import Test.QuickCheck
import Lib

propCongruentDifference :: Int -> Int -> Int -> Property
propCongruentDifference a b m =
  m /= 0 ==> isCongruent a b m == ((a - b) `mod` m == 0)

propCongruentSymmetric :: Int -> Int -> Int -> Property
propCongruentSymmetric a b m =
  m /= 0 ==> isCongruent a b m == isCongruent b a m

propCongruentEqualNumbers :: Int -> Int -> Property
propCongruentEqualNumbers a m =
  m /= 0 ==> isCongruent a a m == True


propFilterByPredicateSatisfiesPredicate :: Fun Int Bool -> [Int] -> Bool
propFilterByPredicateSatisfiesPredicate (Fun _ predicate) xs =
  all predicate (filterByPredicate predicate xs)

propFilterByPredicateLength :: Fun Int Bool -> [Int] -> Bool
propFilterByPredicateLength (Fun _ predicate) xs =
  length (filterByPredicate predicate xs) <= length xs

propFilterByPredicateAlwaysTrue :: [Int] -> Bool
propFilterByPredicateAlwaysTrue xs =
  filterByPredicate (\_ -> True) xs == xs

main :: IO ()
main = do
  quickCheck propCongruentDifference
  quickCheck propCongruentSymmetric
  quickCheck propCongruentEqualNumbers

  quickCheck propFilterByPredicateSatisfiesPredicate
  quickCheck propFilterByPredicateLength
  quickCheck propFilterByPredicateAlwaysTrue