1 -----------------------------------------------------------------------------
4 -- Copyright : (c) The University of Glasgow 2001
5 -- License : BSD-style (see the file libraries/base/LICENSE)
7 -- Maintainer : libraries@haskell.org
8 -- Stability : provisional
9 -- Portability : portable
11 -- An implementation of sets, based on the "Data.FiniteMap".
13 -----------------------------------------------------------------------------
17 Set, -- abstract, instance of: Eq
21 mkSet, -- :: Ord a => [a] -> Set a
22 setToList, -- :: Set a -> [a]
23 unitSet, -- :: a -> Set a
26 elementOf, -- :: Ord a => a -> Set a -> Bool
27 isEmptySet, -- :: Set a -> Bool
28 cardinality, -- :: Set a -> Int
31 union, -- :: Ord a => Set a -> Set a -> Set a
32 unionManySets, -- :: Ord a => [Set a] -> Set a
33 minusSet, -- :: Ord a => Set a -> Set a -> Set a
34 mapSet, -- :: Ord a => (b -> a) -> Set b -> Set a
35 intersect, -- :: Ord a => Set a -> Set a -> Set a
36 addToSet, -- :: Ord a => Set a -> a -> Set a
37 delFromSet, -- :: Ord a => Set a -> a -> Set a
45 -- This can't be a type synonym if you want to use constructor classes.
46 newtype Set a = MkSet (FiniteMap a ())
49 emptySet = MkSet emptyFM
52 unitSet x = MkSet (unitFM x ())
54 setToList :: Set a -> [a]
55 setToList (MkSet set) = keysFM set
57 mkSet :: Ord a => [a] -> Set a
58 mkSet xs = MkSet (listToFM [ (x, ()) | x <- xs])
60 union :: Ord a => Set a -> Set a -> Set a
61 union (MkSet set1) (MkSet set2) = MkSet (plusFM set1 set2)
63 unionManySets :: Ord a => [Set a] -> Set a
64 unionManySets ss = foldr union emptySet ss
66 minusSet :: Ord a => Set a -> Set a -> Set a
67 minusSet (MkSet set1) (MkSet set2) = MkSet (minusFM set1 set2)
69 intersect :: Ord a => Set a -> Set a -> Set a
70 intersect (MkSet set1) (MkSet set2) = MkSet (intersectFM set1 set2)
72 addToSet :: Ord a => Set a -> a -> Set a
73 addToSet (MkSet set) a = MkSet (addToFM set a ())
75 delFromSet :: Ord a => Set a -> a -> Set a
76 delFromSet (MkSet set) a = MkSet (delFromFM set a)
78 elementOf :: Ord a => a -> Set a -> Bool
79 elementOf x (MkSet set) = isJust (lookupFM set x)
81 isEmptySet :: Set a -> Bool
82 isEmptySet (MkSet set) = sizeFM set == 0
84 mapSet :: Ord a => (b -> a) -> Set b -> Set a
85 mapSet f (MkSet set) = MkSet (listToFM [ (f key, ()) | key <- keysFM set ])
87 cardinality :: Set a -> Int
88 cardinality (MkSet set) = sizeFM set
91 instance (Eq a) => Eq (Set a) where
92 (MkSet set_1) == (MkSet set_2) = set_1 == set_2
93 (MkSet set_1) /= (MkSet set_2) = set_1 /= set_2
95 -- but not so clear what the right thing to do is:
97 instance (Ord a) => Ord (Set a) where
98 (MkSet set_1) <= (MkSet set_2) = set_1 <= set_2