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258 lines
6.7 KiB
Haskell
258 lines
6.7 KiB
Haskell
----------------------------------------------------------------------
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-- |
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-- Module : Zipper
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-- Maintainer : AR
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-- Stability : (stable)
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-- Portability : (portable)
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--
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-- > CVS $Date: 2005/06/11 20:27:05 $
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-- > CVS $Author: aarne $
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-- > CVS $Revision: 1.9 $
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--
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-- Gérard Huet's zipper (JFP 7 (1997)). AR 10\/8\/2001
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-----------------------------------------------------------------------------
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module GF.Data.Zipper (-- * types
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Tr(..),
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Path(..),
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Loc(..),
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-- * basic (original) functions
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leaf,
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goLeft, goRight, goUp, goDown,
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changeLoc,
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changeNode,
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forgetNode,
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-- * added sequential representation
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goAhead,
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goBack,
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-- ** n-ary versions
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goAheadN,
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goBackN,
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-- * added mappings between locations and trees
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loc2tree,
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loc2treeMarked,
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tree2loc,
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goRoot,
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goLast,
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goPosition,
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getPosition,
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keepPosition,
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-- * added some utilities
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traverseCollect,
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scanTree,
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mapTr,
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mapTrM,
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mapPath,
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mapPathM,
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mapLoc,
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mapLocM,
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foldTr,
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foldTrM,
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mapSubtrees,
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mapSubtreesM,
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changeRoot,
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nthSubtree,
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arityTree
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) where
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import GF.Data.Operations
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newtype Tr a = Tr (a,[Tr a]) deriving (Show,Eq)
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data Path a =
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Top
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| Node ([Tr a], (Path a, a), [Tr a])
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deriving Show
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leaf :: a -> Tr a
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leaf a = Tr (a,[])
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newtype Loc a = Loc (Tr a, Path a) deriving Show
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goLeft, goRight, goUp, goDown :: Loc a -> Err (Loc a)
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goLeft (Loc (t,p)) = case p of
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Top -> Bad "left of top"
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Node (l:left, upv, right) -> return $ Loc (l, Node (left,upv,t:right))
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Node _ -> Bad "left of first"
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goRight (Loc (t,p)) = case p of
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Top -> Bad "right of top"
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Node (left, upv, r:right) -> return $ Loc (r, Node (t:left,upv,right))
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Node _ -> Bad "right of first"
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goUp (Loc (t,p)) = case p of
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Top -> Bad "up of top"
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Node (left, (up,v), right) ->
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return $ Loc (Tr (v, reverse left ++ (t:right)), up)
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goDown (Loc (t,p)) = case t of
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Tr (v,(t1:trees)) -> return $ Loc (t1,Node ([],(p,v),trees))
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_ -> Bad "down of empty"
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changeLoc :: Loc a -> Tr a -> Err (Loc a)
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changeLoc (Loc (_,p)) t = return $ Loc (t,p)
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changeNode :: (a -> a) -> Loc a -> Loc a
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changeNode f (Loc (Tr (n,ts),p)) = Loc (Tr (f n, ts),p)
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forgetNode :: Loc a -> Err (Loc a)
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forgetNode (Loc (Tr (n,[t]),p)) = return $ Loc (t,p)
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forgetNode _ = Bad $ "not a one-branch tree"
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-- added sequential representation
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-- | a successor function
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goAhead :: Loc a -> Err (Loc a)
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goAhead s@(Loc (t,p)) = case (t,p) of
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(Tr (_,_:_),Node (_,_,_:_)) -> goDown s
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(Tr (_,[]), _) -> upsRight s
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(_, _) -> goDown s
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where
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upsRight t = case goRight t of
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Ok t' -> return t'
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Bad _ -> goUp t >>= upsRight
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-- | a predecessor function
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goBack :: Loc a -> Err (Loc a)
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goBack s@(Loc (t,p)) = case goLeft s of
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Ok s' -> downRight s'
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_ -> goUp s
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where
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downRight s = case goDown s of
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Ok s' -> case goRight s' of
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Ok s'' -> downRight s''
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_ -> downRight s'
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_ -> return s
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-- n-ary versions
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goAheadN :: Int -> Loc a -> Err (Loc a)
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goAheadN i st
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| i < 1 = return st
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| otherwise = goAhead st >>= goAheadN (i-1)
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goBackN :: Int -> Loc a -> Err (Loc a)
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goBackN i st
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| i < 1 = return st
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| otherwise = goBack st >>= goBackN (i-1)
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-- added mappings between locations and trees
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loc2tree :: Loc a -> Tr a
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loc2tree (Loc (t,p)) = case p of
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Top -> t
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Node (left,(p',v),right) ->
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loc2tree (Loc (Tr (v, reverse left ++ (t : right)),p'))
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loc2treeMarked :: Loc a -> Tr (a, Bool)
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loc2treeMarked (Loc (Tr (a,ts),p)) =
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loc2tree (Loc (Tr (mark a, map (mapTr nomark) ts), mapPath nomark p))
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where
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(mark, nomark) = (\a -> (a,True), \a -> (a, False))
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tree2loc :: Tr a -> Loc a
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tree2loc t = Loc (t,Top)
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goRoot :: Loc a -> Loc a
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goRoot = tree2loc . loc2tree
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goLast :: Loc a -> Err (Loc a)
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goLast = rep goAhead where
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rep f s = err (const (return s)) (rep f) (f s)
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goPosition :: [Int] -> Loc a -> Err (Loc a)
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goPosition p = go p . goRoot where
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go [] s = return s
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go (p:ps) s = goDown s >>= apply p goRight >>= go ps
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getPosition :: Loc a -> [Int]
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getPosition = reverse . getp where
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getp (Loc (t,p)) = case p of
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Top -> []
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Node (left,(p',v),_) -> length left : getp (Loc (Tr (v, []),p'))
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keepPosition :: (Loc a -> Err (Loc a)) -> (Loc a -> Err (Loc a))
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keepPosition f s = do
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let p = getPosition s
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s' <- f s
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goPosition p s'
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apply :: Monad m => Int -> (a -> m a) -> a -> m a
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apply n f a = case n of
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0 -> return a
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_ -> f a >>= apply (n-1) f
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-- added some utilities
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traverseCollect :: Path a -> [a]
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traverseCollect p = reverse $ case p of
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Top -> []
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Node (_, (p',v), _) -> v : traverseCollect p'
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scanTree :: Tr a -> [a]
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scanTree (Tr (a,ts)) = a : concatMap scanTree ts
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mapTr :: (a -> b) -> Tr a -> Tr b
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mapTr f (Tr (x,ts)) = Tr (f x, map (mapTr f) ts)
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mapTrM :: Monad m => (a -> m b) -> Tr a -> m (Tr b)
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mapTrM f (Tr (x,ts)) = do
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fx <- f x
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fts <- mapM (mapTrM f) ts
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return $ Tr (fx,fts)
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mapPath :: (a -> b) -> Path a -> Path b
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mapPath f p = case p of
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Node (ts1, (p,v), ts2) ->
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Node (map (mapTr f) ts1, (mapPath f p, f v), map (mapTr f) ts2)
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Top -> Top
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mapPathM :: Monad m => (a -> m b) -> Path a -> m (Path b)
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mapPathM f p = case p of
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Node (ts1, (p,v), ts2) -> do
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ts1' <- mapM (mapTrM f) ts1
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p' <- mapPathM f p
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v' <- f v
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ts2' <- mapM (mapTrM f) ts2
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return $ Node (ts1', (p',v'), ts2')
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Top -> return Top
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mapLoc :: (a -> b) -> Loc a -> Loc b
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mapLoc f (Loc (t,p)) = Loc (mapTr f t, mapPath f p)
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mapLocM :: Monad m => (a -> m b) -> Loc a -> m (Loc b)
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mapLocM f (Loc (t,p)) = do
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t' <- mapTrM f t
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p' <- mapPathM f p
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return $ (Loc (t',p'))
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foldTr :: (a -> [b] -> b) -> Tr a -> b
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foldTr f (Tr (x,ts)) = f x (map (foldTr f) ts)
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foldTrM :: Monad m => (a -> [b] -> m b) -> Tr a -> m b
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foldTrM f (Tr (x,ts)) = do
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fts <- mapM (foldTrM f) ts
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f x fts
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mapSubtrees :: (Tr a -> Tr a) -> Tr a -> Tr a
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mapSubtrees f t = let Tr (x,ts) = f t in Tr (x, map (mapSubtrees f) ts)
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mapSubtreesM :: Monad m => (Tr a -> m (Tr a)) -> Tr a -> m (Tr a)
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mapSubtreesM f t = do
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Tr (x,ts) <- f t
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ts' <- mapM (mapSubtreesM f) ts
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return $ Tr (x, ts')
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-- | change the root without moving the pointer
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changeRoot :: (a -> a) -> Loc a -> Loc a
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changeRoot f loc = case loc of
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Loc (Tr (a,ts),Top) -> Loc (Tr (f a,ts),Top)
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Loc (t, Node (left,pv,right)) -> Loc (t, Node (left,chPath pv,right))
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where
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chPath pv = case pv of
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(Top,a) -> (Top, f a)
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(Node (left,pv,right),v) -> (Node (left, chPath pv,right),v)
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nthSubtree :: Int -> Tr a -> Err (Tr a)
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nthSubtree n (Tr (a,ts)) = ts !? n
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arityTree :: Tr a -> Int
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arityTree (Tr (_,ts)) = length ts
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