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(..), (<$>))
+import Control.Monad
+import Data.Monoid (Monoid(..))
+import Data.Sequence (Seq, empty, singleton, (<|), (|>), fromList,
+ ViewL(..), ViewR(..), viewl, viewr)
+import Data.Foldable (Foldable(foldMap), toList)
+import Data.Traversable (Traversable(traverse))
+import Data.Typeable
+
+#ifdef __GLASGOW_HASKELL__
+import Data.Generics.Basics (Data)
+#endif
+
-- | Multi-way trees, also known as /rose trees/.
-data Tree a = Node a (Forest a) -- ^ a value and zero or more child trees.
+data Tree a = Node {
+ rootLabel :: a, -- ^ label value
+ subForest :: Forest a -- ^ zero or more child trees
+ }
#ifndef __HADDOCK__
+# ifdef __GLASGOW_HASKELL__
+ deriving (Eq, Read, Show, Data)
+# else
deriving (Eq, Read, Show)
+# endif
#else /* __HADDOCK__ (which can't figure these out by itself) */
instance Eq a => Eq (Tree a)
instance Read a => Read (Tree a)
instance Show a => Show (Tree a)
+instance Data a => Data (Tree a)
#endif
type Forest a = [Tree a]
+#include "Typeable.h"
+INSTANCE_TYPEABLE1(Tree,treeTc,"Tree")
+
instance Functor Tree where
- fmap = mapTree
+ fmap f (Node x ts) = Node (f x) (map (fmap f) ts)
+
+instance Applicative Tree where
+ pure x = Node x []
+ Node f tfs <*> tx@(Node x txs) =
+ Node (f x) (map (f <$>) txs ++ map (<*> tx) tfs)
-mapTree :: (a -> b) -> (Tree a -> Tree b)
-mapTree f (Node x ts) = Node (f x) (map (mapTree f) ts)
+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
+
+instance Foldable Tree where
+ foldMap f (Node x ts) = f x `mappend` foldMap (foldMap f) ts
-- | Neat 2-dimensional drawing of a tree.
-drawTree :: Show a => Tree a -> String
-drawTree = unlines . draw . mapTree show
+drawTree :: Tree String -> String
+drawTree = unlines . draw
-- | Neat 2-dimensional drawing of a forest.
-drawForest :: Show a => Forest a -> String
+drawForest :: Forest String -> String
drawForest = unlines . map drawTree
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
-
- rsLoop [] = error "rsLoop:Unexpected empty list."
- rsLoop [t] = grp s5 " " (draw t)
- rsLoop (t:ts) = grp s6 s4 (draw t) ++ [s4] ++ rsLoop ts
+draw (Node x ts0) = x : drawSubTrees ts0
+ where drawSubTrees [] = []
+ drawSubTrees [t] =
+ "|" : shift "`- " " " (draw t)
+ drawSubTrees (t:ts) =
+ "|" : shift "+- " "| " (draw t) ++ drawSubTrees ts
- grp fst0 rst = zipWith (++) (fst0:repeat rst)
-
- [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:Prelude.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 = Prelude.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 (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"
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