+++ /dev/null
------------------------------------------------------------------------------
--- |
--- 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(..), (<$>))
-import Control.Monad
-import Data.Monoid (Monoid(..))
-import Data.Sequence (Seq, empty, singleton, (<|), (|>), fromList,
- ViewL(..), ViewR(..), viewl, viewr)
-import Data.Foldable (Foldable(foldMap), toList)
-import Data.Traversable (Traversable(traverse))
-import Data.Typeable
-
-#ifdef __GLASGOW_HASKELL__
-import Data.Generics.Basics (Data)
-#endif
-
--- | Multi-way trees, also known as /rose trees/.
-data Tree a = Node {
- rootLabel :: a, -- ^ label value
- subForest :: Forest a -- ^ zero or more child trees
- }
-#ifndef __HADDOCK__
-# ifdef __GLASGOW_HASKELL__
- deriving (Eq, Read, Show, Data)
-# else
- deriving (Eq, Read, Show)
-# endif
-#else /* __HADDOCK__ (which can't figure these out by itself) */
-instance Eq a => Eq (Tree a)
-instance Read a => Read (Tree a)
-instance Show a => Show (Tree a)
-instance Data a => Data (Tree a)
-#endif
-type Forest a = [Tree a]
-
-#include "Typeable.h"
-INSTANCE_TYPEABLE1(Tree,treeTc,"Tree")
-
-instance Functor Tree where
- fmap f (Node x ts) = Node (f x) (map (fmap f) ts)
-
-instance Applicative Tree where
- pure x = Node x []
- Node f tfs <*> tx@(Node x txs) =
- Node (f x) (map (f <$>) 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"
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