    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Data.Tree
    -- Copyright   :  (c) The University of Glasgow 2002
    -- License     :  BSD-style (see the file libraries/base/LICENSE)
    --
    -- Maintainer  :  libraries@haskell.org
    -- Stability   :  experimental
    -- Portability :  portable
    --
    -- Multi-way trees (/aka/ rose 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.Data (Data)
    #endif

    -- | Multi-way trees, also known as /rose 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 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

    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

    -- | Neat 2-dimensional drawing of a forest.
    drawForest :: Forest String -> String
    drawForest  = unlines . map drawTree

    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

    	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:Prelude.foldr squish xs ts

    -- | Lists of nodes at each level of the tree.
    levels :: Tree a -> [[a]]
    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"