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Weak refinement in Z

Derrick, John and Boiten, Eerke Albert and Bowman, Howard and Steen, Maarten (1997) Weak refinement in Z. In: Bowen, Jonathan P. and Hinchey, Michael G. and Till, David, eds. ZUM '97: The Z Formal Specification Notation 10th International Conference of Z Users. Lecture Notes in Computer Science . Springer, Berlin, Germany, pp. 369-388. ISBN 978-3-540-62717-3. E-ISBN 978-3-540-68490-9. (doi:10.1007/BFb0027298) (KAR id:21516)


An important aspect in the specification of distributed systems is the role of the internal (or unobservable) operation. Such operations are not part of the user interface (i.e. the user cannot invoke them), however, they are essential to our understanding and correct modelling of the system. Various conventions have been employed to model internal operations when specifying distributed systems in Z. If internal operations are distinguished in the specification notation, then refinement needs to deal with internal operations in appropriate ways. However, in the presence of internal operations, standard Z refinement leads to undesirable implementations.

In this paper we present a generalization of Z refinement, called weak refinement, which treats internal operations differently from observable operations when refining a system. We illustrate some of the properties of weak refinement through a specification of a telecommunications protocol.

Item Type: Book section
DOI/Identification number: 10.1007/BFb0027298
Uncontrolled keywords: Refinement; Distributed Systems; Internal Operations; Process Algebras; Concurrency; Z
Subjects: Q Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming,
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Computing
Funders: Engineering and Physical Sciences Research Council (
Depositing User: Eerke Boiten
Date Deposited: 25 Jul 2009 22:14 UTC
Last Modified: 12 Jul 2022 10:39 UTC
Resource URI: (The current URI for this page, for reference purposes)

University of Kent Author Information

Derrick, John.

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Boiten, Eerke Albert.

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Bowman, Howard.

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Steen, Maarten.

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