Haskell Hierarchical Libraries (base package)ContentsIndex
Data.Traversable
Portabilityportable
Stabilityexperimental
Maintainerross@soi.city.ac.uk
Description

Class of data structures that can be traversed from left to right.

See also Applicative Programming with Effects, by Conor McBride and Ross Paterson, online at http://www.soi.city.ac.uk/~ross/papers/Applicative.html.

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)
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.

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 an 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
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 foldMap in a Foldable instance.
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