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%
% (c) The AQUA Project, Glasgow University, 1994-1995
%
\section[Set]{An implementation of sets}
This new (94/04) implementation of sets sits squarely upon our
implementation of @FiniteMaps@. The interface is (roughly?) as
before.
(95/08: This module is no longer part of the GHC compiler proper; it
is now just a GHC library module).
\begin{code}
module Set (
Set, -- abstract
-- instance of: Eq
emptySet, -- :: Set a
mkSet, -- :: Ord a => [a] -> Set a
setToList, -- :: Set a -> [a]
unitSet, -- :: a -> Set a
singletonSet, -- :: a -> Set a
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
elementOf, -- :: Ord a => a -> Set a -> Bool
isEmptySet, -- :: Set a -> Bool
cardinality -- :: Set a -> Int
) where
import FiniteMap
import Maybe
\end{code}
\begin{code}
-- 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 ())
singletonSet = unitSet -- old;deprecated.
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)
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
-}
\end{code}
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