+{-# LANGUAGE CPP #-}
+
-----------------------------------------------------------------------------
-- |
-- Module : Data.Traversable
-- Copyright : Conor McBride and Ross Paterson 2005
-- License : BSD-style (see the LICENSE file in the distribution)
--
--- Maintainer : ross@soi.city.ac.uk
+-- Maintainer : libraries@haskell.org
-- 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(..),
- fmapDefault,
- foldMapDefault,
- ) where
-
-import Prelude hiding (mapM, sequence)
-import qualified Prelude (mapM)
+ Traversable(..),
+ for,
+ forM,
+ mapAccumL,
+ mapAccumR,
+ fmapDefault,
+ foldMapDefault,
+ ) where
+
+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
+
+#if defined(__GLASGOW_HASKELL__)
+import GHC.Arr
+#elif defined(__HUGS__)
+import Hugs.Array
+#elif defined(__NHC__)
+import Array
+#endif
-- | Functors representing data structures that can be traversed from
-- left to right.
--
-- 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
+-- > 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:
+--
+-- * 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 :: Applicative f => (a -> f b) -> t a -> f (t b)
- traverse f = sequenceA . fmap f
-
- -- | Evaluate each action in the structure from left to right,
- -- and collect the results.
- sequenceA :: Applicative f => t (f a) -> f (t a)
- sequenceA = traverse id
-
- -- | Map each element of a structure to an monadic action, evaluate
- -- these actions from left to right, and collect the results.
- mapM :: Monad m => (a -> m b) -> t a -> m (t b)
- mapM f = unwrapMonad . traverse (WrapMonad . f)
-
- -- | Evaluate each monadic action in the structure from left to right,
- -- and collect the results.
- sequence :: Monad m => t (m a) -> m (t a)
- sequence = mapM id
+ -- | Map each element of a structure to an action, evaluate
+ -- these actions from left to right, and collect the results.
+ traverse :: Applicative f => (a -> f b) -> t a -> f (t b)
+ traverse f = sequenceA . fmap f
+
+ -- | Evaluate each action in the structure from left to right,
+ -- and collect the results.
+ sequenceA :: Applicative f => t (f a) -> f (t a)
+ sequenceA = traverse id
+
+ -- | Map each element of a structure to a monadic action, evaluate
+ -- these actions from left to right, and collect the results.
+ mapM :: Monad m => (a -> m b) -> t a -> m (t b)
+ mapM f = unwrapMonad . traverse (WrapMonad . f)
+
+ -- | Evaluate each monadic action in the structure from left to right,
+ -- and collect the results.
+ sequence :: Monad m => t (m a) -> m (t a)
+ sequence = mapM id
-- instances for Prelude types
instance Traversable Maybe where
- traverse f Nothing = pure Nothing
- traverse f (Just x) = Just <$> f x
+ traverse _ Nothing = pure Nothing
+ traverse f (Just x) = Just <$> f x
instance Traversable [] where
- traverse f = foldr cons_f (pure [])
- where cons_f x ys = (:) <$> f x <*> ys
+ {-# INLINE traverse #-} -- so that traverse can fuse
+ traverse f = Prelude.foldr cons_f (pure [])
+ where cons_f x ys = (:) <$> f x <*> ys
- mapM = Prelude.mapM
+ mapM = Prelude.mapM
instance Ix i => Traversable (Array i) where
- traverse f arr = listArray (bounds arr) <$> traverse f (elems arr)
+ traverse f arr = listArray (bounds arr) `fmap` traverse f (elems arr)
-- general functions
--- | This function may be used as a value for `fmap` in a `Functor` instance.
+-- | '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
+
+-- left-to-right state transformer
+newtype StateL s a = StateL { runStateL :: s -> (s, a) }
+
+instance Functor (StateL s) where
+ fmap f (StateL k) = StateL $ \ s -> let (s', v) = k s in (s', f v)
+
+instance Applicative (StateL s) where
+ pure x = StateL (\ s -> (s, x))
+ StateL kf <*> StateL kv = StateL $ \ s ->
+ let (s', f) = kf s
+ (s'', v) = kv s'
+ in (s'', f v)
+
+-- |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.
+mapAccumL :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c)
+mapAccumL f s t = runStateL (traverse (StateL . flip f) t) s
+
+-- right-to-left state transformer
+newtype StateR s a = StateR { runStateR :: s -> (s, a) }
+
+instance Functor (StateR s) where
+ fmap f (StateR k) = StateR $ \ s -> let (s', v) = k s in (s', f v)
+
+instance Applicative (StateR s) where
+ pure x = StateR (\ s -> (s, x))
+ StateR kf <*> StateR kv = StateR $ \ s ->
+ let (s', v) = kv s
+ (s'', f) = kf s'
+ in (s'', f v)
+
+-- |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.
+mapAccumR :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c)
+mapAccumR f s t = runStateR (traverse (StateR . flip f) t) s
+
+-- | This function may be used as a value for `fmap` in a `Functor`
+-- instance, provided that 'traverse' is defined. (Using
+-- `fmapDefault` with a `Traversable` instance defined only by
+-- 'sequenceA' will result in infinite recursion.)
fmapDefault :: Traversable t => (a -> b) -> t a -> t b
+{-# INLINE fmapDefault #-}
fmapDefault f = getId . traverse (Id . f)
-- | This function may be used as a value for `Data.Foldable.foldMap`
newtype Id a = Id { getId :: a }
instance Functor Id where
- fmap f (Id x) = Id (f x)
+ fmap f (Id x) = Id (f x)
instance Applicative Id where
- pure = Id
- Id f <*> Id x = Id (f x)
+ pure = Id
+ Id f <*> Id x = Id (f x)
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