Data/Tree.hs

    {-# LANGUAGE CPP #-}
    #if __GLASGOW_HASKELL__
    {-# LANGUAGE DeriveDataTypeable, StandaloneDeriving #-}
    #endif
    #if __GLASGOW_HASKELL__ >= 702
    {-# LANGUAGE DeriveGeneric #-}
    #endif
    #if __GLASGOW_HASKELL__ >= 703
    {-# LANGUAGE Trustworthy #-}
    #endif

    #include "containers.h"

    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Data.Tree
    -- Copyright   :  (c) The University of Glasgow 2002
    -- License     :  BSD-style (see the file libraries/base/LICENSE)
    --
    -- Maintainer  :  libraries@haskell.org
    -- Portability :  portable
    --
    -- Multi-way trees (/aka/ rose trees) and forests.
    --
    -----------------------------------------------------------------------------

    module Data.Tree(
        Tree(..), Forest,
        -- * Two-dimensional drawing
        drawTree, drawForest,
        -- * Extraction
        flatten, levels, foldTree,
        -- * Building trees
        unfoldTree, unfoldForest,
        unfoldTreeM, unfoldForestM,
        unfoldTreeM_BF, unfoldForestM_BF,
        ) where

    #if MIN_VERSION_base(4,8,0)
    import Data.Foldable (toList)
    import Control.Applicative (Applicative(..), liftA2)
    #else
    import Control.Applicative (Applicative(..), liftA2, (<$>))
    import Data.Foldable (Foldable(foldMap), toList)
    import Data.Monoid (Monoid(..))
    import Data.Traversable (Traversable(traverse))
    #endif

    import Control.Monad (liftM)
    import Data.Sequence (Seq, empty, singleton, (<|), (|>), fromList,
                ViewL(..), ViewR(..), viewl, viewr)
    import Data.Typeable
    import Control.DeepSeq (NFData(rnf))

    #ifdef __GLASGOW_HASKELL__
    import Data.Data (Data)
    #endif
    #if __GLASGOW_HASKELL__ >= 706
    import GHC.Generics (Generic, Generic1)
    #elif __GLASGOW_HASKELL__ >= 702
    import GHC.Generics (Generic)
    #endif

    #if MIN_VERSION_base(4,4,0)
    import Control.Monad.Zip (MonadZip (..))
    #endif

    #if MIN_VERSION_base(4,8,0)
    import Data.Coerce
    #endif

    #if MIN_VERSION_base(4,9,0)
    import Data.Functor.Classes
    import Data.Semigroup (Semigroup (..))
    #endif

    #if !MIN_VERSION_base(4,8,0)
    import Data.Functor ((<$))
    #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__
    #if __GLASGOW_HASKELL__ >= 706
      deriving (Eq, Read, Show, Data, Generic, Generic1)
    #elif __GLASGOW_HASKELL__ >= 702
      deriving (Eq, Read, Show, Data, Generic)
    #else
      deriving (Eq, Read, Show, Data)
    #endif
    #else
      deriving (Eq, Read, Show)
    #endif
    type Forest a = [Tree a]

    #if MIN_VERSION_base(4,9,0)
    instance Eq1 Tree where
      liftEq eq = leq
        where
          leq (Node a fr) (Node a' fr') = eq a a' && liftEq leq fr fr'

    instance Ord1 Tree where
      liftCompare cmp = lcomp
        where
          lcomp (Node a fr) (Node a' fr') = cmp a a' <> liftCompare lcomp fr fr'

    instance Show1 Tree where
      liftShowsPrec shw shwl p (Node a fr) = showParen (p > 10) $
            showString "Node {rootLabel = " . shw 0 a . showString ", " .
              showString "subForest = " . liftShowList shw shwl fr .
              showString "}"

    instance Read1 Tree where
      liftReadsPrec rd rdl p = readParen (p > 10) $
        \s -> do
          ("Node", s1) <- lex s
          ("{", s2) <- lex s1
          ("rootLabel", s3) <- lex s2
          ("=", s4) <- lex s3
          (a, s5) <- rd 0 s4
          (",", s6) <- lex s5
          ("subForest", s7) <- lex s6
          ("=", s8) <- lex s7
          (fr, s9) <- liftReadList rd rdl s8
          ("}", s10) <- lex s9
          pure (Node a fr, s10)
    #endif

    INSTANCE_TYPEABLE1(Tree)

    instance Functor Tree where
        fmap = fmapTree
        x <$ Node _ ts = Node x (map (x <$) ts)

    fmapTree :: (a -> b) -> Tree a -> Tree b
    fmapTree f (Node x ts) = Node (f x) (map (fmapTree f) ts)
    #if MIN_VERSION_base(4,8,0)
    -- Safe coercions were introduced in 4.7.0, but I am not sure if they played
    -- well enough with RULES to do what we want.
    {-# NOINLINE [1] fmapTree #-}
    {-# RULES
    "fmapTree/coerce" fmapTree coerce = coerce
     #-}
    #endif

    instance Applicative Tree where
        pure x = Node x []
        Node f tfs <*> tx@(Node x txs) =
            Node (f x) (map (f <$>) txs ++ map (<*> tx) tfs)
    #if MIN_VERSION_base(4,10,0)
        liftA2 f (Node x txs) ty@(Node y tys) =
            Node (f x y) (map (f x <$>) tys ++ map (\tx -> liftA2 f tx ty) txs)
    #endif
        Node x txs <* ty@(Node _ tys) =
            Node x (map (x <$) tys ++ map (<* ty) txs)
        Node _ txs *> ty@(Node y tys) =
            Node y (tys ++ map (*> ty) txs)

    instance Monad Tree where
        return = pure
        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) = liftA2 Node (f x) (traverse (traverse f) ts)

    instance Foldable Tree where
        foldMap f (Node x ts) = f x `mappend` foldMap (foldMap f) ts

    #if MIN_VERSION_base(4,8,0)
        null _ = False
        {-# INLINE null #-}
        toList = flatten
        {-# INLINE toList #-}
    #endif

    instance NFData a => NFData (Tree a) where
        rnf (Node x ts) = rnf x `seq` rnf ts

    #if MIN_VERSION_base(4,4,0)
    instance MonadZip Tree where
      mzipWith f (Node a as) (Node b bs)
        = Node (f a b) (mzipWith (mzipWith f) as bs)

      munzip (Node (a, b) ts) = (Node a as, Node b bs)
        where (as, bs) = munzip (map munzip ts)
    #endif

    -- | 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) = lines 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]

    -- | Catamorphism on trees.
    foldTree :: (a -> [b] -> b) -> Tree a -> b
    foldTree f = go where
        go (Node x ts) = f x (map go ts)

    -- | 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
    unfoldForestM :: Monad m => (b -> m (a, [b])) -> [b] -> m (Forest a)
    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"