Copyright	(C) 2015-2018 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	experimental
Portability	portable
Safe Haskell	Safe
Language	Haskell2010

Data.Profunctor.Mapping

Contents

Traversing in terms of Mapping
Closed in terms of Mapping

Description

Synopsis

class (Traversing p, Closed p) => Mapping p where
- map' :: Functor f => p a b -> p (f a) (f b)
- roam :: (forall f. (Distributive f, Applicative f) => (a -> f b) -> s -> f t) -> p a b -> p s t
newtype CofreeMapping p a b = CofreeMapping {
- runCofreeMapping :: forall f. Functor f => p (f a) (f b)
}
data FreeMapping p a b where
- FreeMapping :: Functor f => (f y -> b) -> p x y -> (a -> f x) -> FreeMapping p a b
wanderMapping :: Mapping p => (forall f. Applicative f => (a -> f b) -> s -> f t) -> p a b -> p s t
traverseMapping :: (Mapping p, Functor f) => p a b -> p (f a) (f b)
closedMapping :: Mapping p => p a b -> p (x -> a) (x -> b)

Documentation

class (Traversing p, Closed p) => Mapping p where Source #

Minimal complete definition

Nothing

Methods

map' :: Functor f => p a b -> p (f a) (f b) Source #

Laws:

map' . rmap f ≡ rmap (fmap f) . map'
map' . map' ≡ dimap Compose getCompose . map'
dimap Identity runIdentity . map' ≡ id

roam :: (forall f. (Distributive f, Applicative f) => (a -> f b) -> s -> f t) -> p a b -> p s t Source #

Instances

(Monad m, Distributive m) => Mapping (Kleisli m) Source #
Instance details Defined in Data.Profunctor.Mapping Methods map' :: Functor f => Kleisli m a b -> Kleisli m (f a) (f b) Source # roam :: (forall (f :: Type -> Type). (Distributive f, Applicative f) => (a -> f b) -> s -> f t) -> Kleisli m a b -> Kleisli m s t Source #
(Applicative m, Distributive m) => Mapping (Star m) Source #
Instance details Defined in Data.Profunctor.Mapping Methods map' :: Functor f => Star m a b -> Star m (f a) (f b) Source # roam :: (forall (f :: Type -> Type). (Distributive f, Applicative f) => (a -> f b) -> s -> f t) -> Star m a b -> Star m s t Source #
Mapping (FreeMapping p) Source #
Instance details Defined in Data.Profunctor.Mapping Methods map' :: Functor f => FreeMapping p a b -> FreeMapping p (f a) (f b) Source # roam :: (forall (f :: Type -> Type). (Distributive f, Applicative f) => (a -> f b) -> s -> f t) -> FreeMapping p a b -> FreeMapping p s t Source #
Profunctor p => Mapping (CofreeMapping p) Source #
Instance details Defined in Data.Profunctor.Mapping Methods map' :: Functor f => CofreeMapping p a b -> CofreeMapping p (f a) (f b) Source # roam :: (forall (f :: Type -> Type). (Distributive f, Applicative f) => (a -> f b) -> s -> f t) -> CofreeMapping p a b -> CofreeMapping p s t Source #
Mapping p => Mapping (Coyoneda p) Source #
Instance details Defined in Data.Profunctor.Yoneda Methods map' :: Functor f => Coyoneda p a b -> Coyoneda p (f a) (f b) Source # roam :: (forall (f :: Type -> Type). (Distributive f, Applicative f) => (a -> f b) -> s -> f t) -> Coyoneda p a b -> Coyoneda p s t Source #
Mapping p => Mapping (Yoneda p) Source #
Instance details Defined in Data.Profunctor.Yoneda Methods map' :: Functor f => Yoneda p a b -> Yoneda p (f a) (f b) Source # roam :: (forall (f :: Type -> Type). (Distributive f, Applicative f) => (a -> f b) -> s -> f t) -> Yoneda p a b -> Yoneda p s t Source #
Mapping ((->) :: Type -> Type -> Type) Source #
Instance details Defined in Data.Profunctor.Mapping Methods map' :: Functor f => (a -> b) -> f a -> f b Source # roam :: (forall (f :: Type -> Type). (Distributive f, Applicative f) => (a -> f b) -> s -> f t) -> (a -> b) -> s -> t Source #
(Mapping p, Mapping q) => Mapping (Procompose p q) Source #
Instance details Defined in Data.Profunctor.Composition Methods map' :: Functor f => Procompose p q a b -> Procompose p q (f a) (f b) Source # roam :: (forall (f :: Type -> Type). (Distributive f, Applicative f) => (a -> f b) -> s -> f t) -> Procompose p q a b -> Procompose p q s t Source #

newtype CofreeMapping p a b Source #

Constructors

CofreeMapping
Fields runCofreeMapping :: forall f. Functor f => p (f a) (f b)

Instances

ProfunctorComonad CofreeMapping Source #
Instance details Defined in Data.Profunctor.Mapping Methods proextract :: Profunctor p => CofreeMapping p :-> p Source # produplicate :: Profunctor p => CofreeMapping p :-> CofreeMapping (CofreeMapping p) Source #
ProfunctorFunctor CofreeMapping Source #
Instance details Defined in Data.Profunctor.Mapping Methods promap :: Profunctor p => (p :-> q) -> CofreeMapping p :-> CofreeMapping q Source #
Profunctor p => Profunctor (CofreeMapping p) Source #
Instance details Defined in Data.Profunctor.Mapping Methods dimap :: (a -> b) -> (c -> d) -> CofreeMapping p b c -> CofreeMapping p a d Source # lmap :: (a -> b) -> CofreeMapping p b c -> CofreeMapping p a c Source # rmap :: (b -> c) -> CofreeMapping p a b -> CofreeMapping p a c Source # (#.) :: Coercible c b => q b c -> CofreeMapping p a b -> CofreeMapping p a c Source # (.#) :: Coercible b a => CofreeMapping p b c -> q a b -> CofreeMapping p a c Source #
Profunctor p => Strong (CofreeMapping p) Source #
Instance details Defined in Data.Profunctor.Mapping Methods first' :: CofreeMapping p a b -> CofreeMapping p (a, c) (b, c) Source # second' :: CofreeMapping p a b -> CofreeMapping p (c, a) (c, b) Source #
Profunctor p => Closed (CofreeMapping p) Source #
Instance details Defined in Data.Profunctor.Mapping Methods closed :: CofreeMapping p a b -> CofreeMapping p (x -> a) (x -> b) Source #
Profunctor p => Choice (CofreeMapping p) Source #
Instance details Defined in Data.Profunctor.Mapping Methods left' :: CofreeMapping p a b -> CofreeMapping p (Either a c) (Either b c) Source # right' :: CofreeMapping p a b -> CofreeMapping p (Either c a) (Either c b) Source #
Profunctor p => Traversing (CofreeMapping p) Source #
Instance details Defined in Data.Profunctor.Mapping Methods traverse' :: Traversable f => CofreeMapping p a b -> CofreeMapping p (f a) (f b) Source # wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> CofreeMapping p a b -> CofreeMapping p s t Source #
Profunctor p => Mapping (CofreeMapping p) Source #
Instance details Defined in Data.Profunctor.Mapping Methods map' :: Functor f => CofreeMapping p a b -> CofreeMapping p (f a) (f b) Source # roam :: (forall (f :: Type -> Type). (Distributive f, Applicative f) => (a -> f b) -> s -> f t) -> CofreeMapping p a b -> CofreeMapping p s t Source #

data FreeMapping p a b where Source #

FreeMapping -| CofreeMapping

Constructors

FreeMapping :: Functor f => (f y -> b) -> p x y -> (a -> f x) -> FreeMapping p a b

Instances

ProfunctorMonad FreeMapping Source #
Instance details Defined in Data.Profunctor.Mapping Methods proreturn :: Profunctor p => p :-> FreeMapping p Source # projoin :: Profunctor p => FreeMapping (FreeMapping p) :-> FreeMapping p Source #
ProfunctorFunctor FreeMapping Source #
Instance details Defined in Data.Profunctor.Mapping Methods promap :: Profunctor p => (p :-> q) -> FreeMapping p :-> FreeMapping q Source #
Profunctor (FreeMapping p) Source #
Instance details Defined in Data.Profunctor.Mapping Methods dimap :: (a -> b) -> (c -> d) -> FreeMapping p b c -> FreeMapping p a d Source # lmap :: (a -> b) -> FreeMapping p b c -> FreeMapping p a c Source # rmap :: (b -> c) -> FreeMapping p a b -> FreeMapping p a c Source # (#.) :: Coercible c b => q b c -> FreeMapping p a b -> FreeMapping p a c Source # (.#) :: Coercible b a => FreeMapping p b c -> q a b -> FreeMapping p a c Source #
Strong (FreeMapping p) Source #
Instance details Defined in Data.Profunctor.Mapping Methods first' :: FreeMapping p a b -> FreeMapping p (a, c) (b, c) Source # second' :: FreeMapping p a b -> FreeMapping p (c, a) (c, b) Source #
Closed (FreeMapping p) Source #
Instance details Defined in Data.Profunctor.Mapping Methods closed :: FreeMapping p a b -> FreeMapping p (x -> a) (x -> b) Source #
Choice (FreeMapping p) Source #
Instance details Defined in Data.Profunctor.Mapping Methods left' :: FreeMapping p a b -> FreeMapping p (Either a c) (Either b c) Source # right' :: FreeMapping p a b -> FreeMapping p (Either c a) (Either c b) Source #
Traversing (FreeMapping p) Source #
Instance details Defined in Data.Profunctor.Mapping Methods traverse' :: Traversable f => FreeMapping p a b -> FreeMapping p (f a) (f b) Source # wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> FreeMapping p a b -> FreeMapping p s t Source #
Mapping (FreeMapping p) Source #
Instance details Defined in Data.Profunctor.Mapping Methods map' :: Functor f => FreeMapping p a b -> FreeMapping p (f a) (f b) Source # roam :: (forall (f :: Type -> Type). (Distributive f, Applicative f) => (a -> f b) -> s -> f t) -> FreeMapping p a b -> FreeMapping p s t Source #

Traversing in terms of Mapping

wanderMapping :: Mapping p => (forall f. Applicative f => (a -> f b) -> s -> f t) -> p a b -> p s t Source #

Closed in terms of Mapping

traverseMapping :: (Mapping p, Functor f) => p a b -> p (f a) (f b) Source #

closedMapping :: Mapping p => p a b -> p (x -> a) (x -> b) Source #