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A Logic for ObjectZ
 PROCEEDINGS OF THE 9TH ANNUAL ZUSER MEETING
, 1994
"... This paper presents a logic for ObjectZ which extends W , the logic for Z adopted as the basis of the deductive system in the Z Base Standard. The logic provides a basis on which tool support for reasoning about ObjectZ specifications can be developed. It also formalises the intended meaning of ..."
Abstract

Cited by 24 (7 self)
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This paper presents a logic for ObjectZ which extends W , the logic for Z adopted as the basis of the deductive system in the Z Base Standard. The logic provides a basis on which tool support for reasoning about ObjectZ specifications can be developed. It also formalises the intended meaning of ObjectZ constructs and hence provides an abstract, axiomatic semantics of the language.
MachineAssisted TheoremProving for Software Engineering
 Technical Monograph PRG121, ISBN 0902928953, Oxford University Computing LaboratoryWolfson Building, Parks Road
, 1994
"... The thesis describes the production of a large prototype proof system for Z, and a tactic language in which the proof tactics used in a wide range of systems (including the system described here) can be discussed. The details of the construction of the toolusing the W logic for Z, and implemented ..."
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Cited by 5 (1 self)
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The thesis describes the production of a large prototype proof system for Z, and a tactic language in which the proof tactics used in a wide range of systems (including the system described here) can be discussed. The details of the construction of the toolusing the W logic for Z, and implemented in 2OBJare presented, along with an account of some of the proof tactics which enable W to be applied to typical proofs in Z. A case study gives examples of such proofs. Special attention is paid to soundness concerns, since it is considerably easier to check that a program such as this one produces sound proofs, than to check that each of the impenetrable proofs which it creates is indeed sound. As the first such encoding of W, this helped to find bugs in the published presentations of W, and to demonstrate that W makes proof in Z tractable. The second part of the thesis presents a tactic language, with a formal semantics (independent of any particular tool) and a set of rules for reasoning about tactics written in this language. A small set of these rules is shown to be complete for the finite (nonrecursive)
W Reconstructed
"... An early version of the Z Standard included the deductive system W for reasoning about Z specifications. Later versions contain a different deductive system. In this paper we sketch a proof that W is relatively sound with respect to this new deductive system. We do this by demonstrating a semantic b ..."
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Cited by 4 (1 self)
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An early version of the Z Standard included the deductive system W for reasoning about Z specifications. Later versions contain a different deductive system. In this paper we sketch a proof that W is relatively sound with respect to this new deductive system. We do this by demonstrating a semantic basis for a correspondence between the two systems, then showing that each of the inference rules of W can be simulated as derived rules in the new system. These new rules are presented as tactics over the the inference rules of the new deductive system. 1 Introduction An important part of the Z Standardization activity has been the definition of a logical deductive system for Z. Whilst some have sought to provide support for reasoning about Z specifications by embedding the language in an existing wellunderstood framework (HOL, Eves, PVS, Isabelle, for example; [BG94,Jon92,Saa92,KSW96,ES94]), other research has attempted to provide support for reasoning within Z, making use of Z's type ...
Z and HOL
"... A simple `shallow' semantic embedding of the Z notation into the HOL logic is described. The Z notation is based on set theory and first order predicate logic and is typically used for humanreadable formal specification. The HOL ..."
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A simple `shallow' semantic embedding of the Z notation into the HOL logic is described. The Z notation is based on set theory and first order predicate logic and is typically used for humanreadable formal specification. The HOL