1 -----------------------------------------------------------------------------
4 -- Copyright : (c) The University of Glasgow 2002
5 -- License : BSD-style (see the file libraries/base/LICENSE)
7 -- Maintainer : libraries@haskell.org
8 -- Stability : experimental
9 -- Portability : portable
11 -- Multi-way trees (/aka/ rose trees) and forests.
13 -----------------------------------------------------------------------------
17 -- * Two-dimensional drawing
22 unfoldTree, unfoldForest,
23 unfoldTreeM, unfoldForestM,
24 unfoldTreeM_BF, unfoldForestM_BF,
31 import Control.Applicative (Applicative(..), (<$>))
33 import Data.Monoid (Monoid(..))
34 import Data.Sequence (Seq, empty, singleton, (<|), (|>), fromList,
35 ViewL(..), ViewR(..), viewl, viewr)
36 import Data.Foldable (Foldable(foldMap), toList)
37 import Data.Traversable (Traversable(traverse))
40 #ifdef __GLASGOW_HASKELL__
41 import Data.Generics.Basics (Data)
44 -- | Multi-way trees, also known as /rose trees/.
46 rootLabel :: a, -- ^ label value
47 subForest :: Forest a -- ^ zero or more child trees
50 # ifdef __GLASGOW_HASKELL__
51 deriving (Eq, Read, Show, Data)
53 deriving (Eq, Read, Show)
55 #else /* __HADDOCK__ (which can't figure these out by itself) */
56 instance Eq a => Eq (Tree a)
57 instance Read a => Read (Tree a)
58 instance Show a => Show (Tree a)
59 instance Data a => Data (Tree a)
61 type Forest a = [Tree a]
64 INSTANCE_TYPEABLE1(Tree,treeTc,"Tree")
66 instance Functor Tree where
67 fmap f (Node x ts) = Node (f x) (map (fmap f) ts)
69 instance Applicative Tree where
71 Node f tfs <*> tx@(Node x txs) =
72 Node (f x) (map (f <$>) txs ++ map (<*> tx) tfs)
74 instance Monad Tree where
76 Node x ts >>= f = Node x' (ts' ++ map (>>= f) ts)
77 where Node x' ts' = f x
79 instance Traversable Tree where
80 traverse f (Node x ts) = Node <$> f x <*> traverse (traverse f) ts
82 instance Foldable Tree where
83 foldMap f (Node x ts) = f x `mappend` foldMap (foldMap f) ts
85 -- | Neat 2-dimensional drawing of a tree.
86 drawTree :: Tree String -> String
87 drawTree = unlines . draw
89 -- | Neat 2-dimensional drawing of a forest.
90 drawForest :: Forest String -> String
91 drawForest = unlines . map drawTree
93 draw :: Tree String -> [String]
94 draw (Node x ts0) = x : drawSubTrees ts0
95 where drawSubTrees [] = []
97 "|" : shift "`- " " " (draw t)
99 "|" : shift "+- " "| " (draw t) ++ drawSubTrees ts
101 shift first other = zipWith (++) (first : repeat other)
103 -- | The elements of a tree in pre-order.
104 flatten :: Tree a -> [a]
105 flatten t = squish t []
106 where squish (Node x ts) xs = x:Prelude.foldr squish xs ts
108 -- | Lists of nodes at each level of the tree.
109 levels :: Tree a -> [[a]]
110 levels t = map (map rootLabel) $
111 takeWhile (not . null) $
112 iterate (concatMap subForest) [t]
114 -- | Build a tree from a seed value
115 unfoldTree :: (b -> (a, [b])) -> b -> Tree a
116 unfoldTree f b = let (a, bs) = f b in Node a (unfoldForest f bs)
118 -- | Build a forest from a list of seed values
119 unfoldForest :: (b -> (a, [b])) -> [b] -> Forest a
120 unfoldForest f = map (unfoldTree f)
122 -- | Monadic tree builder, in depth-first order
123 unfoldTreeM :: Monad m => (b -> m (a, [b])) -> b -> m (Tree a)
126 ts <- unfoldForestM f bs
129 -- | Monadic forest builder, in depth-first order
131 unfoldForestM :: Monad m => (b -> m (a, [b])) -> [b] -> m (Forest a)
133 unfoldForestM f = Prelude.mapM (unfoldTreeM f)
135 -- | Monadic tree builder, in breadth-first order,
136 -- using an algorithm adapted from
137 -- /Breadth-First Numbering: Lessons from a Small Exercise in Algorithm Design/,
138 -- by Chris Okasaki, /ICFP'00/.
139 unfoldTreeM_BF :: Monad m => (b -> m (a, [b])) -> b -> m (Tree a)
140 unfoldTreeM_BF f b = liftM getElement $ unfoldForestQ f (singleton b)
141 where getElement xs = case viewl xs of
143 EmptyL -> error "unfoldTreeM_BF"
145 -- | Monadic forest builder, in breadth-first order,
146 -- using an algorithm adapted from
147 -- /Breadth-First Numbering: Lessons from a Small Exercise in Algorithm Design/,
148 -- by Chris Okasaki, /ICFP'00/.
149 unfoldForestM_BF :: Monad m => (b -> m (a, [b])) -> [b] -> m (Forest a)
150 unfoldForestM_BF f = liftM toList . unfoldForestQ f . fromList
152 -- takes a sequence (queue) of seeds
153 -- produces a sequence (reversed queue) of trees of the same length
154 unfoldForestQ :: Monad m => (b -> m (a, [b])) -> Seq b -> m (Seq (Tree a))
155 unfoldForestQ f aQ = case viewl aQ of
156 EmptyL -> return empty
159 tQ <- unfoldForestQ f (Prelude.foldl (|>) aQ as)
160 let (tQ', ts) = splitOnto [] as tQ
161 return (Node b ts <| tQ')
162 where splitOnto :: [a'] -> [b'] -> Seq a' -> (Seq a', [a'])
163 splitOnto as [] q = (q, as)
164 splitOnto as (_:bs) q = case viewr q of
165 q' :> a -> splitOnto (a:as) bs q'
166 EmptyR -> error "unfoldForestQ"