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

import Test.QuickCheck
    
data Set a = Set (a -> Bool)

empty :: Set a
empty = Set (\_ -> False)

insert :: Eq a => a -> Set a -> Set a
insert x (Set f) = Set (\y -> y==x || f y)
                   
isElem :: a -> Set a -> Bool
isElem x (Set f) = f x

union :: Set a -> Set a -> Set a
union (Set f1) (Set f2) = Set (\x -> f1 x || f2 x)


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

instance Show a => Show (Set a) where
  show _ = "some set"