import Prelude
#endif
+import Control.Applicative (Applicative(..), (<$>))
import Control.Monad
-import Data.Maybe
-import Data.Queue
+import Data.Monoid (Monoid(..))
+import Data.Sequence (Seq, empty, singleton, (<|), (|>), fromList,
+ ViewL(..), ViewR(..), viewl, viewr)
+import Data.Foldable (Foldable(foldMap), toList)
+import Data.Traversable (Traversable(traverse))
+import Data.Typeable
+
+#ifdef __GLASGOW_HASKELL__
+import Data.Generics.Basics (Data)
+#endif
-- | Multi-way trees, also known as /rose trees/.
data Tree a = Node {
subForest :: Forest a -- ^ zero or more child trees
}
#ifndef __HADDOCK__
+# ifdef __GLASGOW_HASKELL__
+ deriving (Eq, Read, Show, Data)
+# else
deriving (Eq, Read, Show)
+# endif
#else /* __HADDOCK__ (which can't figure these out by itself) */
instance Eq a => Eq (Tree a)
instance Read a => Read (Tree a)
instance Show a => Show (Tree a)
+instance Data a => Data (Tree a)
#endif
type Forest a = [Tree a]
+#include "Typeable.h"
+INSTANCE_TYPEABLE1(Tree,treeTc,"Tree")
+
instance Functor Tree where
- fmap = mapTree
+ fmap f (Node x ts) = Node (f x) (map (fmap f) ts)
+
+instance Applicative Tree where
+ pure x = Node x []
+ Node f tfs <*> tx@(Node x txs) =
+ Node (f x) (map (f <$>) txs ++ map (<*> tx) tfs)
+
+instance Monad Tree where
+ return x = Node x []
+ Node x ts >>= f = Node x' (ts' ++ map (>>= f) ts)
+ where Node x' ts' = f x
+
+instance Traversable Tree where
+ traverse f (Node x ts) = Node <$> f x <*> traverse (traverse f) ts
-mapTree :: (a -> b) -> (Tree a -> Tree b)
-mapTree f (Node x ts) = Node (f x) (map (mapTree f) ts)
+instance Foldable Tree where
+ foldMap f (Node x ts) = f x `mappend` foldMap (foldMap f) ts
-- | Neat 2-dimensional drawing of a tree.
drawTree :: Tree String -> String
-- | The elements of a tree in pre-order.
flatten :: Tree a -> [a]
flatten t = squish t []
- where squish (Node x ts) xs = x:foldr squish xs ts
+ where squish (Node x ts) xs = x:Prelude.foldr squish xs ts
-- | Lists of nodes at each level of the tree.
levels :: Tree a -> [[a]]
#ifndef __NHC__
unfoldForestM :: Monad m => (b -> m (a, [b])) -> [b] -> m (Forest a)
#endif
-unfoldForestM f = mapM (unfoldTreeM f)
+unfoldForestM f = Prelude.mapM (unfoldTreeM f)
-- | Monadic tree builder, in breadth-first order,
-- using an algorithm adapted from
--- /BreadthÂFirst Numbering: Lessons from a Small Exercise in Algorithm Design/,
+-- /Breadth-First Numbering: Lessons from a Small Exercise in Algorithm Design/,
-- by Chris Okasaki, /ICFP'00/.
unfoldTreeM_BF :: Monad m => (b -> m (a, [b])) -> b -> m (Tree a)
-unfoldTreeM_BF f b = liftM (fst . fromJust . deQueue) $
- unfoldForestQ f (listToQueue [b])
+unfoldTreeM_BF f b = liftM getElement $ unfoldForestQ f (singleton b)
+ where getElement xs = case viewl xs of
+ x :< _ -> x
+ EmptyL -> error "unfoldTreeM_BF"
-- | Monadic forest builder, in breadth-first order,
-- using an algorithm adapted from
--- /BreadthÂFirst Numbering: Lessons from a Small Exercise in Algorithm Design/,
+-- /Breadth-First Numbering: Lessons from a Small Exercise in Algorithm Design/,
-- by Chris Okasaki, /ICFP'00/.
unfoldForestM_BF :: Monad m => (b -> m (a, [b])) -> [b] -> m (Forest a)
-unfoldForestM_BF f = liftM (reverseOnto []) . unfoldForestQ f . listToQueue
- where reverseOnto :: [a'] -> Queue a' -> [a']
- reverseOnto as q = case deQueue q of
- Nothing -> as
- Just (a, q') -> reverseOnto (a:as) q'
-
--- takes a queue of seeds
--- produces a queue of trees of the same length, but in the reverse order
-unfoldForestQ :: Monad m => (b -> m (a, [b])) -> Queue b -> m (Queue (Tree a))
-unfoldForestQ f aQ = case deQueue aQ of
- Nothing -> return emptyQueue
- Just (a, aQ) -> do
+unfoldForestM_BF f = liftM toList . unfoldForestQ f . fromList
+
+-- takes a sequence (queue) of seeds
+-- produces a sequence (reversed queue) of trees of the same length
+unfoldForestQ :: Monad m => (b -> m (a, [b])) -> Seq b -> m (Seq (Tree a))
+unfoldForestQ f aQ = case viewl aQ of
+ EmptyL -> return empty
+ a :< aQ -> do
(b, as) <- f a
- tQ <- unfoldForestQ f (foldl addToQueue aQ as)
- let (ts, tQ') = splitOnto [] as tQ
- return (addToQueue tQ' (Node b ts))
- where splitOnto :: [a'] -> [b'] -> Queue a' -> ([a'], Queue a')
- splitOnto as [] q = (as, q)
- splitOnto as (_:bs) q = case fromJust (deQueue q) of
- (a, q') -> splitOnto (a:as) bs q'
+ tQ <- unfoldForestQ f (Prelude.foldl (|>) aQ as)
+ let (tQ', ts) = splitOnto [] as tQ
+ return (Node b ts <| tQ')
+ where splitOnto :: [a'] -> [b'] -> Seq a' -> (Seq a', [a'])
+ splitOnto as [] q = (q, as)
+ splitOnto as (_:bs) q = case viewr q of
+ q' :> a -> splitOnto (a:as) bs q'
+ EmptyR -> error "unfoldForestQ"