Why is it impossible to build a compiler that can determine if a C++ function will change the value of a particular variable?

Question

I read this line in a book:

It is provably impossible to build a compiler that can actually determine whether or not a C++ function will change the val

Answer 1

I don't think it's necessary to invoke the halting problem to explain that you can't algorithmically know at compile time whether a given function will modify a certain variable or not.

Instead, it's sufficient to point out that a function's behavior often depends on run-time conditions, which the compiler can't know about in advance. E.g.

int y;

int main(int argc, char *argv[]) {
   if (argc > 2) y++;
}

How could the compiler predict with certainty whether y will be modified?