-- Stability : experimental
-- Portability : portable
--
--- Class of data structures that can be traversed from left to right.
+-- Class of data structures that can be traversed from left to right,
+-- performing an action on each element.
--
--- See also /Applicative Programming with Effects/,
--- by Conor McBride and Ross Paterson, online at
--- <http://www.soi.city.ac.uk/~ross/papers/Applicative.html>.
+-- See also
+--
+-- * /Applicative Programming with Effects/,
+-- by Conor McBride and Ross Paterson, online at
+-- <http://www.soi.city.ac.uk/~ross/papers/Applicative.html>.
+--
+-- * /The Essence of the Iterator Pattern/,
+-- by Jeremy Gibbons and Bruno Oliveira,
+-- in /Mathematically-Structured Functional Programming/, 2006, and online at
+-- <http://web.comlab.ox.ac.uk/oucl/work/jeremy.gibbons/publications/#iterator>.
+--
+-- 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.
module Data.Traversable (
Traversable(..),
+ for,
+ forM,
fmapDefault,
foldMapDefault,
) where
-import Prelude hiding (mapM, sequence)
-import qualified Prelude (mapM)
+import Prelude hiding (mapM, sequence, foldr)
+import qualified Prelude (mapM, foldr)
import Control.Applicative
-import Data.Foldable (Foldable)
+import Data.Foldable (Foldable())
import Data.Monoid (Monoid)
import Data.Array
-- 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').
+--
class (Functor t, Foldable t) => Traversable t where
-- | Map each element of a structure to an action, evaluate
-- these actions from left to right, and collect the results.
traverse f (Just x) = Just <$> f x
instance Traversable [] where
- traverse f = foldr cons_f (pure [])
+ traverse f = Prelude.foldr cons_f (pure [])
where cons_f x ys = (:) <$> f x <*> ys
mapM = Prelude.mapM
-- general functions
+-- | 'for' is 'traverse' with its arguments flipped.
+for :: (Traversable t, Applicative f) => t a -> (a -> f b) -> f (t b)
+{-# INLINE for #-}
+for = flip traverse
+
+-- | 'forM' is 'mapM' with its arguments flipped.
+forM :: (Traversable t, Monad m) => t a -> (a -> m b) -> m (t b)
+{-# INLINE forM #-}
+forM = flip mapM
+
-- | This function may be used as a value for `fmap` in a `Functor` instance.
fmapDefault :: Traversable t => (a -> b) -> t a -> t b
fmapDefault f = getId . traverse (Id . f)