Formal Analysis of Concurrent Programs

In this thesis, extensions of Kleene algebras are used to develop algebras for rely-guarantee style reasoning about concurrent programs. In addition to these algebras, detailed denotational models are implemented in the interactive theorem prover Isabelle/HOL. Formal soundness proofs link the algebras to their models. This follows a general algebraic approach for developing correct by construction verification tools within Isabelle. In this approach, algebras provide inference rules and abstract principles for reasoning about the control flow of programs, while the concrete models provide laws for reasoning about data flow. This yields a rapid, lightweight approach for the construction of verification and refinement tools. These tools are used to construct a popular example from the literature, via refinement, within the context of a general-purpose interactive theorem proving environment.