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SML Error: operator and operand don't agree [tycon mismatch]

I'm new to SML and don't quite understand my issue, although I'm certain I'm at fault. First off, here are two short functions I am testing and their descriptions.

MakeInterval - Takes a natural number r, (also used for rp) and a natural number t, and returns the interval [t-r,t+r].

fun MakeInterval(r,rp,t) =
    if r + rp < 0 then []
    else t-r :: MakeInterval(r-1,rp,t);

E.g. MakeInterval(3,3,10) will return [7,8,9,10,11,12,13]. If you have a suggestion for getting rid of rp, please let me know. It's the only way I could think of to keep track of the original value of r while maintaining sorted order.

NotDivisible - Takes a natural number r, a list of natural numbers ts1 and another list of natural numbers ts2. Code using ts2 isn't yet written.

r specifies the lower and upper bounds of the interval, (same as MakeInterval), and ts1 is a list of numbers to be fed into map with the MakeInterval function. 

fun NotDivisible(r, ts1, ts2) = 
    map (fn x => MakeInterval(r,r,x), ts1);

This function should return a list of intervals. E.g. NotDivisible(3, [10,20,30], [2,4,6]) will return (for now) [[7..13], [17..23], [27..33]].

After I get this working, I will begin manipulating these lists to find which numbers out of these intervals are indivisible by any of the numbers in ts2.

But for now, my issue lies with the function definitions as I have them. MakeInterval is defined with no issues and I have tested it on it's own. This is the error I receive when attempting to define NotDivisible:

stdIn:5.33-5.71 Error: operator and operand don't agree [tycon mismatch]
  operator domain: 'Z -> 'Y
  operand:         (int -> int list) * 'X
  in expression:
    map ((fn x => MakeInterval <exp>),ts1)

I've tried specifying all types manually to no avail. Everything makes sense to me logically, but clearly there is a syntax issue here that I am not following.

Solution

  • The issue with the above is the invocation of map, the function is curried

    map : ('a -> 'b) -> 'a list -> 'b list;

    so, a small change to the parentheses:

    fun NotDivisible(r, ts1, ts2) = map (fn x => MakeInterval(r,r,x)) ts1;

    gives you:

    val NotDivisible = fn : int * int list * 'a -> int list list