Haskell Language Definition of Traversable


class (Functor t, Foldable t) => Traversable t where
    {-# MINIMAL traverse | sequenceA #-}
    traverse :: Applicative f => (a -> f b) -> t a -> f (t b)
    traverse f = sequenceA . fmap f
    sequenceA :: Applicative f => t (f a) -> f (t a)
    sequenceA = traverse id
    mapM :: Monad m => (a -> m b) -> t a -> m (t b)
    mapM = traverse
    sequence :: Monad m => t (m a) -> m (t a)
    sequence = sequenceA

Traversable structures t are finitary containers of elements a which can be operated on with an effectful "visitor" operation. The visitor function f :: a -> f b performs a side-effect on each element of the structure and traverse composes those side-effects using Applicative. Another way of looking at it is that sequenceA says Traversable structures commute with Applicatives.