(Right
b) unassocE (Right
(Right
c)) =Right
c)
Instances
class Profunctor p => Cochoice (p :: Type -> Type -> Type) where #
unleft :: p (Either a d) (Either b d) -> p a b #
Laws:
unleft
≡unright
.
dimap
swapE swapE where swapE ::Either
a b ->Either
b a swapE =either
Right
Left
rmap
(either
id
absurd
) ≡unleft
.
lmap
(either
id
absurd
)unfirst
.
rmap
(second
f) ≡unfirst
.
lmap
(second
f)unleft
.
unleft
≡unleft
.
dimap
assocE unassocE where assocE ::Either
(Either
a b) c ->Either
a (Either
b c) assocE (Left
(Left
a)) =Left
a assocE (Left
(Right
b)) =Right
(Left
b) assocE (Right
c) =Right
(Right
c) unassocE ::Either
a (Either
b c) ->Either
(Either
a b) c unassocE (Left
a) =Left
(Left
a) unassocE (Right
(Left
b) =Left
(Right
b) unassocE (Right
(Right
c)) =Right
c)
unright :: p (Either d a) (Either d b) -> p a b #
Laws:
unright
≡unleft
.
dimap
swapE swapE where swapE ::Either
a b ->Either
b a swapE =either
Right
Left
rmap
(either
absurd
id
) ≡unright
.
lmap
(either
absurd
id
)unsecond
.
rmap
(first
f) ≡unsecond
.
lmap
(first
f)unright
.
unright
≡unright
.
dimap
unassocE assocE where assocE ::Either
(Either
a b) c ->Either
a (Either
b c) assocE (Left
(Left
a)) =Left
a assocE (Left
(Right
b)) =Right
(Left
b) assocE (Right
c) =Right
(Right
c) unassocE ::Either
a (Either
b c) ->Either
(Either
a b) c unassocE (Left
a) =Left
(Left
a) unassocE (Right
(Left
b) =Left
(Right
b) unassocE (Right
(Right
c)) =Right
c)
Instances
class Profunctor p => Closed (p :: Type -> Type -> Type) where #
A strong profunctor allows the monoidal structure to pass through.
A closed profunctor allows the closed structure to pass through.
Instances
(Distributive f, Monad f) => Closed (Kleisli f) | |
Defined in Data.Profunctor.Closed | |
Closed (Environment p) | |
Defined in Data.Profunctor.Closed closed :: Environment p a b -> Environment p (x -> a) (x -> b) # | |
Closed p => Closed (Coyoneda p) | |
Defined in Data.Profunctor.Yoneda | |
Closed p => Closed (Yoneda p) | |
Defined in Data.Profunctor.Yoneda | |
Profunctor p => Closed (Closure p) | |
Defined in Data.Profunctor.Closed | |
Distributive f => Closed (Star f) | |
Defined in Data.Profunctor.Closed | |
Functor f => Closed (Costar f) | |
Defined in Data.Profunctor.Closed | |
Closed (Tagged :: Type -> Type -> Type) | |
Defined in Data.Profunctor.Closed | |
Closed ((->) :: Type -> Type -> Type) | |
Defined in Data.Profunctor.Closed | |
Functor f => Closed (Cokleisli f) | |
Defined in Data.Profunctor.Closed | |
Closed (GrateRep a b) Source # | |
Defined in Data.Profunctor.Optic.Grate | |
(Closed p, Closed q) => Closed (Product p q) | |
Defined in Data.Profunctor.Closed | |
(Functor f, Closed p) => Closed (Tannen f p) | |
Defined in Data.Profunctor.Closed |
class Profunctor p => Strong (p :: Type -> Type -> Type) where #
Generalizing Star
of a strong Functor
Note: Every Functor
in Haskell is strong with respect to (,)
.
This describes profunctor strength with respect to the product structure of Hask.
http://www-kb.is.s.u-tokyo.ac.jp/~asada/papers/arrStrMnd.pdf
Instances
class Profunctor p => Costrong (p :: Type -> Type -> Type) where #
Instances
MonadFix m => Costrong (Kleisli m) | |
Costrong p => Costrong (Coyoneda p) | |
Costrong p => Costrong (Yoneda p) | |
Costrong (Cotambara p) | |
Costrong (Copastro p) | |
Functor f => Costrong (Costar f) | |
ArrowLoop p => Costrong (WrappedArrow p) | |
Defined in Data.Profunctor.Strong unfirst :: WrappedArrow p (a, d) (b, d) -> WrappedArrow p a b # unsecond :: WrappedArrow p (d, a) (d, b) -> WrappedArrow p a b # | |
Costrong (Tagged :: Type -> Type -> Type) | |
Costrong ((->) :: Type -> Type -> Type) | |
Defined in Data.Profunctor.Strong | |
Functor f => Costrong (Cokleisli f) | |
Costrong (GrateRep a b) Source # | |
Strong p => Costrong (Re p s t) Source # | |
(Costrong p, Costrong q) => Costrong (Product p q) | |
(Functor f, Costrong p) => Costrong (Tannen f p) | |
type (:->) (p :: Type -> Type -> Type) (q :: Type -> Type -> Type) = forall a b. p a b -> q a b infixr 0 #
newtype Star (f :: Type -> Type) d c #
Lift a Functor
into a Profunctor
(forwards).
Instances
Functor f => Representable (Star f) | |
Applicative f => Choice (Star f) | |
Traversable f => Cochoice (Star f) | |
Distributive f => Closed (Star f) | |
Defined in Data.Profunctor.Closed | |
Functor m => Strong (Star m) | |
Functor f => Profunctor (Star f) | |
Defined in Data.Profunctor.Types | |
Functor f => Sieve (Star f) f | |
Defined in Data.Profunctor.Sieve | |
Monad f => Category (Star f :: Type -> Type -> Type) | |
Monad f => Monad (Star f a) | |
Functor f => Functor (Star f a) | |
Applicative f => Applicative (Star f a) | |
Contravariant f => Contravariant (Star f a) Source # | |
Alternative f => Alternative (Star f a) | |
MonadPlus f => MonadPlus (Star f a) | |
Distributive f => Distributive (Star f a) | |
Defined in Data.Profunctor.Types | |
Apply f => Apply (Star f a) Source # | |
type Rep (Star f) | |
Defined in Data.Profunctor.Rep |
newtype Costar (f :: Type -> Type) d c #
Lift a Functor
into a Profunctor
(backwards).
Instances
Contravariant f => Bifunctor (Costar f) Source # | |
Functor f => Corepresentable (Costar f) | |
Traversable w => Choice (Costar w) | |
Applicative f => Cochoice (Costar f) | |
Functor f => Closed (Costar f) | |
Defined in Data.Profunctor.Closed | |
Comonad f => Strong (Costar f) Source # | |
Functor f => Costrong (Costar f) | |
Functor f => Profunctor (Costar f) | |
Defined in Data.Profunctor.Types | |
Functor f => Cosieve (Costar f) f | |
Defined in Data.Profunctor.Sieve | |
Monad (Costar f a) | |
Functor (Costar f a) | |
Applicative (Costar f a) | |
Defined in Data.Profunctor.Types | |
Distributive (Costar f d) | |
Defined in Data.Profunctor.Types | |
type Corep (Costar f) | |
Defined in Data.Profunctor.Rep |
newtype WrappedArrow (p :: Type -> Type -> Type) a b #
Wrap an arrow for use as a Profunctor
.
WrapArrow | |
|
Instances
Instances
Representable (Forget r) | |
Monoid r => Choice (Forget r) | |
Cochoice (Forget r) Source # | |
Strong (Forget r) | |
Profunctor (Forget r) | |
Defined in Data.Profunctor.Types | |
Sieve (Forget r) (Const r :: Type -> Type) | |
Defined in Data.Profunctor.Sieve | |
Functor (Forget r a) | |
Foldable (Forget r a) | |
Defined in Data.Profunctor.Types fold :: Monoid m => Forget r a m -> m # foldMap :: Monoid m => (a0 -> m) -> Forget r a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Forget r a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Forget r a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Forget r a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Forget r a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Forget r a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Forget r a a0 -> a0 # toList :: Forget r a a0 -> [a0] # null :: Forget r a a0 -> Bool # length :: Forget r a a0 -> Int # elem :: Eq a0 => a0 -> Forget r a a0 -> Bool # maximum :: Ord a0 => Forget r a a0 -> a0 # minimum :: Ord a0 => Forget r a a0 -> a0 # | |
Traversable (Forget r a) | |
Defined in Data.Profunctor.Types | |
type Rep (Forget r) | |
class Profunctor (p :: Type -> Type -> Type) where #
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 ilmap
(f.
g) ≡lmap
g.
lmap
frmap
(f.
g) ≡rmap
f.
rmap
g
Instances
Monad m => Profunctor (Kleisli m) | |
Defined in Data.Profunctor.Unsafe dimap :: (a -> b) -> (c -> d) -> Kleisli m b c -> Kleisli m a d # lmap :: (a -> b) -> Kleisli m b c -> Kleisli m a c # rmap :: (b -> c) -> Kleisli m a b -> Kleisli m a c # (#.) :: Coercible c b => q b c -> Kleisli m a b -> Kleisli m a c # (.#) :: Coercible b a => Kleisli m b c -> q a b -> Kleisli m a c # | |
Profunctor (Pastro p) | |
Defined in Data.Profunctor.Strong | |
Profunctor (Environment p) | |
Defined in Data.Profunctor.Closed dimap :: (a -> b) -> (c -> d) -> Environment p b c -> Environment p a d # lmap :: (a -> b) -> Environment p b c -> Environment p a c # rmap :: (b -> c) -> Environment p a b -> Environment p a c # (#.) :: Coercible c b => q b c -> Environment p a b -> Environment p a c # (.#) :: Coercible b a => Environment p b c -> q a b -> Environment p a c # | |
Profunctor (PastroSum p) | |
Defined in Data.Profunctor.Choice dimap :: (a -> b) -> (c -> d) -> PastroSum p b c -> PastroSum p a d # lmap :: (a -> b) -> PastroSum p b c -> PastroSum p a c # rmap :: (b -> c) -> PastroSum p a b -> PastroSum p a c # (#.) :: Coercible c b => q b c -> PastroSum p a b -> PastroSum p a c # (.#) :: Coercible b a => PastroSum p b c -> q a b -> PastroSum p a c # | |
Profunctor (Coyoneda p) | |
Defined in Data.Profunctor.Yoneda dimap :: (a -> b) -> (c -> d) -> Coyoneda p b c -> Coyoneda p a d # lmap :: (a -> b) -> Coyoneda p b c -> Coyoneda p a c # rmap :: (b -> c) -> Coyoneda p a b -> Coyoneda p a c # (#.) :: Coercible c b => q b c -> Coyoneda p a b -> Coyoneda p a c # (.#) :: Coercible b a => Coyoneda p b c -> q a b -> Coyoneda p a c # | |
Profunctor (Yoneda p) | |
Defined in Data.Profunctor.Yoneda | |
Profunctor p => Profunctor (TambaraSum p) | |
Defined in Data.Profunctor.Choice dimap :: (a -> b) -> (c -> d) -> TambaraSum p b c -> TambaraSum p a d # lmap :: (a -> b) -> TambaraSum p b c -> TambaraSum p a c # rmap :: (b -> c) -> TambaraSum p a b -> TambaraSum p a c # (#.) :: Coercible c b => q b c -> TambaraSum p a b -> TambaraSum p a c # (.#) :: Coercible b a => TambaraSum p b c -> q a b -> TambaraSum p a c # | |
Profunctor (CotambaraSum p) | |
Defined in Data.Profunctor.Choice dimap :: (a -> b) -> (c -> d) -> CotambaraSum p b c -> CotambaraSum p a d # lmap :: (a -> b) -> CotambaraSum p b c -> CotambaraSum p a c # rmap :: (b -> c) -> CotambaraSum p a b -> CotambaraSum p a c # (#.) :: Coercible c b => q b c -> CotambaraSum p a b -> CotambaraSum p a c # (.#) :: Coercible b a => CotambaraSum p b c -> q a b -> CotambaraSum p a c # | |
Profunctor (CopastroSum p) | |
Defined in Data.Profunctor.Choice dimap :: (a -> b) -> (c -> d) -> CopastroSum p b c -> CopastroSum p a d # lmap :: (a -> b) -> CopastroSum p b c -> CopastroSum p a c # rmap :: (b -> c) -> CopastroSum p a b -> CopastroSum p a c # (#.) :: Coercible c b => q b c -> CopastroSum p a b -> CopastroSum p a c # (.#) :: Coercible b a => CopastroSum p b c -> q a b -> CopastroSum p a c # | |
Profunctor p => Profunctor (Closure p) | |
Defined in Data.Profunctor.Closed dimap :: (a -> b) -> (c -> d) -> Closure p b c -> Closure p a d # lmap :: (a -> b) -> Closure p b c -> Closure p a c # rmap :: (b -> c) -> Closure p a b -> Closure p a c # (#.) :: Coercible c b => q b c -> Closure p a b -> Closure p a c # (.#) :: Coercible b a => Closure p b c -> q a b -> Closure p a c # | |
Profunctor p => Profunctor (Tambara p) | |
Defined in Data.Profunctor.Strong dimap :: (a -> b) -> (c -> d) -> Tambara p b c -> Tambara p a d # lmap :: (a -> b) -> Tambara p b c -> Tambara p a c # rmap :: (b -> c) -> Tambara p a b -> Tambara p a c # (#.) :: Coercible c b => q b c -> Tambara p a b -> Tambara p a c # (.#) :: Coercible b a => Tambara p b c -> q a b -> Tambara p a c # | |
Profunctor (Cotambara p) | |
Defined in Data.Profunctor.Strong dimap :: (a -> b) -> (c -> d) -> Cotambara p b c -> Cotambara p a d # lmap :: (a -> b) -> Cotambara p b c -> Cotambara p a c # rmap :: (b -> c) -> Cotambara p a b -> Cotambara p a c # (#.) :: Coercible c b => q b c -> Cotambara p a b -> Cotambara p a c # (.#) :: Coercible b a => Cotambara p b c -> q a b -> Cotambara p a c # | |
Profunctor (Copastro p) | |
Defined in Data.Profunctor.Strong dimap :: (a -> b) -> (c -> d) -> Copastro p b c -> Copastro p a d # lmap :: (a -> b) -> Copastro p b c -> Copastro p a c # rmap :: (b -> c) -> Copastro p a b -> Copastro p a c # (#.) :: Coercible c b => q b c -> Copastro p a b -> Copastro p a c # (.#) :: Coercible b a => Copastro p b c -> q a b -> Copastro p a c # | |
Functor f => Profunctor (Star f) | |
Defined in Data.Profunctor.Types | |
Functor f => Profunctor (Costar f) | |
Defined in Data.Profunctor.Types | |
Arrow p => Profunctor (WrappedArrow p) | |
Defined in Data.Profunctor.Types dimap :: (a -> b) -> (c -> d) -> WrappedArrow p b c -> WrappedArrow p a d # lmap :: (a -> b) -> WrappedArrow p b c -> WrappedArrow p a c # rmap :: (b -> c) -> WrappedArrow p a b -> WrappedArrow p a c # (#.) :: Coercible c b => q b c -> WrappedArrow p a b -> WrappedArrow p a c # (.#) :: Coercible b a => WrappedArrow p b c -> q a b -> WrappedArrow p a c # | |
Profunctor (Forget r) | |
Defined in Data.Profunctor.Types | |
Profunctor (Tagged :: Type -> Type -> Type) | |
Defined in Data.Profunctor.Unsafe | |
Profunctor (Index a) Source # | |
Defined in Data.Profunctor.Optic.Index | |
Profunctor (Fold0Rep r) Source # | |
Defined in Data.Profunctor.Optic.Fold0 dimap :: (a -> b) -> (c -> d) -> Fold0Rep r b c -> Fold0Rep r a d # lmap :: (a -> b) -> Fold0Rep r b c -> Fold0Rep r a c # rmap :: (b -> c) -> Fold0Rep r a b -> Fold0Rep r a c # (#.) :: Coercible c b => q b c -> Fold0Rep r a b -> Fold0Rep r a c # (.#) :: Coercible b a => Fold0Rep r b c -> q a b -> Fold0Rep r a c # | |
Profunctor ((->) :: Type -> Type -> Type) | |
Functor w => Profunctor (Cokleisli w) | |
Defined in Data.Profunctor.Unsafe dimap :: (a -> b) -> (c -> d) -> Cokleisli w b c -> Cokleisli w a d # lmap :: (a -> b) -> Cokleisli w b c -> Cokleisli w a c # rmap :: (b -> c) -> Cokleisli w a b -> Cokleisli w a c # (#.) :: Coercible c b => q b c -> Cokleisli w a b -> Cokleisli w a c # (.#) :: Coercible b a => Cokleisli w b c -> q a b -> Cokleisli w a c # | |
Profunctor (IsoRep a b) Source # | |
Defined in Data.Profunctor.Optic.Iso dimap :: (a0 -> b0) -> (c -> d) -> IsoRep a b b0 c -> IsoRep a b a0 d # lmap :: (a0 -> b0) -> IsoRep a b b0 c -> IsoRep a b a0 c # rmap :: (b0 -> c) -> IsoRep a b a0 b0 -> IsoRep a b a0 c # (#.) :: Coercible c b0 => q b0 c -> IsoRep a b a0 b0 -> IsoRep a b a0 c # (.#) :: Coercible b0 a0 => IsoRep a b b0 c -> q a0 b0 -> IsoRep a b a0 c # | |
Profunctor (CoprismRep a b) Source # | |
Defined in Data.Profunctor.Optic.Prism dimap :: (a0 -> b0) -> (c -> d) -> CoprismRep a b b0 c -> CoprismRep a b a0 d # lmap :: (a0 -> b0) -> CoprismRep a b b0 c -> CoprismRep a b a0 c # rmap :: (b0 -> c) -> CoprismRep a b a0 b0 -> CoprismRep a b a0 c # (#.) :: Coercible c b0 => q b0 c -> CoprismRep a b a0 b0 -> CoprismRep a b a0 c # (.#) :: Coercible b0 a0 => CoprismRep a b b0 c -> q a0 b0 -> CoprismRep a b a0 c # | |
Profunctor (PrismRep a b) Source # | |
Defined in Data.Profunctor.Optic.Prism dimap :: (a0 -> b0) -> (c -> d) -> PrismRep a b b0 c -> PrismRep a b a0 d # lmap :: (a0 -> b0) -> PrismRep a b b0 c -> PrismRep a b a0 c # rmap :: (b0 -> c) -> PrismRep a b a0 b0 -> PrismRep a b a0 c # (#.) :: Coercible c b0 => q b0 c -> PrismRep a b a0 b0 -> PrismRep a b a0 c # (.#) :: Coercible b0 a0 => PrismRep a b b0 c -> q a0 b0 -> PrismRep a b a0 c # | |
Profunctor (LensRep a b) Source # | |
Defined in Data.Profunctor.Optic.Lens dimap :: (a0 -> b0) -> (c -> d) -> LensRep a b b0 c -> LensRep a b a0 d # lmap :: (a0 -> b0) -> LensRep a b b0 c -> LensRep a b a0 c # rmap :: (b0 -> c) -> LensRep a b a0 b0 -> LensRep a b a0 c # (#.) :: Coercible c b0 => q b0 c -> LensRep a b a0 b0 -> LensRep a b a0 c # (.#) :: Coercible b0 a0 => LensRep a b b0 c -> q a0 b0 -> LensRep a b a0 c # | |
Profunctor (GrateRep a b) Source # | |
Defined in Data.Profunctor.Optic.Grate dimap :: (a0 -> b0) -> (c -> d) -> GrateRep a b b0 c -> GrateRep a b a0 d # lmap :: (a0 -> b0) -> GrateRep a b b0 c -> GrateRep a b a0 c # rmap :: (b0 -> c) -> GrateRep a b a0 b0 -> GrateRep a b a0 c # (#.) :: Coercible c b0 => q b0 c -> GrateRep a b a0 b0 -> GrateRep a b a0 c # (.#) :: Coercible b0 a0 => GrateRep a b b0 c -> q a0 b0 -> GrateRep a b a0 c # | |
Profunctor (Traversal0Rep u v) Source # | |
Defined in Data.Profunctor.Optic.Traversal0 dimap :: (a -> b) -> (c -> d) -> Traversal0Rep u v b c -> Traversal0Rep u v a d # lmap :: (a -> b) -> Traversal0Rep u v b c -> Traversal0Rep u v a c # rmap :: (b -> c) -> Traversal0Rep u v a b -> Traversal0Rep u v a c # (#.) :: Coercible c b => q b c -> Traversal0Rep u v a b -> Traversal0Rep u v a c # (.#) :: Coercible b a => Traversal0Rep u v b c -> q a b -> Traversal0Rep u v a c # | |
Functor f => Profunctor (Joker f :: Type -> Type -> Type) | |
Defined in Data.Profunctor.Unsafe | |
Contravariant f => Profunctor (Clown f :: Type -> Type -> Type) | |
Defined in Data.Profunctor.Unsafe | |
Profunctor p => Profunctor (Re p s t) Source # | |
Defined in Data.Profunctor.Optic.Type | |
Profunctor (IxlensRep i a b) Source # | |
Defined in Data.Profunctor.Optic.Lens dimap :: (a0 -> b0) -> (c -> d) -> IxlensRep i a b b0 c -> IxlensRep i a b a0 d # lmap :: (a0 -> b0) -> IxlensRep i a b b0 c -> IxlensRep i a b a0 c # rmap :: (b0 -> c) -> IxlensRep i a b a0 b0 -> IxlensRep i a b a0 c # (#.) :: Coercible c b0 => q b0 c -> IxlensRep i a b a0 b0 -> IxlensRep i a b a0 c # (.#) :: Coercible b0 a0 => IxlensRep i a b b0 c -> q a0 b0 -> IxlensRep i a b a0 c # | |
(Profunctor p, Profunctor q) => Profunctor (Sum p q) | |
Defined in Data.Profunctor.Unsafe | |
(Profunctor p, Profunctor q) => Profunctor (Product p q) | |
Defined in Data.Profunctor.Unsafe dimap :: (a -> b) -> (c -> d) -> Product p q b c -> Product p q a d # lmap :: (a -> b) -> Product p q b c -> Product p q a c # rmap :: (b -> c) -> Product p q a b -> Product p q a c # (#.) :: Coercible c b => q0 b c -> Product p q a b -> Product p q a c # (.#) :: Coercible b a => Product p q b c -> q0 a b -> Product p q a c # | |
(Functor f, Profunctor p) => Profunctor (Tannen f p) | |
Defined in Data.Profunctor.Unsafe dimap :: (a -> b) -> (c -> d) -> Tannen f p b c -> Tannen f p a d # lmap :: (a -> b) -> Tannen f p b c -> Tannen f p a c # rmap :: (b -> c) -> Tannen f p a b -> Tannen f p a c # (#.) :: Coercible c b => q b c -> Tannen f p a b -> Tannen f p a c # (.#) :: Coercible b a => Tannen f p b c -> q a b -> Tannen f p a c # | |
(Profunctor p, Functor f, Functor g) => Profunctor (Biff p f g) | |
Defined in Data.Profunctor.Unsafe dimap :: (a -> b) -> (c -> d) -> Biff p f g b c -> Biff p f g a d # lmap :: (a -> b) -> Biff p f g b c -> Biff p f g a c # rmap :: (b -> c) -> Biff p f g a b -> Biff p f g a c # (#.) :: Coercible c b => q b c -> Biff p f g a b -> Biff p f g a c # (.#) :: Coercible b a => Biff p f g b c -> q a b -> Biff p f g a c # |