Encoding Fairness in a Synchronous Concurrent Program Algebra
Concurrent program refinement algebra provides a suitable basis for supporting mechanised reasoning about shared-memory concurrent programs in a compositional manner, for example, it supports the rely/guarantee approach of Jones. The algebra makes use of a synchronous parallel operator motivated by Aczel’s trace model of concurrency and with similarities to Milner’s SCCS. This paper looks at defining a form of fairness within the program algebra. The encoding allows one to reason about the fair execution of a single process in isolation as well as define fair-parallel in terms of a base parallel operator, of which no fairness properties are assumed. An algebraic theory to support fairness and fair-parallel is developed.
This research was supported Australian Research Council Discovery Grant DP130102901. Thanks are due to Robert Colvin, Rob Van Glabbeek, Peter Höfner, Cliff Jones, and Kirsten Winter, for feedback on ideas presented here. This research has benefited greatly from feedback members of IFIP Working Group 2.3 on Programming Methodology, in particular, at the meeting in Villebrumier.
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