profunctors-5.2.1: Profunctors

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LanguageHaskell2010

Data.Profunctor.Traversing

Contents

Synopsis

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) #

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 (->) # 

Methods

traverse' :: 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) # 

Methods

traverse' :: 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) # 

Methods

traverse' :: 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) # 

Methods

traverse' :: 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 #

Traversing (FreeTraversing p) # 

Methods

traverse' :: 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 p => Traversing (CofreeTraversing p) # 

Methods

traverse' :: 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 #

Traversing (FreeMapping p) # 

Methods

traverse' :: 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 #

Profunctor p => Traversing (CofreeMapping p) # 

Methods

traverse' :: 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) # 

Methods

traverse' :: 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) # 

Methods

traverse' :: 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) # 

Methods

traverse' :: 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 

Fields

Instances

ProfunctorComonad CofreeTraversing # 
ProfunctorFunctor CofreeTraversing # 
Profunctor p => Profunctor (CofreeTraversing p) # 

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 #

(#.) :: 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 #

Profunctor p => Strong (CofreeTraversing p) # 

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) # 

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) # 

Methods

traverse' :: 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

ProfunctorMonad FreeTraversing # 
ProfunctorFunctor FreeTraversing # 

Methods

promap :: Profunctor p => (p :-> q) -> FreeTraversing p :-> FreeTraversing q #

Profunctor (FreeTraversing p) # 

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 #

(#.) :: 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 #

Strong (FreeTraversing p) # 

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) # 

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) # 

Methods

traverse' :: 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) #