-- 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
--
-- or qualify uses of these function names with an alias for this module.
module Data.Traversable (
- Traversable(..),
- for,
- forM,
- fmapDefault,
- foldMapDefault,
- ) where
+ 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.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.
-- ('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 = Prelude.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
{-# 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.
fmapDefault :: Traversable t => (a -> b) -> t a -> t b
fmapDefault f = getId . traverse (Id . f)
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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