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:
Functor instance, fmap should be equivalent to traversal with the identity applicative functor (fmapDefault).Foldable instance, 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.
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.
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