How to find loop invariant?

Question

I was doing exercise about program verification, and I had some difficulties in finding this loop invariant:

y = 0;
while (y != x) {
    y = y + 1;
}

the precondition is x>=0 and the postcondition is x=y

In the loop there is just one variable so I couldn't think any possible relation that is preserved throughout the program. One weak invariant so far is (y>= 0 && y<=x). So what is the suitable loop invariant for this program?

Answer 1

Let me give you a hint: loop invariants must be expressed in terms of each iteration i . That is, it must be something like " P is true before the execution of every iteration i ". The invariant you've come up with is not expressed as a function of i . Try modifying it a little bit and I think you'll find a more suitable loop invariant.

If you get stuck, I recommend you check out the book title "Discrete Mathematics with Applications", by Susanna Epp; it has a chapter on loop invariants and the book is very gentle for beginners.