Simple Set

simpleSet.hs

{-
  Simple version of set data structure.
  Inspired by CSE130 sp18 final.
-}

data Set a = Set (a -> Bool)

showSet :: (Show a) => Set a -> String
showSet _ = "Actually you can't show this because it you will never know what contains here"

instance Show a => Show (Set a) where
  show t = showSet t

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

has :: Set a -> a -> Bool
has (Set s) n = s n

insert :: Eq a => Set a -> a -> Set a
insert s n = if (has s n) then s else Set (\x -> (x == n) || (has s x))  -- prefer this personally
-- insert s n = Set (\x -> (x == n) || (has s x))

remove :: Eq a => Set a -> a -> Set a
remove s n = if not (has s n) then s else Set (\x -> (x /= n) && (has s x))  -- prefer this personally
-- remove s n = Set (\x -> (x /= n) && (has s x))

intersect :: Eq a => Set a -> Set a -> Set a
intersect s1 s2 = Set (\x -> (has s1 x) && (has s2 x))

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