Traversable(..),
for,
forM,
+ mapAccumL,
+ mapAccumR,
fmapDefault,
foldMapDefault,
) where
import Data.Foldable (Foldable())
import Data.Monoid (Monoid)
+#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
+-- > 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
-- instances for Prelude types
instance Traversable Maybe where
- traverse f Nothing = pure Nothing
+ traverse _ Nothing = pure Nothing
traverse f (Just x) = Just <$> f x
instance Traversable [] where
+ {-# INLINE traverse #-} -- so that traverse can fuse
traverse f = Prelude.foldr cons_f (pure [])
where cons_f x ys = (:) <$> f x <*> ys
mapM = Prelude.mapM
+instance Ix i => Traversable (Array i) where
+ traverse f arr = listArray (bounds arr) `fmap` traverse f (elems arr)
+
-- general functions
-- | 'for' is 'traverse' with its arguments flipped.
{-# 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)