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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}