base-4.1.0.0: Basic librariesContentsIndex
Data.Traversable
Portabilityportable
Stabilityexperimental
Maintainerlibraries@haskell.org
Description

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

See also

Note that the functions mapM and sequence generalize Prelude functions of the same names from lists to any Traversable functor. To avoid ambiguity, either import the Prelude hiding these names or qualify uses of these function names with an alias for this module.

Synopsis
class (Functor t, Foldable t) => Traversable t where
traverse :: Applicative f => (a -> f b) -> t a -> f (t b)
sequenceA :: Applicative f => t (f a) -> f (t a)
mapM :: Monad m => (a -> m b) -> t a -> m (t b)
sequence :: Monad m => t (m a) -> m (t a)
for :: (Traversable t, Applicative f) => t a -> (a -> f b) -> f (t b)
forM :: (Traversable t, Monad m) => t a -> (a -> m b) -> m (t b)
mapAccumL :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c)
mapAccumR :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c)
fmapDefault :: Traversable t => (a -> b) -> t a -> t b
foldMapDefault :: (Traversable t, Monoid m) => (a -> m) -> t a -> m
Documentation
class (Functor t, Foldable t) => Traversable t where

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
    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)
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)
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)
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)
Evaluate each monadic action in the structure from left to right, and collect the results.
show/hide Instances
for :: (Traversable t, Applicative f) => t a -> (a -> f b) -> f (t b)
for is traverse with its arguments flipped.
forM :: (Traversable t, Monad m) => t a -> (a -> m b) -> m (t b)
forM is mapM with its arguments flipped.
mapAccumL :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c)
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)
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 b
This function may be used as a value for fmap in a Functor instance.
foldMapDefault :: (Traversable t, Monoid m) => (a -> m) -> t a -> m
This function may be used as a value for Data.Foldable.foldMap in a Foldable instance.
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