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

-- Implementing sets by a list of elements:
data Set a = Set [a]
 deriving Show

empty :: Set a
empty = Set []

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

isElem :: Eq a => a -> Set a -> Bool
isElem x (Set xs) = x `elem` xs

union :: Eq a => Set a -> Set a -> Set a
union (Set [])     s2 = s2
union (Set (x:xs)) s2 = insert x (union (Set xs) s2)
-- > quadratic complexity w.r.t. size of the first set!