X-Git-Url: http://git.megacz.com/?a=blobdiff_plain;f=Data%2FTree.hs;h=fec58569b2fc39148b90a7dd08b502c3c46933ff;hb=fcfae9ff37f58672a139c5e214d3cff4b91d1eda;hp=763afa702ace1ce5c6334682c1a8cfc41bf412fe;hpb=e6492fce6f70270acda18b5747f408d3add29724;p=haskell-directory.git

diff --git a/Data/Tree.hs b/Data/Tree.hs
index 763afa7..fec5856 100644
--- a/Data/Tree.hs
+++ b/Data/Tree.hs
@@ -10,63 +10,150 @@
 --
 -- Multi-way trees (/aka/ rose trees) and forests.
 --
--- Also included are neat presentations for trees and forests.
---
 -----------------------------------------------------------------------------
 
 module Data.Tree(
 	Tree(..), Forest,
+	-- * Two-dimensional drawing
+	drawTree, drawForest,
+	-- * Extraction
 	flatten, levels,
+	-- * Building trees
+	unfoldTree, unfoldForest,
+	unfoldTreeM, unfoldForestM,
+	unfoldTreeM_BF, unfoldForestM_BF,
     ) where
 
+#ifdef __HADDOCK__
+import Prelude
+#endif
+
+import Control.Applicative (Applicative(..))
+import Control.Monad
+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 a (Forest a) -- ^ a value and zero or more child trees.
+data Tree a   = Node {
+		rootLabel :: a,		-- ^ label value
+		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
 
 mapTree              :: (a -> b) -> (Tree a -> Tree b)
 mapTree f (Node x ts) = Node (f x) (map (mapTree f) ts)
 
-instance Show a => Show (Tree a) where
-  show = showTree
-  showList ts s = showForest ts ++ s
-
-showTree :: Show a => Tree a -> String
-showTree  = drawTree . mapTree show
+instance Traversable Tree where
+  traverse f (Node x ts) = Node <$> f x <*> traverse (traverse f) ts
 
-showForest :: Show a => Forest a -> String
-showForest  = unlines . map showTree
+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
 drawTree  = unlines . draw
 
-draw :: Tree String -> [String]
-draw (Node x ts0) = grp this (space (length this)) (stLoop ts0)
- where this          = s1 ++ x ++ " "
-
-       space n       = replicate n ' '
-
-       stLoop []     = [""]
-       stLoop [t]    = grp s2 "  " (draw t)
-       stLoop (t:ts) = grp s3 s4 (draw t) ++ [s4] ++ rsLoop ts
+-- | Neat 2-dimensional drawing of a forest.
+drawForest :: Forest String -> String
+drawForest  = unlines . map drawTree
 
-       rsLoop []     = error "rsLoop:Unexpected empty list."
-       rsLoop [t]    = grp s5 "  " (draw t)
-       rsLoop (t:ts) = grp s6 s4 (draw t) ++ [s4] ++ rsLoop ts
-
-       grp fst0 rst  = zipWith (++) (fst0:repeat rst)
+draw :: Tree String -> [String]
+draw (Node x ts0) = x : drawSubTrees ts0
+  where drawSubTrees [] = []
+	drawSubTrees [t] =
+		"|" : shift "`- " "   " (draw t)
+	drawSubTrees (t:ts) =
+		"|" : shift "+- " "|  " (draw t) ++ drawSubTrees ts
 
-       [s1,s2,s3,s4,s5,s6] = ["- ", "--", "-+", " |", " `", " +"]
+	shift first other = zipWith (++) (first : repeat other)
 
 -- | 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:foldr squish xs ts
 
 -- | Lists of nodes at each level of the tree.
 levels :: Tree a -> [[a]]
-levels t = map (map root) $ takeWhile (not . null) $ iterate subforest [t]
- where root (Node x _) = x
-       subforest f     = [t | Node _ ts <- f, t <- ts]
+levels t = map (map rootLabel) $
+		takeWhile (not . null) $
+		iterate (concatMap subForest) [t]
+
+-- | Build a tree from a seed value
+unfoldTree :: (b -> (a, [b])) -> b -> Tree a
+unfoldTree f b = let (a, bs) = f b in Node a (unfoldForest f bs)
+
+-- | Build a forest from a list of seed values
+unfoldForest :: (b -> (a, [b])) -> [b] -> Forest a
+unfoldForest f = map (unfoldTree f)
+
+-- | Monadic tree builder, in depth-first order
+unfoldTreeM :: Monad m => (b -> m (a, [b])) -> b -> m (Tree a)
+unfoldTreeM f b = do
+	(a, bs) <- f b
+	ts <- unfoldForestM f bs
+	return (Node a ts)
+
+-- | Monadic forest builder, in depth-first order
+#ifndef __NHC__
+unfoldForestM :: Monad m => (b -> m (a, [b])) -> [b] -> m (Forest a)
+#endif
+unfoldForestM f = mapM (unfoldTreeM f)
+
+-- | Monadic tree builder, in breadth-first order,
+-- using an algorithm adapted from
+-- /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 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
+-- /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 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 (|>) 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"