X-Git-Url: http://git.megacz.com/?a=blobdiff_plain;f=Data%2FSet.hs;h=04d0100132b30e2b798f1802275bae90a1e4d25c;hb=6b1a36a595eddf1e124529646afdb75c76a9966d;hp=33641de4b0fef9a7b5f37328dd8188350da8c0f1;hpb=7acdd16c9b9058c39ab2aea39e0f2ef879f8f89c;p=haskell-directory.git

diff --git a/Data/Set.hs b/Data/Set.hs
index 33641de..04d0100 100644
--- a/Data/Set.hs
+++ b/Data/Set.hs
@@ -9,10 +9,11 @@
 --
 -- An efficient implementation of sets.
 --
--- This module is intended to be imported @qualified@, to avoid name
--- clashes with "Prelude" functions.  eg.
+-- Since many function names (but not the type name) clash with
+-- "Prelude" names, this module is usually imported @qualified@, e.g.
 --
--- >  import Data.Set as Set
+-- >  import Data.Set (Set)
+-- >  import qualified Data.Set as Set
 --
 -- The implementation of 'Set' is based on /size balanced/ binary trees (or
 -- trees of /bounded balance/) as described by:
@@ -26,7 +27,7 @@
 --	SIAM journal of computing 2(1), March 1973.
 --
 -- Note that the implementation is /left-biased/ -- the elements of a
--- first argument are always perferred to the second, for example in
+-- first argument are always preferred to the second, for example in
 -- 'union' or 'insert'.  Of course, left-biasing can only be observed
 -- when equality is an equivalence relation instead of structural
 -- equality.
@@ -43,6 +44,7 @@ module Data.Set  (
             , null
             , size
             , member
+            , notMember
             , isSubsetOf
             , isProperSubsetOf
             
@@ -77,6 +79,8 @@ module Data.Set  (
             , deleteMax
             , deleteFindMin
             , deleteFindMax
+            , maxView
+            , minView
 
             -- * Conversion
 
@@ -94,26 +98,13 @@ module Data.Set  (
             , showTree
             , showTreeWith
             , valid
-
-	-- * Old interface, DEPRECATED
-	,emptySet,       -- :: Set a
-	mkSet,          -- :: Ord a => [a]  -> Set a
-	setToList,      -- :: Set a -> [a] 
-	unitSet,        -- :: a -> Set a
-	elementOf,      -- :: Ord a => a -> Set a -> Bool
-	isEmptySet,     -- :: Set a -> Bool
-	cardinality,    -- :: Set a -> Int
-	unionManySets,  -- :: Ord a => [Set a] -> Set a
-	minusSet,       -- :: Ord a => Set a -> Set a -> Set a
-	mapSet,         -- :: Ord a => (b -> a) -> Set b -> Set a
-	intersect,      -- :: Ord a => Set a -> Set a -> Set a
-	addToSet,      	-- :: Ord a => Set a -> a -> Set a
-	delFromSet,    	-- :: Ord a => Set a -> a -> Set a
             ) where
 
 import Prelude hiding (filter,foldr,null,map)
 import qualified Data.List as List
+import Data.Monoid (Monoid(..))
 import Data.Typeable
+import Data.Foldable (Foldable(foldMap))
 
 {-
 -- just for testing
@@ -123,6 +114,7 @@ import qualified List
 -}
 
 #if __GLASGOW_HASKELL__
+import Text.Read
 import Data.Generics.Basics
 import Data.Generics.Instances
 #endif
@@ -145,6 +137,15 @@ data Set a    = Tip
 
 type Size     = Int
 
+instance Ord a => Monoid (Set a) where
+    mempty  = empty
+    mappend = union
+    mconcat = unions
+
+instance Foldable Set where
+    foldMap f Tip = mempty
+    foldMap f (Bin _s k l r) = foldMap f l `mappend` f k `mappend` foldMap f r
+
 #if __GLASGOW_HASKELL__
 
 {--------------------------------------------------------------------
@@ -159,6 +160,7 @@ instance (Data a, Ord a) => Data (Set a) where
   toConstr _     = error "toConstr"
   gunfold _ _    = error "gunfold"
   dataTypeOf _   = mkNorepType "Data.Set.Set"
+  dataCast1 f    = gcast1 f
 
 #endif
 
@@ -190,6 +192,10 @@ member x t
                GT -> member x r
                EQ -> True       
 
+-- | /O(log n)/. Is the element not in the set?
+notMember :: Ord a => a -> Set a -> Bool
+notMember x t = not $ member x t
+
 {--------------------------------------------------------------------
   Construction
 --------------------------------------------------------------------}
@@ -298,9 +304,7 @@ unions ts
 union :: Ord a => Set a -> Set a -> Set a
 union Tip t2  = t2
 union t1 Tip  = t1
-union t1 t2
-  | size t1 >= size t2  = hedgeUnion (const LT) (const GT) t1 t2
-  | otherwise           = hedgeUnion (const LT) (const GT) t2 t1
+union t1 t2 = hedgeUnion (const LT) (const GT) t1 t2
 
 hedgeUnion cmplo cmphi t1 Tip 
   = t1
@@ -336,24 +340,32 @@ hedgeDiff cmplo cmphi t (Bin _ x l r)
   Intersection
 --------------------------------------------------------------------}
 -- | /O(n+m)/. The intersection of two sets.
--- Intersection is more efficient on (bigset `intersection` smallset).
+-- Elements of the result come from the first set, so for example
+--
+-- > import qualified Data.Set as S
+-- > data AB = A | B deriving Show
+-- > instance Ord AB where compare _ _ = EQ
+-- > instance Eq AB where _ == _ = True
+-- > main = print (S.singleton A `S.intersection` S.singleton B,
+-- >               S.singleton B `S.intersection` S.singleton A)
+--
+-- prints @(fromList [A],fromList [B])@.
 intersection :: Ord a => Set a -> Set a -> Set a
 intersection Tip t = Tip
 intersection t Tip = Tip
-intersection t1 t2
-  | size t1 >= size t2  = intersect' t1 t2
-  | otherwise           = intersect' t2 t1
-
-intersect' Tip t = Tip
-intersect' t Tip = Tip
-intersect' t (Bin _ x l r)
-  | found     = join x tl tr
-  | otherwise = merge tl tr
-  where
-    (lt,found,gt) = splitMember x t
-    tl            = intersect' lt l
-    tr            = intersect' gt r
-
+intersection t1@(Bin s1 x1 l1 r1) t2@(Bin s2 x2 l2 r2) =
+   if s1 >= s2 then
+      let (lt,found,gt) = splitLookup x2 t1
+          tl            = intersection lt l2
+          tr            = intersection gt r2
+      in case found of
+      Just x -> join x tl tr
+      Nothing -> merge tl tr
+   else let (lt,found,gt) = splitMember x1 t2
+            tl            = intersection l1 lt
+            tr            = intersection r1 gt
+        in if found then join x1 tl tr
+           else merge tl tr
 
 {--------------------------------------------------------------------
   Filter and partition
@@ -512,7 +524,8 @@ instance Ord a => Ord (Set a) where
   Show
 --------------------------------------------------------------------}
 instance Show a => Show (Set a) where
-  showsPrec d s  = showSet (toAscList s)
+  showsPrec p xs = showParen (p > 10) $
+    showString "fromList " . shows (toList xs)
 
 showSet :: (Show a) => [a] -> ShowS
 showSet []     
@@ -527,17 +540,20 @@ showSet (x:xs)
   Read
 --------------------------------------------------------------------}
 instance (Read a, Ord a) => Read (Set a) where
-  readsPrec _ = readParen False $ \ r ->
-            [(fromList xs,t)     | ("{",s) <- lex r,
-                                   (xs,t)  <- readl s]
-      where readl s  = [([],t)   | ("}",t) <- lex s] ++
-                       [(x:xs,u) | (x,t)   <- reads s
-                                 , (xs,u)  <- readl' t]
-            readl' s = [([],t)   | ("}",t) <- lex s] ++
-                       [(x:xs,v) | (",",t) <- lex s
-                                 , (x,u)   <- reads t
-                                 , (xs,v)  <- readl' u]
-    
+#ifdef __GLASGOW_HASKELL__
+  readPrec = parens $ prec 10 $ do
+    Ident "fromList" <- lexP
+    xs <- readPrec
+    return (fromList xs)
+
+  readListPrec = readListPrecDefault
+#else
+  readsPrec p = readParen (p > 10) $ \ r -> do
+    ("fromList",s) <- lex r
+    (xs,t) <- reads s
+    return (fromList xs,t)
+#endif
+
 {--------------------------------------------------------------------
   Typeable/Data
 --------------------------------------------------------------------}
@@ -625,12 +641,18 @@ split x (Bin sy y l r)
 -- | /O(log n)/. Performs a 'split' but also returns whether the pivot
 -- element was found in the original set.
 splitMember :: Ord a => a -> Set a -> (Set a,Bool,Set a)
-splitMember x Tip = (Tip,False,Tip)
-splitMember x (Bin sy y l r)
-  = case compare x y of
-      LT -> let (lt,found,gt) = splitMember x l in (lt,found,join y gt r)
-      GT -> let (lt,found,gt) = splitMember x r in (join y l lt,found,gt)
-      EQ -> (l,True,r)
+splitMember x t = let (l,m,r) = splitLookup x t in
+     (l,maybe False (const True) m,r)
+
+-- | /O(log n)/. Performs a 'split' but also returns the pivot
+-- element that was found in the original set.
+splitLookup :: Ord a => a -> Set a -> (Set a,Maybe a,Set a)
+splitLookup x Tip = (Tip,Nothing,Tip)
+splitLookup x (Bin sy y l r)
+   = case compare x y of
+       LT -> let (lt,found,gt) = splitLookup x l in (lt,found,join y gt r)
+       GT -> let (lt,found,gt) = splitLookup x r in (join y l lt,found,gt)
+       EQ -> (l,Just y,r)
 
 {--------------------------------------------------------------------
   Utility functions that maintain the balance properties of the tree.
@@ -731,6 +753,18 @@ deleteFindMax t
       Bin _ x l r   -> let (xm,r') = deleteFindMax r in (xm,balance x l r')
       Tip           -> (error "Set.deleteFindMax: can not return the maximal element of an empty set", Tip)
 
+-- | /O(log n)/. Retrieves the minimal key of the set, and the set stripped from that element
+-- @fail@s (in the monad) when passed an empty set.
+minView :: Monad m => Set a -> m (a, Set a)
+minView Tip = fail "Set.minView: empty set"
+minView x = return (deleteFindMin x)
+
+-- | /O(log n)/. Retrieves the maximal key of the set, and the set stripped from that element
+-- @fail@s (in the monad) when passed an empty set.
+maxView :: Monad m => Set a -> m (a, Set a)
+maxView Tip = fail "Set.maxView: empty set"
+maxView x = return (deleteFindMax x)
+
 
 {--------------------------------------------------------------------
   [balance x l r] balances two trees with value x.
@@ -1113,72 +1147,3 @@ prop_List :: [Int] -> Bool
 prop_List xs
   = (sort (nub xs) == toList (fromList xs))
 -}
-
-{--------------------------------------------------------------------
-  Old Data.Set compatibility interface
---------------------------------------------------------------------}
-
-{-# DEPRECATED emptySet "Use empty instead" #-}
--- | Obsolete equivalent of 'empty'.
-emptySet :: Set a
-emptySet = empty
-
-{-# DEPRECATED mkSet "Use fromList instead" #-}
--- | Obsolete equivalent of 'fromList'.
-mkSet :: Ord a => [a]  -> Set a
-mkSet = fromList
-
-{-# DEPRECATED setToList "Use elems instead." #-}
--- | Obsolete equivalent of 'elems'.
-setToList :: Set a -> [a] 
-setToList = elems
-
-{-# DEPRECATED unitSet "Use singleton instead." #-}
--- | Obsolete equivalent of 'singleton'.
-unitSet :: a -> Set a
-unitSet = singleton
-
-{-# DEPRECATED elementOf "Use member instead." #-}
--- | Obsolete equivalent of 'member'.
-elementOf :: Ord a => a -> Set a -> Bool
-elementOf = member
-
-{-# DEPRECATED isEmptySet "Use null instead." #-}
--- | Obsolete equivalent of 'null'.
-isEmptySet :: Set a -> Bool
-isEmptySet = null
-
-{-# DEPRECATED cardinality "Use size instead." #-}
--- | Obsolete equivalent of 'size'.
-cardinality :: Set a -> Int
-cardinality = size
-
-{-# DEPRECATED unionManySets "Use unions instead." #-}
--- | Obsolete equivalent of 'unions'.
-unionManySets :: Ord a => [Set a] -> Set a
-unionManySets = unions
-
-{-# DEPRECATED minusSet "Use difference instead." #-}
--- | Obsolete equivalent of 'difference'.
-minusSet :: Ord a => Set a -> Set a -> Set a
-minusSet = difference
-
-{-# DEPRECATED mapSet "Use map instead." #-}
--- | Obsolete equivalent of 'map'.
-mapSet :: (Ord a, Ord b) => (b -> a) -> Set b -> Set a
-mapSet = map
-
-{-# DEPRECATED intersect "Use intersection instead." #-}
--- | Obsolete equivalent of 'intersection'.
-intersect :: Ord a => Set a -> Set a -> Set a
-intersect = intersection
-
-{-# DEPRECATED addToSet "Use 'flip insert' instead." #-}
--- | Obsolete equivalent of @'flip' 'insert'@.
-addToSet :: Ord a => Set a -> a -> Set a
-addToSet = flip insert
-
-{-# DEPRECATED delFromSet "Use `flip delete' instead." #-}
--- | Obsolete equivalent of @'flip' 'delete'@.
-delFromSet :: Ord a => Set a -> a -> Set a
-delFromSet = flip delete