Haskell Matrix Addition/Subtraction

Question

this is what I have for matrix addition in Haskell

    > add :: (Num a) => [[a]] -> [[a]] -> [[a]]
    > add [] [] = [] 
    > add (x:xs) (y:ys) = zipWith (+) x y : add xs ys

add [[1,2], [3,4]] [[5,6], [7,8]] gives me [[6,8],[10,12]]

However, I am trying do with one line instead

    > add :: (Num a) => [[a]] -> [[a]] -> [[a]]
    > add = map ((zipWith (+))

How come the map function doesn't work?

Answer 1

The map function doesn't work here because you're iterating over two lists instead of one. To iterate over two lists in parallel, you use zipWith, just like you are already doing for the inner loop.

Prelude> let add = zipWith (zipWith (+))
Prelude> add [[1, 2], [3, 4]] [[5, 6], [7, 8]]
[[6,8],[10,12]]

Answer 2

map takes in a single list: you're trying to give it two.

Try something like:

add = zipWith (zipWith (+))