Inner Functions With SML NJ

Question

I am a complete newbie to sml and am having trouble with the syntax for inner functions. What I need to do is take a list of a list of ints, average each list, and return a list of reals. This is the psuedo-ish code I have so far.

 fun listAvg [] = 0  
    else (sum (x) div size (x))

        fun sum[] = 0
        | sum(head::rest)= head + sum rest;


        fun size [] = 0
        | size(head::rest) = 1 + size rest;

    listAvg([[1,3,6,8,9], [4,2,6,5,1], [9,5,9,7], [5,4], [3,6,4,8]]); 

any advice would be greatly appreciated. Thanks!

Answer 1

Use a let, as in

fun listAvg [] = 0  
  | listAvg x =
    let
        fun sum[] = 0
          | sum(head::tail)= head + sum tail;
        fun size [] = 0
          | size(head::tail) = 1 + size tail;
     in
         (sum x) div (size x)
     end

You have to pass an int list to this function e.g.

listAvg [1, 2, 3, 4];

This is no change to your code, except to rearrange the order and putting the keywords let, in, and end. If this is not homework, I would recommend using a few built-in standard library functions in the List structure that could reduce this function to two lines, including the pattern match on the empty list.

EDIT:

There are two possible meanings to "average a list of a list of ints." The first is to average each list and then take the average of the averages, and the second is to join the lists together into one long list and take the average over the entire list. The two methods are equivalent (except for rounding errors) when all the lists of ints are of the same length, but as your example shows, they don't have to be the same length.

Since this is homework, I'm not going to give you the answer directly, but consider the following, which might be helpful:

• If you're using the first interpretation of "average a list of a list of ints:" there is a built-in SML function that will let you apply another function to each element of a list, and get the resulting list. This might be helpful for getting the individual averages, which you can then combine together into an overall average.
• If you're using the second interpretation: there is a built-in SML function (it looks like an operator, but many of the things that look like operators in SML are just infix functions) to join two lists together, and a built-in SML function to apply a function to elements going down the list, along with an accumulator value, to generate a single value. You might be able to use those two functions to create one long list of all the numbers, which you can then average.