Map Function using list implementation haskell

Question

Is there a way to write an implementation of the Haskell map function using list implementation?

I keep getting an error and I do not think I am on the right track. This is what I have:

map' :: (a -> b) -> [a] -> [b]
map' _ [] = []
map' xs ys = [ (x, y) | x <- xs | y <- ys ]

Any help or link that will guide me in the right direction would be much appreciated.

Answer 1

I believe you mean "comprehension", instead of "implementation".

Either way, this would work:

map' f as = [f a | a <- as]
map' (* 2) [1..5]