Nonlocal Flow of Control and Kleene Algebra with Tests

Abstract

Kleene algebra with tests (KAT) is an equational system for program verification that combines Kleene algebra (KA), or the algebra of regular expressions, with Boolean algebra. It can model basic programming and verification constructs such as conditional tests, while loops, and Hoare triples, thus providing a relatively simple equational approach to program equivalence and partial correctness. In this paper we show how KAT can be used to give a rigorous equational treatment of control constructs involving nonlocal transfer of control such as unconditional jumps, loop statements with multi-level breaks, and exception handlers. We develop a compositional semantics and a complete equational axiomatization. The approach has some novel technical features, including a treatment of multi-level break statements that is reminiscent of de Bruijn indices in the variable-free lambda calculus. We illustrate the use of the system by giving a purely calculational proof that every deterministic flowchart is equivalent to a loop program with multi-level breaks.