Verification of parallel programs with the Owicki-Gries and Rely-Guarantee methods in Isabelle, HOL

Hoare Logic for Parallel Programs

In the following theories a formalization of the Owicki-Gries and the relyguarantee methods is presented. These methods are widely used for correctness proofs of parallel imperative programs with shared variables. We define syntax, semantics and proof rules in Isabelle/HOL. The proof rules also provide for programs parameterized in the number of parallel components. Their correctness w.r.t. the...

Verifying Single and Multi-mutator Garbage Collectors with Owicki-Gries in Isabelle/HOL

Incremental Verification of Owicki/Gries Proof Outlines Using PVS

Verifications of parallel programs are frequently based on automated state-space exploration techniques known as model checking. To avoid state-space explosion problems, theorem proving techniques can be used, for example by manually annotating programs with suitable assertions and using these assertions to prove their correctness (e.g. using the Owicki/Gries theory). We propose a method to sup...

Controlled Owicki-Gries Concurrency: Reasoning about the Preemptible eChronos Embedded Operating System

We introduce a controlled concurrency framework, derived from the Owicki-Gries method, for describing a hardware interface in detail sufficient to support the modelling and verification of small, embedded operating systems (OS’s) whose run-time responsiveness is paramount. Such real-time systems run with interrupts mostly enabled, including during scheduling. That differs from many other succes...

Algebraic Principles for Rely-Guarantee Style Concurrency Verification Tools

We provide simple equational principles for deriving relyguarantee-style inference rules and refinement laws based on idempotent semirings. We link the algebraic layer with concrete models of programs based on languages and execution traces. We have implemented the approach in Isabelle/HOL as a lightweight concurrency verification tool that supports reasoning about the control and data flow of ...