Lecture Notes on Loop Variants and Convergence

Since not all loops have a fixed finite number of rounds, this axiom isn’t quite sufficient. But that’s similar to the case of box modalities, where we also first understood the elementary axioms reducing programs and later went for a study of loop invariants for while loops with unbounded repetitions. Our key to understanding what to do with [while(Q)α]P formulas is to first understand induction principles for [α∗]P with more general nondeterministic repetitions α∗ of program α, under complete ignorance of the loop guard. We will proceed in similar ways again for diamond properties of while loops.