Using Haskell's map function to calculate the sum of a list

Question

Haskell

addm::[Int]->Int
addm (x:xs) = sum(x:xs)

I was able to achieve to get a sum of a list using sum function but is it possible to get the sum of a list using map function? Also what the use of map function?

Answer 1

You can't really use map to sum up a list, because map treats each list element independently from the others. You can use map for example to increment each value in a list like in

map (+1) [1,2,3,4] -- gives [2,3,4,5]

Another way to implement your addm would be to use foldl:

addm' = foldl (+) 0

Answer 2

Here it is, the supposedly impossible definition of sum in terms of map:

sum' xs  =  let { ys = 0 : map (\(a,b) -> a + b) (zip xs ys) } in last ys

this actually shows how scanl can be implemented in terms of map (and zip and last), the above being equivalent to foldl (+) 0 xs === last $ scanl (+) 0 xs:

scanl' f z xs  =  let { ys = z : map (uncurry f) (zip ys xs) } in ys

I expect one can calculate many things with map, arranging for all kinds of information flow through zip.

edit: the above is just a zipWith in disguise of course (and zipWith is kind of a map2):

sum' xs  =  let { ys = 0 : zipWith (+) ys xs } in last ys

This seems to suggest that scanl is more versatile than foldl.