You are right, the problem is undecidable in general. If the compiler is unsure whether a constraint is satisfied it will have to add a runtime check. This is

You are right, the problem is undecidable in general. If the compiler is unsure whether a constraint is satisfied it will have to add a runtime check. This is similar to the behavior of array accesses in Java: If you access an invalid index the JVM is required to throw an out of bounds exception. In practice this would be unacceptably slow and if the compiler can prove that such an exception can never happen, the check will be removed. As for the "simple" example of testing "y == 0", this is actually already undecidable. If you are interested, you might have a look at Nielson's "Principles of Program Analysis", I think that this particular example (undecidability of MOP Constant Propagation) is worked out there. Also, the book is a nice introduction to the subject.