base-3.0.2.0: Basic librariesSource codeContentsIndex
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)
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 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
    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:

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.
show/hide Instances
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.
fmapDefault :: Traversable t => (a -> b) -> t a -> t bSource
This function may be used as a value for fmap in a Functor instance.
foldMapDefault :: (Traversable t, Monoid m) => (a -> m) -> t a -> mSource
This function may be used as a value for foldMap in a Foldable instance.
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