profunctors-5.6: Profunctors

Data.Profunctor.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

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
 Monad m => Traversing (Kleisli m) Source # Instance detailsDefined in Data.Profunctor.Traversing Methodstraverse' :: Traversable f => Kleisli m a b -> Kleisli m (f a) (f b) Source #wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> Kleisli m a b -> Kleisli m s t Source # Source # Instance detailsDefined in Data.Profunctor.Traversing Methodstraverse' :: Traversable f => FreeTraversing p a b -> FreeTraversing p (f a) (f b) Source #wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> FreeTraversing p a b -> FreeTraversing p s t Source # Source # Instance detailsDefined in Data.Profunctor.Traversing Methodstraverse' :: Traversable f => CofreeTraversing p a b -> CofreeTraversing p (f a) (f b) Source #wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> CofreeTraversing p a b -> CofreeTraversing p s t Source # Source # Instance detailsDefined in Data.Profunctor.Mapping Methodstraverse' :: 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 # Source # Instance detailsDefined in Data.Profunctor.Mapping Methodstraverse' :: 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 # Traversing p => Traversing (Coyoneda p) Source # Instance detailsDefined in Data.Profunctor.Yoneda Methodstraverse' :: Traversable f => Coyoneda p a b -> Coyoneda p (f a) (f b) Source #wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> Coyoneda p a b -> Coyoneda p s t Source # Traversing p => Traversing (Yoneda p) Source # Instance detailsDefined in Data.Profunctor.Yoneda Methodstraverse' :: Traversable f => Yoneda p a b -> Yoneda p (f a) (f b) Source #wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> Yoneda p a b -> Yoneda p s t Source # Traversing ((->) :: Type -> Type -> Type) Source # Instance detailsDefined in Data.Profunctor.Traversing Methodstraverse' :: Traversable f => (a -> b) -> f a -> f b Source #wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> (a -> b) -> s -> t Source # Monoid m => Traversing (Forget m :: Type -> Type -> Type) Source # Instance detailsDefined in Data.Profunctor.Traversing Methodstraverse' :: Traversable f => Forget m a b -> Forget m (f a) (f b) Source #wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> Forget m a b -> Forget m s t Source # Applicative m => Traversing (Star m) Source # Instance detailsDefined in Data.Profunctor.Traversing Methodstraverse' :: Traversable f => Star m a b -> Star m (f a) (f b) Source #wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> Star m a b -> Star m s t Source # (Functor f, Traversing p) => Traversing (Tannen f p) Source # Instance detailsDefined in Data.Profunctor.Traversing Methodstraverse' :: Traversable f0 => Tannen f p a b -> Tannen f p (f0 a) (f0 b) Source #wander :: (forall (f0 :: Type -> Type). Applicative f0 => (a -> f0 b) -> s -> f0 t) -> Tannen f p a b -> Tannen f p s t Source # (Traversing p, Traversing q) => Traversing (Procompose p q) Source # Instance detailsDefined in Data.Profunctor.Composition Methodstraverse' :: Traversable f => Procompose p q a b -> Procompose p q (f a) (f b) Source #wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> Procompose p q a b -> Procompose p q s t Source # (Functor f, Traversing p) => Traversing (Cayley f p) Source # Instance detailsDefined in Data.Profunctor.Cayley Methodstraverse' :: Traversable f0 => Cayley f p a b -> Cayley f p (f0 a) (f0 b) Source #wander :: (forall (f0 :: Type -> Type). Applicative f0 => (a -> f0 b) -> s -> f0 t) -> Cayley f p a b -> Cayley f p s t Source #

newtype CofreeTraversing p a b Source #

Constructors

 CofreeTraversing FieldsrunCofreeTraversing :: forall f. Traversable f => p (f a) (f b)
Instances
 Source # Instance detailsDefined in Data.Profunctor.Traversing Methods Source # Instance detailsDefined in Data.Profunctor.Traversing Methodsdimap :: (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 => q b c -> CofreeTraversing p a b -> CofreeTraversing p a c Source #(.#) :: Coercible b a => CofreeTraversing p b c -> q a b -> CofreeTraversing p a c Source # Source # Instance detailsDefined in Data.Profunctor.Traversing Methodsfirst' :: CofreeTraversing p a b -> CofreeTraversing p (a, c) (b, c) Source #second' :: CofreeTraversing p a b -> CofreeTraversing p (c, a) (c, b) Source # Source # Instance detailsDefined in Data.Profunctor.Traversing Methodsleft' :: 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 # Source # Instance detailsDefined in Data.Profunctor.Traversing Methodstraverse' :: Traversable f => CofreeTraversing p a b -> CofreeTraversing p (f a) (f b) Source #wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> CofreeTraversing p a b -> CofreeTraversing p s t Source # Source # Instance detailsDefined in Data.Profunctor.Traversing Methodspromap :: Profunctor p => (p :-> q) -> CofreeTraversing p :-> CofreeTraversing q 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
 Source # Instance detailsDefined in Data.Profunctor.Traversing Methods Source # Instance detailsDefined in Data.Profunctor.Traversing Methodsdimap :: (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 => q b c -> FreeTraversing p a b -> FreeTraversing p a c Source #(.#) :: Coercible b a => FreeTraversing p b c -> q a b -> FreeTraversing p a c Source # Source # Instance detailsDefined in Data.Profunctor.Traversing Methodsfirst' :: FreeTraversing p a b -> FreeTraversing p (a, c) (b, c) Source #second' :: FreeTraversing p a b -> FreeTraversing p (c, a) (c, b) Source # Source # Instance detailsDefined in Data.Profunctor.Traversing Methodsleft' :: 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 # Source # Instance detailsDefined in Data.Profunctor.Traversing Methodstraverse' :: Traversable f => FreeTraversing p a b -> FreeTraversing p (f a) (f b) Source #wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> FreeTraversing p a b -> FreeTraversing p s t Source # Source # Instance detailsDefined in Data.Profunctor.Traversing Methodspromap :: Profunctor p => (p :-> q) -> FreeTraversing p :-> FreeTraversing q 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 #