import Test.LeanCheck
import Test.LeanCheck.Function

type A = Int

prop_foldlr :: (A -> A -> A) -> A -> [A] -> Bool
prop_foldlr f z xs  =  foldr f z xs == foldl f z xs

-- correct version of the property above
prop_foldlr' :: (A -> A -> A) -> A -> [A] -> Bool
prop_foldlr' f z xs  =  foldl (flip f) z (reverse xs) == foldr f z xs

prop_mapFilter :: (A -> A) -> (A -> Bool) -> [A] -> Bool
prop_mapFilter f p xs  =  filter p (map f xs) == map f (filter p xs)

main :: IO ()
main = do
  check prop_foldlr
  check prop_foldlr'
  check prop_mapFilter