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 think the key word in "whether or not a C++ function will change the value of a particular variable" is "will". It is certainly possible to build a compiler that checks whether or not a C++ function is allowed to change the value of a particular variable, you cannot say with certainty that the change is going to happen:

void maybe(int& val) {
    cout << "Should I change value? [Y/N] >";
    string reply;
    cin >> reply;
    if (reply == "Y") {
        val = 42;
    }
}