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))
42 -- | Multi-way trees, also known as /rose trees/.
44 rootLabel :: a, -- ^ label value
45 subForest :: Forest a -- ^ zero or more child trees
48 deriving (Eq, Read, Show)
49 #else /* __HADDOCK__ (which can't figure these out by itself) */
50 instance Eq a => Eq (Tree a)
51 instance Read a => Read (Tree a)
52 instance Show a => Show (Tree a)
54 type Forest a = [Tree a]
56 INSTANCE_TYPEABLE1(Tree,treeTc,"Tree")
58 instance Functor Tree where
61 mapTree :: (a -> b) -> (Tree a -> Tree b)
62 mapTree f (Node x ts) = Node (f x) (map (mapTree f) ts)
64 instance Traversable Tree where
65 traverse f (Node x ts) = Node <$> f x <*> traverse (traverse f) ts
67 instance Foldable Tree where
68 foldMap f (Node x ts) = f x `mappend` foldMap (foldMap f) ts
70 -- | Neat 2-dimensional drawing of a tree.
71 drawTree :: Tree String -> String
72 drawTree = unlines . draw
74 -- | Neat 2-dimensional drawing of a forest.
75 drawForest :: Forest String -> String
76 drawForest = unlines . map drawTree
78 draw :: Tree String -> [String]
79 draw (Node x ts0) = x : drawSubTrees ts0
80 where drawSubTrees [] = []
82 "|" : shift "`- " " " (draw t)
84 "|" : shift "+- " "| " (draw t) ++ drawSubTrees ts
86 shift first other = zipWith (++) (first : repeat other)
88 -- | The elements of a tree in pre-order.
89 flatten :: Tree a -> [a]
90 flatten t = squish t []
91 where squish (Node x ts) xs = x:foldr squish xs ts
93 -- | Lists of nodes at each level of the tree.
94 levels :: Tree a -> [[a]]
95 levels t = map (map rootLabel) $
96 takeWhile (not . null) $
97 iterate (concatMap subForest) [t]
99 -- | Build a tree from a seed value
100 unfoldTree :: (b -> (a, [b])) -> b -> Tree a
101 unfoldTree f b = let (a, bs) = f b in Node a (unfoldForest f bs)
103 -- | Build a forest from a list of seed values
104 unfoldForest :: (b -> (a, [b])) -> [b] -> Forest a
105 unfoldForest f = map (unfoldTree f)
107 -- | Monadic tree builder, in depth-first order
108 unfoldTreeM :: Monad m => (b -> m (a, [b])) -> b -> m (Tree a)
111 ts <- unfoldForestM f bs
114 -- | Monadic forest builder, in depth-first order
116 unfoldForestM :: Monad m => (b -> m (a, [b])) -> [b] -> m (Forest a)
118 unfoldForestM f = mapM (unfoldTreeM f)
120 -- | Monadic tree builder, in breadth-first order,
121 -- using an algorithm adapted from
122 -- /Breadth-First Numbering: Lessons from a Small Exercise in Algorithm Design/,
123 -- by Chris Okasaki, /ICFP'00/.
124 unfoldTreeM_BF :: Monad m => (b -> m (a, [b])) -> b -> m (Tree a)
125 unfoldTreeM_BF f b = liftM getElement $ unfoldForestQ f (singleton b)
126 where getElement xs = case viewl xs of
128 EmptyL -> error "unfoldTreeM_BF"
130 -- | Monadic forest builder, in breadth-first order,
131 -- using an algorithm adapted from
132 -- /Breadth-First Numbering: Lessons from a Small Exercise in Algorithm Design/,
133 -- by Chris Okasaki, /ICFP'00/.
134 unfoldForestM_BF :: Monad m => (b -> m (a, [b])) -> [b] -> m (Forest a)
135 unfoldForestM_BF f = liftM toList . unfoldForestQ f . fromList
137 -- takes a sequence (queue) of seeds
138 -- produces a sequence (reversed queue) of trees of the same length
139 unfoldForestQ :: Monad m => (b -> m (a, [b])) -> Seq b -> m (Seq (Tree a))
140 unfoldForestQ f aQ = case viewl aQ of
141 EmptyL -> return empty
144 tQ <- unfoldForestQ f (foldl (|>) aQ as)
145 let (tQ', ts) = splitOnto [] as tQ
146 return (Node b ts <| tQ')
147 where splitOnto :: [a'] -> [b'] -> Seq a' -> (Seq a', [a'])
148 splitOnto as [] q = (q, as)
149 splitOnto as (_:bs) q = case viewr q of
150 q' :> a -> splitOnto (a:as) bs q'
151 EmptyR -> error "unfoldForestQ"