content: {-# LANGUAGE CPP #-}
  #if __GLASGOW_HASKELL__
  {-# LANGUAGE DeriveDataTypeable, StandaloneDeriving #-}
  #endif
  #if __GLASGOW_HASKELL__ >= 703
  {-# LANGUAGE Safe #-}
  #endif
  -----------------------------------------------------------------------------
  -- |
  -- 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
  
  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
  import Control.DeepSeq (NFData(rnf))
  
  #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
      }
  #ifdef __GLASGOW_HASKELL__
    deriving (Eq, Read, Show, Data)
  #else
    deriving (Eq, Read, Show)
  #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
  
  instance NFData a => NFData (Tree a) where
      rnf (Node x ts) = rnf x `seq` rnf 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"
  