Owicki/Gries in Isabelle/HOL

Abstract

Abstract. We present a formalization of the Gries/Owicki method for correctness proofs of concurrent imperative programs with shared variables in the theorem prover Isabelle/HOL. Syntax, semantics and proof rules are defined in higher-order logic. The correctness of the proof rules w.r.t. the semantics is proved. The verification of some typical example programs like producer/consumer is presented.

Incremental Verification of Owicki/Gries Proof Outlines Using PVS

“…On a current desktop computer, each example required less than a minute of time. Our results are better than the ones in [PN02,NPN99], e.g. for the ticket algorithm they require human intervention to provide explicit case distinctions.…”

“…The most-related work is [PN02,NPN99], in which the Owicki/Gries theory is formalized in the Isabelle [Pau94] theorem prover. This work has nice theoretical aspects.…”

The Rely-Guarantee Method in Isabelle/HOL

“…From the theorem prover angle, much work has been done on formalizing different concurrency paradigms like UNITY, CSP, CCS or TLA among others (see [8] for a list of references). Remarkable formalizations for compositional approaches are [2,9] for the UNITY framework in Isabelle/HOL and the soundness proof of McMillan assume-guarantee rule [6] in PVS [12].…”

“…In [10] we proved that the extended Owicki-Gries system of [8] is complete for parameterized programs. Using this result, we prove completeness of the rely-guarantee system for parameterized programs by reduction.…”

“…The rely-guarantee method can be considered as a reformulation of the classical non-compositional Owicki-Gries method (also formalized in Isabelle/HOL [8]). To apply the Owicki-Gries method, programs have to be annotated with an assertion at every point of interference.…”