Implement reverse in Haskell that runs in linear time

Question

I'm just learning Haskell, so sorry if my question is stupid. I'm reading learnyouahaskell.com and now I'm at chapter 5 "Recursion". There's an example of implementation of standard 'reverse' function:

reverse' :: [a] -> [a]  
reverse' [] = []  
reverse' (x:xs) = reverse' xs ++ [x]  

But it seems that it runs in O(N^2) time, while the standard reverse runs in O(N) (I hope so). The following code illustrates this:

sum (reverse [1,2..1000000]) -- runs pretty fast
sum (reverse' [1,2..1000000]) -- never finishes

So, I started thinking how to implement my own reverse faster. It's pretty easy to do in imperative languages. Maybe I need some more advanced material from subsequent chapters to do this? Any hints are welcomed.

Answer 1

It can be implemented efficiently using an extra accumulator parameter, like the second parameter of fac in this example:

factorial n = fac n 1
  where
    fac 0 r = r
    fac n r = fac (n-1) (r*n)

If you just want to know how it's done in the standard library, you can also look at the source code.

Answer 2

reverse is defined in the Prelude.

You can implement it as:

reverse = foldl (flip (:)) []