# SetOrd - module SetOrd...

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Unformatted text preview: module SetOrd (Set(..),emptySet,isEmpty,inSet,subSet,insertSet, deleteSet,powerSet,takeSet,(!!!),list2set) where import List (sort) {-- Sets implemented as ordered lists without duplicates --} newtype Set a = Set [a] deriving (Eq,Ord) instance (Show a) => Show (Set a) where showsPrec _ (Set s) str = showSet s str showSet str = showString "{}" str showSet (x:xs) str = showChar '{' ( shows x ( showl xs str)) where showl str = showChar '}' str showl (x:xs) str = showChar ',' (shows x (showl xs str)) emptySet :: Set a emptySet = Set isEmpty :: Set a -> Bool isEmpty (Set ) = True isEmpty _ = False inSet :: (Ord a) => a -> Set a -> Bool inSet x (Set s) = elem x (takeWhile (<= x) s) subSet :: (Ord a) => Set a -> Set a -> Bool subSet (Set ) _ = True subSet (Set (x:xs)) set = (inSet x set) && subSet (Set xs) set insertSet :: (Ord a) => a -> Set a -> Set a insertSet x (Set s) = Set (insertList x s) insertList x = [x] insertList x ys@(y:ys') = case compare GT -> EQ -> _ -> x y of y : insertList x ys' ys x : ys deleteSet :: Ord a => a -> Set a -> Set a deleteSet x (Set s) = Set (deleteList x s) deleteList x = deleteList x ys@(y:ys') = case compare GT -> EQ -> _ -> x y of y : deleteList x ys' ys' ys list2set :: Ord a => [a] -> Set a list2set = Set list2set (x:xs) = insertSet x (list2set xs) -- list2set xs = Set (foldr insertList xs) powerSet :: Ord a => Set a -> Set (Set a) powerSet (Set xs) = Set (sort (map (\xs -> (list2set xs)) (powerList xs))) powerList powerList powerList :: [a] -> [[a]] = [] (x:xs) = (powerList xs) ++ (map (x:) (powerList xs)) takeSet :: Eq a => Int -> Set a -> Set a takeSet n (Set xs) = Set (take n xs) infixl 9 !!! (!!!) :: Eq a => Set a -> Int -> a (Set xs) !!! n = xs !! n ...
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## This note was uploaded on 11/10/2010 for the course CS 332F taught by Professor Russel during the Spring '10 term at California State University Los Angeles .

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SetOrd - module SetOrd...

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