-----------------------------------------------------------------------------
-- |
-- 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.Generics.Basics (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 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: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 = 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 (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"