set.sh

data Set a = Set (a->Bool)

contains (Set a) x = a x
singletonSet x = Set(\y-> x==y)
union a b = Set(\x -> contains a x || contains b x)
intersect a b = Set(\x -> contains a x && contains b x)

forall s p = 
  let 
    iter i 
      | i < 1000 =  (not (contains s i) || p i) && (iter (i+1))
      | otherwise = True
   in iter (-1000)

exists s p = forall s p || not (forall s (\x-> not (p x)))

map s t = 
  let 
    iter i 
      | i < 1000 = let
        
      | otherwise = True
   in iter (-1000)

main = do
  putStrLn "Hello"
  putStrLn "World"
  --let un = union (singletonSet 1) (singletonSet 2)
  --print (contains un 2)
  --print (contains un 3)

  --let intersected = intersect un (singletonSet 2)
  --print (contains intersected 1)
  --print (contains intersected 2)
  let testS = union (singletonSet 10) (singletonSet 20)
  print (forall testS (\x -> x < 20 || x > 10))
  print (exists testS (\x -> x > 20))