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Language	Haskell2010

Data.Profunctor.Traversing

Contents

Profunctor in terms of Traversing
Strong in terms of Traversing
Choice in terms of Traversing

Synopsis

Documentation

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

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) Source #

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 Source #

This combinator is mutually defined in terms of traverse'

Instances

Traversing (->) Source #
Methods traverse' :: Traversable f => (a -> b) -> f a -> f b Source # wander :: (forall f. Applicative f => (a -> f b) -> s -> f t) -> (a -> b) -> s -> t Source #
Monad m => Traversing (Kleisli m) Source #
Methods traverse' :: Traversable f => Kleisli m a b -> Kleisli m (f a) (f b) Source # wander :: (forall f. Applicative f => (a -> f b) -> s -> f t) -> Kleisli m a b -> Kleisli m s t Source #
Monoid m => Traversing (Forget m) Source #
Methods traverse' :: Traversable f => Forget m a b -> Forget m (f a) (f b) Source # wander :: (forall f. Applicative f => (a -> f b) -> s -> f t) -> Forget m a b -> Forget m s t Source #
Applicative m => Traversing (Star m) Source #
Methods traverse' :: Traversable f => Star m a b -> Star m (f a) (f b) Source # wander :: (forall f. Applicative f => (a -> f b) -> s -> f t) -> Star m a b -> Star m s t Source #
Traversing (FreeTraversing p) Source #
Methods traverse' :: Traversable f => FreeTraversing p a b -> FreeTraversing p (f a) (f b) Source # wander :: (forall f. Applicative f => (a -> f b) -> s -> f t) -> FreeTraversing p a b -> FreeTraversing p s t Source #
Profunctor p => Traversing (CofreeTraversing p) Source #
Methods traverse' :: Traversable f => CofreeTraversing p a b -> CofreeTraversing p (f a) (f b) Source # wander :: (forall f. Applicative f => (a -> f b) -> s -> f t) -> CofreeTraversing p a b -> CofreeTraversing p s t Source #
Traversing (FreeMapping p) Source #
Methods traverse' :: Traversable f => FreeMapping p a b -> FreeMapping p (f a) (f b) Source # wander :: (forall f. Applicative f => (a -> f b) -> s -> f t) -> FreeMapping p a b -> FreeMapping p s t Source #
Profunctor p => Traversing (CofreeMapping p) Source #
Methods traverse' :: Traversable f => CofreeMapping p a b -> CofreeMapping p (f a) (f b) Source # wander :: (forall f. Applicative f => (a -> f b) -> s -> f t) -> CofreeMapping p a b -> CofreeMapping p s t Source #
Traversing p => Traversing (Coyoneda p) Source #
Methods traverse' :: Traversable f => Coyoneda p a b -> Coyoneda p (f a) (f b) Source # wander :: (forall f. Applicative f => (a -> f b) -> s -> f t) -> Coyoneda p a b -> Coyoneda p s t Source #
Traversing p => Traversing (Yoneda p) Source #
Methods traverse' :: Traversable f => Yoneda p a b -> Yoneda p (f a) (f b) Source # wander :: (forall f. Applicative f => (a -> f b) -> s -> f t) -> Yoneda p a b -> Yoneda p s t Source #
(Traversing p, Traversing q) => Traversing (Procompose p q) Source #
Methods traverse' :: Traversable f => Procompose p q a b -> Procompose p q (f a) (f b) Source # wander :: (forall f. Applicative f => (a -> f b) -> s -> f t) -> Procompose p q a b -> Procompose p q s t Source #

newtype CofreeTraversing p a b Source #

Constructors

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

Instances

ProfunctorComonad CofreeTraversing Source #
Methods proextract :: Profunctor p => CofreeTraversing p :-> p Source # produplicate :: Profunctor p => CofreeTraversing p :-> CofreeTraversing (CofreeTraversing p) Source #
ProfunctorFunctor CofreeTraversing Source #
Methods promap :: Profunctor p => (p :-> q) -> CofreeTraversing p :-> CofreeTraversing q Source #
Profunctor p => Profunctor (CofreeTraversing p) Source #
Methods dimap :: (a -> b) -> (c -> d) -> CofreeTraversing p b c -> CofreeTraversing p a d Source # lmap :: (a -> b) -> CofreeTraversing p b c -> CofreeTraversing p a c Source # rmap :: (b -> c) -> CofreeTraversing p a b -> CofreeTraversing p a c Source # (#.) :: Coercible * c b => (b -> c) -> CofreeTraversing p a b -> CofreeTraversing p a c Source # (.#) :: Coercible * b a => CofreeTraversing p b c -> (a -> b) -> CofreeTraversing p a c Source #
Profunctor p => Strong (CofreeTraversing p) Source #
Methods first' :: CofreeTraversing p a b -> CofreeTraversing p (a, c) (b, c) Source # second' :: CofreeTraversing p a b -> CofreeTraversing p (c, a) (c, b) Source #
Profunctor p => Choice (CofreeTraversing p) Source #
Methods left' :: CofreeTraversing p a b -> CofreeTraversing p (Either a c) (Either b c) Source # right' :: CofreeTraversing p a b -> CofreeTraversing p (Either c a) (Either c b) Source #
Profunctor p => Traversing (CofreeTraversing p) Source #
Methods traverse' :: Traversable f => CofreeTraversing p a b -> CofreeTraversing p (f a) (f b) Source # wander :: (forall f. Applicative f => (a -> f b) -> s -> f t) -> CofreeTraversing p a b -> CofreeTraversing p s t Source #

data FreeTraversing p a b where Source #

FreeTraversing -| CofreeTraversing

Constructors

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

Instances

ProfunctorMonad FreeTraversing Source #
Methods proreturn :: Profunctor p => p :-> FreeTraversing p Source # projoin :: Profunctor p => FreeTraversing (FreeTraversing p) :-> FreeTraversing p Source #
ProfunctorFunctor FreeTraversing Source #
Methods promap :: Profunctor p => (p :-> q) -> FreeTraversing p :-> FreeTraversing q Source #
Profunctor (FreeTraversing p) Source #
Methods dimap :: (a -> b) -> (c -> d) -> FreeTraversing p b c -> FreeTraversing p a d Source # lmap :: (a -> b) -> FreeTraversing p b c -> FreeTraversing p a c Source # rmap :: (b -> c) -> FreeTraversing p a b -> FreeTraversing p a c Source # (#.) :: Coercible * c b => (b -> c) -> FreeTraversing p a b -> FreeTraversing p a c Source # (.#) :: Coercible * b a => FreeTraversing p b c -> (a -> b) -> FreeTraversing p a c Source #
Strong (FreeTraversing p) Source #
Methods first' :: FreeTraversing p a b -> FreeTraversing p (a, c) (b, c) Source # second' :: FreeTraversing p a b -> FreeTraversing p (c, a) (c, b) Source #
Choice (FreeTraversing p) Source #
Methods left' :: FreeTraversing p a b -> FreeTraversing p (Either a c) (Either b c) Source # right' :: FreeTraversing p a b -> FreeTraversing p (Either c a) (Either c b) Source #
Traversing (FreeTraversing p) Source #
Methods traverse' :: Traversable f => FreeTraversing p a b -> FreeTraversing p (f a) (f b) Source # wander :: (forall f. Applicative f => (a -> f b) -> s -> f t) -> FreeTraversing p a b -> FreeTraversing p s t Source #

Profunctor in terms of Traversing

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

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

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

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 Source #

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) Source #

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

Choice in terms of Traversing

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

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