Two Disturbing Divergences

Abstract

At the end of the previous chapter, we charged the reader with an impossible task, viz. to prove, with the Core rules of the Owicki/Gries theory, that the little multiprogram

• Pre: x = 0

• A: x = x + 1

• B: x = x + 1

establishes postcondition x = 2. This impossibility, which we shall prove in a moment, is really disturbing, first, because from an operational point of view it is absolutely obvious that the final state satisfies x = 2, and, second, because it makes us wonder how many other surprises there are in store for us. (To reassure the reader, things will turn out reasonably well.)