quantifiers.hs

first (x,_,_) = x
second (_,y,_) = y
third (_,_,z) = z

filterFirst p x = p (first x)
filterSecond p x = p (second x)
filterThird p x = p (third x)

exists :: Int -> (a -> Bool) -> [(a,a,a)] -> [(a,a,a)]
exists 0 p xs = filter (filterFirst p) xs
exists 1 p xs = filter (filterSecond p) xs
exists 2 p xs = filter (filterThird p) xs

forall :: Eq a => Int -> (a -> Bool) -> [(a,a,a)] -> [(a,a,a)]
forall 0 p xs = do let ys = filter (filterFirst p) xs
                    if ys == xs
                       then xs
                    else []
forall 1 p xs = do let ys = filter (filterSecond p) xs
                    if ys == xs
                       then xs
                    else []
forall 2 p xs = do let ys = filter (filterThird p) xs
                    if ys == xs
                       then xs
                    else []

list = [(1,3,5),(1,5,4),(25,4,16),(1,5,250)]

list2 = exists 0 (< 1) list

list3  = exists 0 (== 1) list
      |: exists 1 (== 5) |: exists 2 (> 100)

-- Composition operator for quantifiers

infixl 0 |:
(|:) :: Eq a => [(a,a,a)] -> ([(a,a,a)] -> [(a,a,a)]) -> [(a,a,a)]
(|:) x f = f x