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Guards, Preconditions, and Refinement in Z

Miarka, Ralph and Boiten, Eerke Albert and Derrick, John (2000) Guards, Preconditions, and Refinement in Z. In: Bowen, Jonathan P. and Dunne, Steve and Galloway, Andy and King, Steve, eds. ZB 2000: Formal Specification and Development in Z and B First International Conference of B and Z Users. Lecture Notes in Computer Science . Springer, Berlin, Germany, pp. 286-303. ISBN 978-3-540-67944-8. E-ISBN 978-3-540-44525-8. (doi:10.1007/3-540-44525-0_17) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:21990)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided.
Official URL:
http://dx.doi.org/10.1007/3-540-44525-0_17

Abstract

In the common Z specification style operations are, in general, partial relations. The domains of these partial operations are traditionally called preconditions, and there are two interpretations of the result of applying an operation outside its domain. In the traditional interpretation anything may result whereas in the alternative, guarded, interpretation the operation is blocked outside its precondition. In fact these two interpretations can be combined, and this allows representation of both refusals and underspecification in the same model. In this paper we explore this issue, and we extend existing work in this area by allowing arbitrary predicates in the guard. To do so we adopt a non-standard three valued interpretation of an operation by introducing a third truth value. This value corresponds to a situation where we don't care what effect the operation has, i.e.~the guard holds but we may be outside the precondition. Using such a three valued interpretation leads to a simple and intuitive semantics for operation refinement, where refinement means reduction of undefinedness or reduction of non-determinism. We illustrate the ideas in the paper by means of a small example.

Item Type: Book section
DOI/Identification number: 10.1007/3-540-44525-0_17
Uncontrolled keywords: Z, Undefinedness, Guards, Preconditions, Refinement
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
Depositing User: Eerke Boiten
Date Deposited: 12 Sep 2009 10:20 UTC
Last Modified: 16 Nov 2021 10:00 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/21990 (The current URI for this page, for reference purposes)

University of Kent Author Information

Boiten, Eerke Albert.

Creator's ORCID: https://orcid.org/0000-0002-9184-8968
CReDIT Contributor Roles:

Derrick, John.

Creator's ORCID:
CReDIT Contributor Roles:
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