profunctors-5.2.1: Profunctors

Data.Profunctor.Traversing

Synopsis

# Documentation

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

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) #

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

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

newtype CofreeTraversing p a b #

Constructors

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

Instances

 # Methods # Methodspromap :: Profunctor p => (p :-> q) -> CofreeTraversing p :-> CofreeTraversing q # # Methodsdimap :: (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 #(#.) :: Coercible * c b => (b -> c) -> CofreeTraversing p a b -> CofreeTraversing p a c #(.#) :: Coercible * b a => CofreeTraversing p b c -> (a -> b) -> CofreeTraversing p a c # # Methodsfirst' :: CofreeTraversing p a b -> CofreeTraversing p (a, c) (b, c) #second' :: CofreeTraversing p a b -> CofreeTraversing p (c, a) (c, b) # # Methodsleft' :: 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) # # Methodstraverse' :: Traversable f => CofreeTraversing p a b -> CofreeTraversing p (f a) (f b) #wander :: (forall f. Applicative f => (a -> f b) -> s -> f t) -> CofreeTraversing p a b -> CofreeTraversing p s t #

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

 # Methods # Methodspromap :: Profunctor p => (p :-> q) -> FreeTraversing p :-> FreeTraversing q # # Methodsdimap :: (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 #(#.) :: Coercible * c b => (b -> c) -> FreeTraversing p a b -> FreeTraversing p a c #(.#) :: Coercible * b a => FreeTraversing p b c -> (a -> b) -> FreeTraversing p a c # # Methodsfirst' :: FreeTraversing p a b -> FreeTraversing p (a, c) (b, c) #second' :: FreeTraversing p a b -> FreeTraversing p (c, a) (c, b) # # Methodsleft' :: 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) # # Methodstraverse' :: Traversable f => FreeTraversing p a b -> FreeTraversing p (f a) (f b) #wander :: (forall f. Applicative f => (a -> f b) -> s -> f t) -> FreeTraversing p a b -> FreeTraversing p s t #

# 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) #