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|
----------------------------------------------------------------------
-- |
-- Module : Zipper
-- Maintainer : AR
-- Stability : (stable)
-- Portability : (portable)
--
-- > CVS $Date: 2005/02/24 11:46:36 $
-- > CVS $Author: peb $
-- > CVS $Revision: 1.7 $
--
-- Gérard Huet's zipper (JFP 7 (1997)). AR 10\/8\/2001
-----------------------------------------------------------------------------
module Zipper (-- * types
Tr(..),
Path(..),
Loc(..),
-- * basic (original) functions
leaf,
goLeft, goRight, goUp, goDown,
changeLoc,
changeNode,
forgetNode,
-- * added sequential representation
goAhead,
goBack,
-- ** n-ary versions
goAheadN,
goBackN,
-- * added mappings between locations and trees
loc2tree,
loc2treeMarked,
tree2loc,
goRoot,
goLast,
goPosition,
-- * added some utilities
traverseCollect,
scanTree,
mapTr,
mapTrM,
mapPath,
mapPathM,
mapLoc,
mapLocM,
foldTr,
foldTrM,
mapSubtrees,
mapSubtreesM,
changeRoot,
nthSubtree,
arityTree
) where
import Operations
newtype Tr a = Tr (a,[Tr a]) deriving (Show,Eq)
data Path a =
Top
| Node ([Tr a], (Path a, a), [Tr a])
deriving Show
leaf :: a -> Tr a
leaf a = Tr (a,[])
newtype Loc a = Loc (Tr a, Path a) deriving Show
goLeft, goRight, goUp, goDown :: Loc a -> Err (Loc a)
goLeft (Loc (t,p)) = case p of
Top -> Bad "left of top"
Node (l:left, upv, right) -> return $ Loc (l, Node (left,upv,t:right))
Node _ -> Bad "left of first"
goRight (Loc (t,p)) = case p of
Top -> Bad "right of top"
Node (left, upv, r:right) -> return $ Loc (r, Node (t:left,upv,right))
Node _ -> Bad "right of first"
goUp (Loc (t,p)) = case p of
Top -> Bad "up of top"
Node (left, (up,v), right) ->
return $ Loc (Tr (v, reverse left ++ (t:right)), up)
goDown (Loc (t,p)) = case t of
Tr (v,(t1:trees)) -> return $ Loc (t1,Node ([],(p,v),trees))
_ -> Bad "down of empty"
changeLoc :: Loc a -> Tr a -> Err (Loc a)
changeLoc (Loc (_,p)) t = return $ Loc (t,p)
changeNode :: (a -> a) -> Loc a -> Loc a
changeNode f (Loc (Tr (n,ts),p)) = Loc (Tr (f n, ts),p)
forgetNode :: Loc a -> Err (Loc a)
forgetNode (Loc (Tr (n,[t]),p)) = return $ Loc (t,p)
forgetNode _ = Bad $ "not a one-branch tree"
-- added sequential representation
-- | a successor function
goAhead :: Loc a -> Err (Loc a)
goAhead s@(Loc (t,p)) = case (t,p) of
(Tr (_,_:_),Node (_,_,_:_)) -> goDown s
(Tr (_,[]), _) -> upsRight s
(_, _) -> goDown s
where
upsRight t = case goRight t of
Ok t' -> return t'
Bad _ -> goUp t >>= upsRight
-- | a predecessor function
goBack :: Loc a -> Err (Loc a)
goBack s@(Loc (t,p)) = case goLeft s of
Ok s' -> downRight s'
_ -> goUp s
where
downRight s = case goDown s of
Ok s' -> case goRight s' of
Ok s'' -> downRight s''
_ -> downRight s'
_ -> return s
-- n-ary versions
goAheadN :: Int -> Loc a -> Err (Loc a)
goAheadN i st
| i < 1 = return st
| otherwise = goAhead st >>= goAheadN (i-1)
goBackN :: Int -> Loc a -> Err (Loc a)
goBackN i st
| i < 1 = return st
| otherwise = goBack st >>= goBackN (i-1)
-- added mappings between locations and trees
loc2tree :: Loc a -> Tr a
loc2tree (Loc (t,p)) = case p of
Top -> t
Node (left,(p',v),right) ->
loc2tree (Loc (Tr (v, reverse left ++ (t : right)),p'))
loc2treeMarked :: Loc a -> Tr (a, Bool)
loc2treeMarked (Loc (Tr (a,ts),p)) =
loc2tree (Loc (Tr (mark a, map (mapTr nomark) ts), mapPath nomark p))
where
(mark, nomark) = (\a -> (a,True), \a -> (a, False))
tree2loc :: Tr a -> Loc a
tree2loc t = Loc (t,Top)
goRoot :: Loc a -> Loc a
goRoot = tree2loc . loc2tree
goLast :: Loc a -> Err (Loc a)
goLast = rep goAhead where
rep f s = err (const (return s)) (rep f) (f s)
goPosition :: [Int] -> Loc a -> Err (Loc a)
goPosition p = go p . goRoot where
go [] s = return s
go (p:ps) s = goDown s >>= apply p goRight >>= go ps
apply :: Monad m => Int -> (a -> m a) -> a -> m a
apply n f a = case n of
0 -> return a
_ -> f a >>= apply (n-1) f
-- added some utilities
traverseCollect :: Path a -> [a]
traverseCollect p = reverse $ case p of
Top -> []
Node (_, (p',v), _) -> v : traverseCollect p'
scanTree :: Tr a -> [a]
scanTree (Tr (a,ts)) = a : concatMap scanTree ts
mapTr :: (a -> b) -> Tr a -> Tr b
mapTr f (Tr (x,ts)) = Tr (f x, map (mapTr f) ts)
mapTrM :: Monad m => (a -> m b) -> Tr a -> m (Tr b)
mapTrM f (Tr (x,ts)) = do
fx <- f x
fts <- mapM (mapTrM f) ts
return $ Tr (fx,fts)
mapPath :: (a -> b) -> Path a -> Path b
mapPath f p = case p of
Node (ts1, (p,v), ts2) ->
Node (map (mapTr f) ts1, (mapPath f p, f v), map (mapTr f) ts2)
Top -> Top
mapPathM :: Monad m => (a -> m b) -> Path a -> m (Path b)
mapPathM f p = case p of
Node (ts1, (p,v), ts2) -> do
ts1' <- mapM (mapTrM f) ts1
p' <- mapPathM f p
v' <- f v
ts2' <- mapM (mapTrM f) ts2
return $ Node (ts1', (p',v'), ts2')
Top -> return Top
mapLoc :: (a -> b) -> Loc a -> Loc b
mapLoc f (Loc (t,p)) = Loc (mapTr f t, mapPath f p)
mapLocM :: Monad m => (a -> m b) -> Loc a -> m (Loc b)
mapLocM f (Loc (t,p)) = do
t' <- mapTrM f t
p' <- mapPathM f p
return $ (Loc (t',p'))
foldTr :: (a -> [b] -> b) -> Tr a -> b
foldTr f (Tr (x,ts)) = f x (map (foldTr f) ts)
foldTrM :: Monad m => (a -> [b] -> m b) -> Tr a -> m b
foldTrM f (Tr (x,ts)) = do
fts <- mapM (foldTrM f) ts
f x fts
mapSubtrees :: (Tr a -> Tr a) -> Tr a -> Tr a
mapSubtrees f t = let Tr (x,ts) = f t in Tr (x, map (mapSubtrees f) ts)
mapSubtreesM :: Monad m => (Tr a -> m (Tr a)) -> Tr a -> m (Tr a)
mapSubtreesM f t = do
Tr (x,ts) <- f t
ts' <- mapM (mapSubtreesM f) ts
return $ Tr (x, ts')
-- | change the root without moving the pointer
changeRoot :: (a -> a) -> Loc a -> Loc a
changeRoot f loc = case loc of
Loc (Tr (a,ts),Top) -> Loc (Tr (f a,ts),Top)
Loc (t, Node (left,pv,right)) -> Loc (t, Node (left,chPath pv,right))
where
chPath pv = case pv of
(Top,a) -> (Top, f a)
(Node (left,pv,right),v) -> (Node (left, chPath pv,right),v)
nthSubtree :: Int -> Tr a -> Err (Tr a)
nthSubtree n (Tr (a,ts)) = ts !? n
arityTree :: Tr a -> Int
arityTree (Tr (_,ts)) = length ts
|
