--
-- 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:
, deleteMax
, deleteFindMin
, deleteFindMax
+ , maxView
+ , minView
-- * Conversion
, 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)
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 (Set a, a)
+minView Tip = fail "Set.minView: empty set"
+minView x = return (swap $ 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 (Set a, a)
+maxView Tip = fail "Set.maxView: empty set"
+maxView x = return (swap $ deleteFindMax x)
+
+swap (a,b) = (b,a)
+
+
{--------------------------------------------------------------------
[balance x l r] balances two trees with value x.
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