Data.Profunctor.Traversing

Documentation

class (Choice p, Strong p) => Traversing p where

Note: Definitions in terms of wander are much more efficient!

Minimal complete definition

wander | traverse'

Methods

traverse' :: Traversable f => p a b -> p (f a) (f b)

Laws:

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

wander :: (forall f. Applicative f => (a -> f b) -> s -> f t) -> p a b -> p s t

This combinator is mutually defined in terms of traverse'

Instances

Monad m => Traversing (Kleisli m)

Defined in Data.Profunctor.Traversing

Methods

traverse' :: Traversable f => Kleisli m a b -> Kleisli m (f a) (f b)

wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> Kleisli m a b -> Kleisli m s t

Traversing (FreeTraversing p)

Defined in Data.Profunctor.Traversing

Methods

traverse' :: Traversable f => FreeTraversing p a b -> FreeTraversing p (f a) (f b)

wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> FreeTraversing p a b -> FreeTraversing p s t

Profunctor p => Traversing (CofreeTraversing p)

Defined in Data.Profunctor.Traversing

Methods

traverse' :: Traversable f => CofreeTraversing p a b -> CofreeTraversing p (f a) (f b)

wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> CofreeTraversing p a b -> CofreeTraversing p s t

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

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

Traversing p => Traversing (Coyoneda p)

Defined in Data.Profunctor.Yoneda

Methods

traverse' :: Traversable f => Coyoneda p a b -> Coyoneda p (f a) (f b)

wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> Coyoneda p a b -> Coyoneda p s t

Traversing p => Traversing (Yoneda p)

Defined in Data.Profunctor.Yoneda

Methods

traverse' :: Traversable f => Yoneda p a b -> Yoneda p (f a) (f b)

wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> Yoneda p a b -> Yoneda p s t

Traversing ((->) :: Type -> Type -> Type)

Defined in Data.Profunctor.Traversing

Methods

traverse' :: Traversable f => (a -> b) -> f a -> f b

wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> (a -> b) -> s -> t

Monoid m => Traversing (Forget m :: Type -> Type -> Type)

Defined in Data.Profunctor.Traversing

Methods

traverse' :: Traversable f => Forget m a b -> Forget m (f a) (f b)

wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> Forget m a b -> Forget m s t

Applicative m => Traversing (Star m)

Defined in Data.Profunctor.Traversing

Methods

traverse' :: Traversable f => Star m a b -> Star m (f a) (f b)

wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> Star m a b -> Star m s t

(Functor f, Traversing p) => Traversing (Tannen f p)

Defined in Data.Profunctor.Traversing

Methods

traverse' :: Traversable f0 => Tannen f p a b -> Tannen f p (f0 a) (f0 b)

wander :: (forall (f0 :: Type -> Type). Applicative f0 => (a -> f0 b) -> s -> f0 t) -> Tannen f p a b -> Tannen f p s t

(Traversing p, Traversing q) => Traversing (Procompose p q)

Defined in Data.Profunctor.Composition

Methods

traverse' :: Traversable f => Procompose p q a b -> Procompose p q (f a) (f b)

wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> Procompose p q a b -> Procompose p q s t

(Functor f, Traversing p) => Traversing (Cayley f p)

Defined in Data.Profunctor.Cayley

Methods

traverse' :: Traversable f0 => Cayley f p a b -> Cayley f p (f0 a) (f0 b)

wander :: (forall (f0 :: Type -> Type). Applicative f0 => (a -> f0 b) -> s -> f0 t) -> Cayley f p a b -> Cayley f p s t

newtype CofreeTraversing p a b

Constructors

CofreeTraversing

Fields

• runCofreeTraversing :: forall f. Traversable f => p (f a) (f b)

Instances

ProfunctorComonad CofreeTraversing

Defined in Data.Profunctor.Traversing

Methods

proextract :: forall (p :: Type -> Type -> Type). Profunctor p => CofreeTraversing p :-> p

produplicate :: forall (p :: Type -> Type -> Type). Profunctor p => CofreeTraversing p :-> CofreeTraversing (CofreeTraversing p)

Profunctor p => Profunctor (CofreeTraversing p)

Defined in Data.Profunctor.Traversing

Methods

dimap :: (a -> b) -> (c -> d) -> CofreeTraversing p b c -> CofreeTraversing p a d

lmap :: (a -> b) -> CofreeTraversing p b c -> CofreeTraversing p a c

rmap :: (b -> c) -> CofreeTraversing p a b -> CofreeTraversing p a c

(#.) :: forall a b c q. Coercible c b => q b c -> CofreeTraversing p a b -> CofreeTraversing p a c

(.#) :: forall a b c q. Coercible b a => CofreeTraversing p b c -> q a b -> CofreeTraversing p a c

Profunctor p => Strong (CofreeTraversing p)

Defined in Data.Profunctor.Traversing

Methods

first' :: CofreeTraversing p a b -> CofreeTraversing p (a, c) (b, c)

second' :: CofreeTraversing p a b -> CofreeTraversing p (c, a) (c, b)

Profunctor p => Choice (CofreeTraversing p)

Defined in Data.Profunctor.Traversing

Methods

left' :: CofreeTraversing p a b -> CofreeTraversing p (Either a c) (Either b c)

right' :: CofreeTraversing p a b -> CofreeTraversing p (Either c a) (Either c b)

Profunctor p => Traversing (CofreeTraversing p)

Defined in Data.Profunctor.Traversing

Methods

traverse' :: Traversable f => CofreeTraversing p a b -> CofreeTraversing p (f a) (f b)

wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> CofreeTraversing p a b -> CofreeTraversing p s t

ProfunctorFunctor CofreeTraversing

Defined in Data.Profunctor.Traversing

Methods

promap :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type). Profunctor p => (p :-> q) -> CofreeTraversing p :-> CofreeTraversing q

data FreeTraversing p a b where

FreeTraversing -| CofreeTraversing

Constructors

FreeTraversing :: Traversable f => (f y -> b) -> p x y -> (a -> f x) -> FreeTraversing p a b

Instances

ProfunctorMonad FreeTraversing

Defined in Data.Profunctor.Traversing

Methods

proreturn :: forall (p :: Type -> Type -> Type). Profunctor p => p :-> FreeTraversing p

projoin :: forall (p :: Type -> Type -> Type). Profunctor p => FreeTraversing (FreeTraversing p) :-> FreeTraversing p

Profunctor (FreeTraversing p)

Defined in Data.Profunctor.Traversing

Methods

dimap :: (a -> b) -> (c -> d) -> FreeTraversing p b c -> FreeTraversing p a d

lmap :: (a -> b) -> FreeTraversing p b c -> FreeTraversing p a c

rmap :: (b -> c) -> FreeTraversing p a b -> FreeTraversing p a c

(#.) :: forall a b c q. Coercible c b => q b c -> FreeTraversing p a b -> FreeTraversing p a c

(.#) :: forall a b c q. Coercible b a => FreeTraversing p b c -> q a b -> FreeTraversing p a c

Strong (FreeTraversing p)

Defined in Data.Profunctor.Traversing

Methods

first' :: FreeTraversing p a b -> FreeTraversing p (a, c) (b, c)

second' :: FreeTraversing p a b -> FreeTraversing p (c, a) (c, b)

Choice (FreeTraversing p)

Defined in Data.Profunctor.Traversing

Methods

left' :: FreeTraversing p a b -> FreeTraversing p (Either a c) (Either b c)

right' :: FreeTraversing p a b -> FreeTraversing p (Either c a) (Either c b)

Traversing (FreeTraversing p)

Defined in Data.Profunctor.Traversing

Methods

traverse' :: Traversable f => FreeTraversing p a b -> FreeTraversing p (f a) (f b)

wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> FreeTraversing p a b -> FreeTraversing p s t

ProfunctorFunctor FreeTraversing

Defined in Data.Profunctor.Traversing

Methods

promap :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type). Profunctor p => (p :-> q) -> FreeTraversing p :-> FreeTraversing q

Functor (FreeTraversing p a)

Defined in Data.Profunctor.Traversing

Methods

fmap :: (a0 -> b) -> FreeTraversing p a a0 -> FreeTraversing p a b

(<$) :: a0 -> FreeTraversing p a b -> FreeTraversing p a a0

Profunctor in terms of Traversing

dimapWandering :: Traversing p => (a' -> a) -> (b -> b') -> p a b -> p a' b'

A definition of dimap for Traversing instances that define an explicit wander.

lmapWandering :: Traversing p => (a -> b) -> p b c -> p a c

lmapWandering may be a more efficient implementation of lmap than the default produced from dimapWandering.

rmapWandering :: Traversing p => (b -> c) -> p a b -> p a c

rmapWandering is the same as the default produced from dimapWandering.

Strong in terms of Traversing

firstTraversing :: Traversing p => p a b -> p (a, c) (b, c)

secondTraversing :: Traversing p => p a b -> p (c, a) (c, b)

Choice in terms of Traversing

leftTraversing :: Traversing p => p a b -> p (Either a c) (Either b c)

rightTraversing :: Traversing p => p a b -> p (Either c a) (Either c b)