Automated Reasoning in Kleene Algebra

It has often been claimed that model checking, special purpose automated deduction or interactive theorem proving are needed for formal program development. We demonstrate that off-the-shelf automated proof and counterexample search is an interesting alternative if combined with the right domain model. We implement variants of Kleene algebras axiomatically in Prover9/Mace4 and perform proof experiments about Hoare, dynamic, temporal logics, concurrency control and termination analysis. They confirm that a simple automated analysis of some important program properties is possible. Particular benefits of this approach include "soft" model checking in a first-order setting, cross-theory reasoning between standard formalisms and full automation of some (co)inductive arguments. Kleene algebras might therefore provide light-weight formal methods with heavy-weight automation.

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