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

-- Implementing sets by their characteristic function:
data Set a = Set (a -> Bool)

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

insert :: Eq a => a -> Set a -> Set a
insert x (Set fs) = Set (\y -> y==x || fs y)

isElem :: Eq a => a -> Set a -> Bool
isElem x (Set fs) = fs x

union :: Eq a => Set a -> Set a -> Set a
union (Set fs1) (Set fs2) = Set (\y -> fs1 y || fs2 y)

-- We cannot show functions, thus we provide a trivial instance:
instance Show a => Show (Set a) where
  show _ = "some set"