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

To make the question more specific I suggest the following set of constraints may have been what the author of the book may have had in mind:

1. Assume the compiler is examining the behavior of a specific function with respect to const-ness of a variable. For correctness a compiler would have to assume (because of aliasing as explained below) if the function called another function the variable is changed, so assumption #1 only applies to code fragments that don't make function calls.
2. Assume the variable isn't modified by an asynchronous or concurrent activity.
3. Assume the compiler is only determining if the variable can be modified, not whether it will be modified. In other words the compiler is only performing static analysis.
4. Assume the compiler is only considering correctly functioning code (not considering array overruns/underruns, bad pointers, etc.)

In the context of compiler design, I think assumptions 1,3,4 make perfect sense in the view of a compiler writer in the context of code gen correctness and/or code optimization. Assumption 2 makes sense in the absence of the volatile keyword. And these assumptions also focus the question enough to make judging a proposed answer much more definitive :-)

Given those assumptions, a key reason why const-ness can't be assumed is due to variable aliasing. The compiler can't know whether another variable points to the const variable. Aliasing could be due to another function in the same compilation unit, in which case the compiler could look across functions and use a call tree to statically determine that aliasing could occur. But if the aliasing is due to a library or other foreign code, then the compiler has no way to know upon function entry whether variables are aliased.

You could argue that if a variable/argument is marked const then it shouldn't be subject to change via aliasing, but for a compiler writer that's pretty risky. It can even be risky for a human programmer to declare a variable const as part of, say a large project where he doesn't know the behavior of the whole system, or the OS, or a library, to really know a variable won't change.