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|
-----------------------------------------------------------------------------
-- |
-- Module : Data.Set
-- Copyright : (c) The University of Glasgow 2001
-- License : BSD-style (see the file libraries/base/LICENSE)
--
-- Maintainer : libraries@haskell.org
-- Stability : provisional
-- Portability : portable
--
-- An implementation of sets, based on the "Data.FiniteMap".
--
-----------------------------------------------------------------------------
module Data.Set (
-- * The @Set@ type
Set, -- abstract, instance of: Eq
-- * Construction
emptySet, -- :: Set a
mkSet, -- :: Ord a => [a] -> Set a
setToList, -- :: Set a -> [a]
unitSet, -- :: a -> Set a
-- * Inspection
elementOf, -- :: Ord a => a -> Set a -> Bool
isEmptySet, -- :: Set a -> Bool
cardinality, -- :: Set a -> Int
-- * Operations
union, -- :: Ord a => Set a -> Set a -> Set a
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
import Data.FiniteMap
import Data.Maybe
-- This can't be a type synonym if you want to use constructor classes.
newtype Set a = MkSet (FiniteMap a ())
emptySet :: Set a
emptySet = MkSet emptyFM
unitSet :: a -> Set a
unitSet x = MkSet (unitFM x ())
setToList :: Set a -> [a]
setToList (MkSet set) = keysFM set
mkSet :: Ord a => [a] -> Set a
mkSet xs = MkSet (listToFM [ (x, ()) | x <- xs])
union :: Ord a => Set a -> Set a -> Set a
union (MkSet set1) (MkSet set2) = MkSet (plusFM set1 set2)
unionManySets :: Ord a => [Set a] -> Set a
unionManySets ss = foldr union emptySet ss
minusSet :: Ord a => Set a -> Set a -> Set a
minusSet (MkSet set1) (MkSet set2) = MkSet (minusFM set1 set2)
intersect :: Ord a => Set a -> Set a -> Set a
intersect (MkSet set1) (MkSet set2) = MkSet (intersectFM set1 set2)
addToSet :: Ord a => Set a -> a -> Set a
addToSet (MkSet set) a = MkSet (addToFM set a ())
delFromSet :: Ord a => Set a -> a -> Set a
delFromSet (MkSet set) a = MkSet (delFromFM set a)
elementOf :: Ord a => a -> Set a -> Bool
elementOf x (MkSet set) = isJust (lookupFM set x)
isEmptySet :: Set a -> Bool
isEmptySet (MkSet set) = sizeFM set == 0
mapSet :: Ord a => (b -> a) -> Set b -> Set a
mapSet f (MkSet set) = MkSet (listToFM [ (f key, ()) | key <- keysFM set ])
cardinality :: Set a -> Int
cardinality (MkSet set) = sizeFM set
-- fair enough...
instance (Eq a) => Eq (Set a) where
(MkSet set_1) == (MkSet set_2) = set_1 == set_2
(MkSet set_1) /= (MkSet set_2) = set_1 /= set_2
-- but not so clear what the right thing to do is:
{- NO:
instance (Ord a) => Ord (Set a) where
(MkSet set_1) <= (MkSet set_2) = set_1 <= set_2
-}
|
