Portability	portable
Stability	experimental
Maintainer	libraries@haskell.org

Data.Traversable

Description

Class of data structures that can be traversed from left to right, performing an action on each element.

Documentation

class (Functor t, Foldable t) => Traversable t whereSource

Functors representing data structures that can be traversed from left to right.

Minimal complete definition: traverse or sequenceA.

Instances are similar to Functor, e.g. given a data type

 data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)

a suitable instance would be

 instance Traversable Tree where
    traverse f Empty = pure Empty
    traverse f (Leaf x) = Leaf <$> f x
    traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r

This is suitable even for abstract types, as the laws for <*> imply a form of associativity.

The superclass instances should satisfy the following:

In the Functor instance, fmap should be equivalent to traversal with the identity applicative functor (fmapDefault).
In the Foldable instance, Data.Foldable.foldMap should be equivalent to traversal with a constant applicative functor (foldMapDefault).

Methods

traverse :: Applicative f => (a -> f b) -> t a -> f (t b)Source

Map each element of a structure to an action, evaluate these actions from left to right, and collect the results.

sequenceA :: Applicative f => t (f a) -> f (t a)Source

Evaluate each action in the structure from left to right, and collect the results.

mapM :: Monad m => (a -> m b) -> t a -> m (t b)Source

Map each element of a structure to a monadic action, evaluate these actions from left to right, and collect the results.

sequence :: Monad m => t (m a) -> m (t a)Source

Evaluate each monadic action in the structure from left to right, and collect the results.

Instances

Traversable []
Traversable Maybe
Ix i => Traversable (Array i)

for :: (Traversable t, Applicative f) => t a -> (a -> f b) -> f (t b)Source

for is traverse with its arguments flipped.

forM :: (Traversable t, Monad m) => t a -> (a -> m b) -> m (t b)Source

forM is mapM with its arguments flipped.

mapAccumL :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c)Source

The mapAccumL function behaves like a combination of fmap and foldl; it applies a function to each element of a structure, passing an accumulating parameter from left to right, and returning a final value of this accumulator together with the new structure.

mapAccumR :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c)Source

The mapAccumR function behaves like a combination of fmap and foldr; it applies a function to each element of a structure, passing an accumulating parameter from right to left, and returning a final value of this accumulator together with the new structure.

fmapDefault :: Traversable t => (a -> b) -> t a -> t bSource

This function may be used as a value for fmap in a Functor instance, provided that traverse is defined. (Using fmapDefault with a Traversable instance defined only by sequenceA will result in infinite recursion.)

foldMapDefault :: (Traversable t, Monoid m) => (a -> m) -> t a -> mSource

This function may be used as a value for Data.Foldable.foldMap in a Foldable instance.