Universität Augsburg Concurrent Kleene Algebra

A concurrent Kleene algebra offers, next to choice and iteration, two composition operators, one that stands for sequential execution and the other for concurrent execution. They are related by an inequational form of the exchange law. We show the applicability of the algebra to a partially-ordered trace model of program execution semantics and demonstrate its usefulness by validating familiar proof rules for sequential programs (Hoare triples) and for concurrent programming (Jones’s rely/guarantee calculus). The latter involves an algebraic notion of invariants; for these the exchange inequation strengthens to an equational distributivity law. Most of our reasoning has been checked by computer.