How can I sum up the values in lists within lists

问题:

As I try to learn Haskell just for fun and the experience I have no other possibility than to ask you the "dumb" questions of a total beginner ^^. I stumbled across the problem how it might be possible to find the sums of lists whithin lists e.g. [[1,3],[4,7],[2,5]] = [4,11,7] and I have found no solution so far. Does anybody have a clue how this might work in Haskell?

回答1:

Think about function types, it may help.

You have [[Int]] and you want a function [[Int]] -> [Int] to get [Int]

The function you want is map sum :: [[Int]] -> [Int]

The following codes was run in ghci

First you have list of list of ints. Note that in this example you need to guide ghci with [[Int]] to get the type you want instead of the confusing generic [[1,3],[4,7],[2,5]] :: Num t => [[t]]

Prelude> let xs = [[1,3],[4,7],[2,5]] :: [[Int]]

Next, you might already know sum, let make one that specific for [Int] instead of generic sum :: (Foldable t, Num a) => t a -> a, this will make the type easier to read

Prelude> let sumInts = sum :: [Int] -> Int

Next, let test the sumInts on some element of xs = [[1,3],[4,7],[2,5]]

Prelude> :t sumInts [1,3]
sumInts [1,3] :: Int
Prelude> sumInts [1,3]
4

Now you can do sum on an element of a list, to do that to entire list you can use map

Prelude> :t map
map :: (a -> b) -> [a] -> [b]

Let see if you pass sumInts to a map what type you will get?

Prelude> :t map sumInts 
map sumInts :: [[Int]] -> [Int]

This should work with xs :: [[Int]] but let check type first to make sure

Prelude> :t map sumInts xs
map sumInts xs :: [Int]

Now do the computation

Prelude> map sumInts xs
[4,11,7]

Since sumInts = sum , this also mean sum would work too

Prelude> :t map sum xs
map sum xs :: [Int]
Prelude> map sum xs
[4,11,7]

Note 1: map sum real type is map sum :: (Foldable t, Num b) => [t b] -> [b]) in the last example it was inferred by type [[Int]] of xs to [[Int]] -> [Int]

回答2:

You can sum a list with sum and you can apply any function to each element of a list with map so the function you are looking for is:

map sum

when you apply the function:

map sum [[1,3],[4,7],[2,5]]

you get your [4,11,7]. What happens is that map walks over the outer list and keeps applying the function that it gets as its first argument (in this case it is the sum function) to every element. At the same time, map collects the results in an output list. So sum is applied to [1,3] with the result 4 to [4,7] with the result 11 and to [2,5] with the result 7, all of which are placed in a list [4,11,7].