Data/Tree.hs

{-# 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"