--
-- 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.Monad
+import Data.Maybe
+import Data.Queue
+
-- | 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__
+ deriving (Eq, Read, Show)
+#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)
+#endif
type Forest a = [Tree a]
instance Functor Tree where
mapTree :: (a -> b) -> (Tree a -> Tree b)
mapTree f (Node x ts) = Node (f x) (map (mapTree f) ts)
--- explicit instance for Haddock's benefit
-instance Eq a => Eq (Tree a) where
- Node x ts == Node x' ts' = x == x' && ts == 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
-
-showForest :: Show a => Forest a -> String
-showForest = unlines . map showTree
-
+-- | 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 ' '
+-- | Neat 2-dimensional drawing of a forest.
+drawForest :: Forest String -> String
+drawForest = unlines . map drawTree
- stLoop [] = [""]
- stLoop [t] = grp s2 " " (draw t)
- stLoop (t:ts) = grp s3 s4 (draw t) ++ [s4] ++ rsLoop ts
-
- 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 (fst . fromJust . deQueue) $
+ unfoldForestQ f (listToQueue [b])
+
+-- | 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 (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
+ (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'