A singleton failures semantics for Communicating Sequential Processes

This paper defines a new denotational semantics for the language of Communicating Sequential Processes (CSP). The semantics lies between the existing traces and failures models of CSP, providing a treatment of non-determinism in terms of singleton failures. Although the semantics does not represent a congruence upon the full language, it is adequate for sequential tests of non-deterministic processes. This semantics corresponds exactly to a commonly used notion of data refinement in Z and Object-Z: an abstract data type is refined when the corresponding process is refined in terms of singleton failures. The semantics is used to explore the relationship between data refinement and process refinement, and to derive a rule for data refinement that is both sound and complete. Received October 2001 Revised September 2002, February 2003, June 2004 and October 2005 Accepted November 2005 by I. J. Hayes