Well, it took a little bit of persuasion to let GHC not cache the list(s), but with
fibs :: Int -> Integer fibs k = igo i !! k where i | k < 1000000 = 1 | otherwise = 2 igo :: Integer -> [Integer] igo i = let go = 0 : i : zipWith (+) go (tail go) in go
etc., benchmarking
main :: IO () main = defaultMain $ [ bench "fibs " (whnf fibs 20000) , bench "fibsP" (whnf fibsP 20000) , bench "fibs'" (whnf fibs' 20000) ]
shows a clear difference:
benchmarking fibs mean: 14.50178 ms, lb 14.27410 ms, ub 14.78909 ms, ci 0.950 benchmarking fibsP mean: 13.69060 ms, lb 13.59516 ms, ub 13.81583 ms, ci 0.950 benchmarking fibs' mean: 3.155886 ms, lb 3.137776 ms, ub 3.177367 ms, ci 0.950
Right, I'm not arguing that it's impossible to produce a difference, but I think that if you're defining the sequence of fibs, the most likely scenario might be that you're actually interested in a prefix, and more importantly, you can still, from the outside, force the prefix even if you're only interested in a particular element. The second point, imho, is what makes zipWith inherently different from a function such as foldl'. You can equivalently define zipWith' as a wrapper around zipWith: zipWith' :: (a -> b -> c) -> [a] -> [b] -> [c] zipWith' f xs ys = strictify (zipWith f xs ys) where strictify :: [a] -> [a] strictify [] = [] strictify (x : xs) = x `seq` x : strictify xs You cannot easily do the same for foldl and foldl'. Cheers, Andres