Encoding Fairness in a Synchronous Concurrent Program Algebra

• Published in: Formal Methods Vol. 10951; pp. 222 - 239
• Main Authors: Hayes, Ian J., Meinicke, Larissa A.
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2018; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Fair Execution; Fairness Properties; Refinement Algebra; Shared-memory Concurrency; Steppe Environment
• ISBN: 9783319955810; 3319955810
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-95582-7_13

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.