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 :: ((a -> b) -> s -> 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 #

Minimal complete definition

Nothing

Methods

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

Laws:

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

roam :: ((a -> b) -> s -> t) -> p a b -> p s t #

Instances

Instances details

(Monad m, Distributive m) => Mapping (Kleisli m) #
Instance details Defined in Data.Profunctor.Mapping Methods map' :: Functor f => Kleisli m a b -> Kleisli m (f a) (f b) # roam :: ((a -> b) -> s -> t) -> Kleisli m a b -> Kleisli m s t #
Mapping (FreeMapping p) #
Instance details Defined in Data.Profunctor.Mapping Methods map' :: Functor f => FreeMapping p a b -> FreeMapping p (f a) (f b) # roam :: ((a -> b) -> s -> t) -> FreeMapping p a b -> FreeMapping p s t #
Profunctor p => Mapping (CofreeMapping p) #
Instance details Defined in Data.Profunctor.Mapping Methods map' :: Functor f => CofreeMapping p a b -> CofreeMapping p (f a) (f b) # roam :: ((a -> b) -> s -> t) -> CofreeMapping p a b -> CofreeMapping p s t #
Mapping p => Mapping (Coyoneda p) #
Instance details Defined in Data.Profunctor.Yoneda Methods map' :: Functor f => Coyoneda p a b -> Coyoneda p (f a) (f b) # roam :: ((a -> b) -> s -> t) -> Coyoneda p a b -> Coyoneda p s t #
Mapping p => Mapping (Yoneda p) #
Instance details Defined in Data.Profunctor.Yoneda Methods map' :: Functor f => Yoneda p a b -> Yoneda p (f a) (f b) # roam :: ((a -> b) -> s -> t) -> Yoneda p a b -> Yoneda p s t #
Mapping ((->) :: Type -> Type -> Type) #
Instance details Defined in Data.Profunctor.Mapping Methods map' :: Functor f => (a -> b) -> f a -> f b # roam :: ((a -> b) -> s -> t) -> (a -> b) -> s -> t #
(Applicative m, Distributive m) => Mapping (Star m) #
Instance details Defined in Data.Profunctor.Mapping Methods map' :: Functor f => Star m a b -> Star m (f a) (f b) # roam :: ((a -> b) -> s -> t) -> Star m a b -> Star m s t #
(Functor f, Mapping p) => Mapping (Tannen f p) #
Instance details Defined in Data.Profunctor.Mapping Methods map' :: Functor f0 => Tannen f p a b -> Tannen f p (f0 a) (f0 b) # roam :: ((a -> b) -> s -> t) -> Tannen f p a b -> Tannen f p s t #
(Mapping p, Mapping q) => Mapping (Procompose p q) #
Instance details Defined in Data.Profunctor.Composition Methods map' :: Functor f => Procompose p q a b -> Procompose p q (f a) (f b) # roam :: ((a -> b) -> s -> t) -> Procompose p q a b -> Procompose p q s t #
(Functor f, Mapping p) => Mapping (Cayley f p) #
Instance details Defined in Data.Profunctor.Cayley Methods map' :: Functor f0 => Cayley f p a b -> Cayley f p (f0 a) (f0 b) # roam :: ((a -> b) -> s -> t) -> Cayley f p a b -> Cayley f p s t #

newtype CofreeMapping p a b #

Constructors

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

Instances

Instances details

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

data FreeMapping p a b where #

FreeMapping -| CofreeMapping

Constructors

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

Instances

Instances details

ProfunctorMonad FreeMapping #
Instance details Defined in Data.Profunctor.Mapping Methods proreturn :: forall (p :: Type -> Type -> Type). Profunctor p => p :-> FreeMapping p # projoin :: forall (p :: Type -> Type -> Type). Profunctor p => FreeMapping (FreeMapping p) :-> FreeMapping p #
Profunctor (FreeMapping p) #
Instance details Defined in Data.Profunctor.Mapping Methods dimap :: (a -> b) -> (c -> d) -> FreeMapping p b c -> FreeMapping p a d # lmap :: (a -> b) -> FreeMapping p b c -> FreeMapping p a c # rmap :: (b -> c) -> FreeMapping p a b -> FreeMapping p a c # (#.) :: forall a b c q. Coercible c b => q b c -> FreeMapping p a b -> FreeMapping p a c # (.#) :: forall a b c q. Coercible b a => FreeMapping p b c -> q a b -> FreeMapping p a c #
Strong (FreeMapping p) #
Instance details Defined in Data.Profunctor.Mapping Methods first' :: FreeMapping p a b -> FreeMapping p (a, c) (b, c) # second' :: FreeMapping p a b -> FreeMapping p (c, a) (c, b) #
Closed (FreeMapping p) #
Instance details Defined in Data.Profunctor.Mapping Methods closed :: FreeMapping p a b -> FreeMapping p (x -> a) (x -> b) #
Choice (FreeMapping p) #
Instance details Defined in Data.Profunctor.Mapping Methods left' :: FreeMapping p a b -> FreeMapping p (Either a c) (Either b c) # right' :: FreeMapping p a b -> FreeMapping p (Either c a) (Either c b) #
Traversing (FreeMapping p) #
Instance details Defined in Data.Profunctor.Mapping Methods traverse' :: Traversable f => FreeMapping p a b -> FreeMapping p (f a) (f b) # wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> FreeMapping p a b -> FreeMapping p s t #
Mapping (FreeMapping p) #
Instance details Defined in Data.Profunctor.Mapping Methods map' :: Functor f => FreeMapping p a b -> FreeMapping p (f a) (f b) # roam :: ((a -> b) -> s -> t) -> FreeMapping p a b -> FreeMapping p s t #
ProfunctorFunctor FreeMapping #
Instance details Defined in Data.Profunctor.Mapping Methods promap :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type). Profunctor p => (p :-> q) -> FreeMapping p :-> FreeMapping q #
Functor (FreeMapping p a) #
Instance details Defined in Data.Profunctor.Mapping Methods fmap :: (a0 -> b) -> FreeMapping p a a0 -> FreeMapping p a b # (<$) :: a0 -> FreeMapping p a b -> FreeMapping p a a0 #

Traversing in terms of Mapping

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

Closed in terms of Mapping

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

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