Iteration of Conjunctive Statements

Abstract

In our preceding treatment of iteration, we have considered the situation where the body of the iteration is either monotonic or continuous. In this chapter, we look at some of the additional properties that iterative statements have when the bodies are conjunctive. We show how weak and strong iteration are related in this case. We also prove two important properties that hold for iterations of conjunctive predicate transformers: the decomposition property, which shows how iteration of a meet can be rewritten in terms of iteration and sequential composition only, and the leapfrog property. The chapter also gives examples of program transformations that are used to modify the control structure of program statements.