module SetsByLists(Set, empty, insert, isElem, union) where

import Test.QuickCheck
    
data Set a = Set [a]
  deriving Show

empty :: Set a
empty = Set []

insert :: Eq a => a -> Set a -> Set a
insert x (Set s) = Set (if x `elem` s then s else x:s)
                   
isElem :: Eq a => a -> Set a -> Bool
isElem x (Set s) = x `elem` s

union :: Eq a => Set a -> Set a -> Set a
union (Set []) s2 = s2
union (Set (x:xs)) s2 = insert x (union (Set xs) s2)


instance (Eq a, Arbitrary a) => Arbitrary (Set a) where
  arbitrary = do xs <- arbitrary
                 return ((foldr :: (a->b->b) -> b -> [a] -> b) insert empty xs)