-- Reference/prototype implementation for sets:

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

-- set === characteristic function
data Set a = Set (a -> Bool)

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

empty :: Set a
empty = Set (\e -> False)
        
insert :: Eq a => a -> Set a -> Set a
insert x (Set s) = Set (\y -> x==y || s y)

isElem :: a -> Set a -> Bool
isElem x (Set s) = s x

union :: Set a -> Set a -> Set a
union (Set s1) (Set s2) = Set (\x -> s1 x || s2 x)