Data.Profunctor.Mapping

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

(Monad m, Distributive m) => Mapping (Kleisli m)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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

ProfunctorComonad CofreeMapping

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)

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)

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)

Defined in Data.Profunctor.Mapping

Methods

closed :: CofreeMapping p a b -> CofreeMapping p (x -> a) (x -> b)

Profunctor p => Choice (CofreeMapping p)

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)

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)

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

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

ProfunctorMonad FreeMapping

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)

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)

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)

Defined in Data.Profunctor.Mapping

Methods

closed :: FreeMapping p a b -> FreeMapping p (x -> a) (x -> b)

Choice (FreeMapping p)

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)

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)

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

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)

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)