zipWith with variable number of arguments

DoWeNeedDependentTypes.hs

module Main
    where

-- See "Do We Need Dependent Types?" by Fridlender & Indrika
-- http://www.brics.dk/RS/01/10/

(<<) :: [a -> b] -> [a] -> [b]
(f:fs) << (a:as) = f a : (fs << as)
_ << _           = []

succF :: ([b] -> t) -> [a -> b] -> [a] -> t
succF n fs as = n (fs << as)

zero :: a -> a
zero = id

one :: [a -> b] -> [a] -> [b]
one = succF zero

two :: [a -> a1 -> b] -> [a] -> [a1] -> [b]
two = succF one

three :: [a -> a1 -> a2 -> b] -> [a] -> [a1] -> [a2] -> [b]
three = succF two

four :: [a -> a1 -> a2 -> a3 -> b] -> [a] -> [a1] -> [a2] -> [a3] -> [b]
four = succF three

zipWithN :: ([a] -> t) -> a -> t
zipWithN n f = n (repeat f)

f4 :: Num a => a -> a -> a -> a -> a
f4 a b c d = a + b + c + d

l :: [Integer]
l = zipWithN four f4 [1..] [2..] [3..] [4..]

main :: IO ()
main = print $ take 7 l