Abstract
In this paper we explore the relationship between refinement in Object-Z and refinement in CSP. We prove with a simple counter-example that refinement within Object-Z, established using the standard simulation rules, does not imply failures-divergences refinement in CSP. This contradicts accepted results.
Having established that data refinement in Object-Z and failures refinement in CSP are not equivalent we identify alternative refinement orderings that may be used to compare Object-Z classes and CSP processes. When reasoning about concurrent properties we need the strength of the failures-divergences refinement ordering and hence identify equivalent simulation rules for Object-Z. However, when reasoning about sequential properties it is sufficient to work within the simpler relational semantics of Object-Z. We discuss an alternative denotational semantics for CSP, the singleton failures semantic model, which has the same information content as the relational model of Object-Z.
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Bolton, C., Davies, J. (2002). Refinement in Object-Z and CSP. In: Butler, M., Petre, L., Sere, K. (eds) Integrated Formal Methods. IFM 2002. Lecture Notes in Computer Science, vol 2335. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47884-1_13
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DOI: https://doi.org/10.1007/3-540-47884-1_13
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