J.P.Bowen and M.J.C. Gordon. Z and HOL. In J.P. Bowen and J.A. Hall, editors, Z User Workshop, Cambridge 1994, Workshops in Computing, pages 141--167. Springer-Verlag, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....keep the embedding simple, it is advisable to reuse HOL s infrastructure as much as possible. For typed formalisms, this means that its typing system should ideally be represented by that of HOL. This is a problem in the case of Z as it would require record types not present in HOL. Previous work [7, 8] on Z embeddings has side stepped this problem by encoding schemas before analyzing them in HOL. This resulted in shallow embeddings well suited for reasoning about individual specifications. However, the encoding made it difficult to derive general theorems about the Z schema calculus itself. It ....

J.P.Bowen and M.J.C. Gordon. Z and HOL. In J.P. Bowen and J.A. Hall, editors, Z User Workshop, Cambridge 1994, Workshops in Computing, pages 141--167. Springer-Verlag, 1994.

....Post , in which identifiers denote values in some state, we must reason at the lifted level; but to discharge obligations like w is a list of fresh identifiers , in which identifiers denote themselves, we must reason in ordinary first order logic. 17 Instead of building a deep embedding [BG94] of the higher order refinement calculus in Ergo, we use a shallow embedding , where we treat certain definable concepts axiomatically. Our approach is to build an axiomatic theory of weakest preconditions upon which we define refinement and the refinement calculus. This axiomatic theory is ....

Jonathan Bowen and Mike Gordon. Z and HOL. In J. P. Bowen and J. A. Hall, editors, Z User Workshop, Cambridge 1994, BCS FACS Workshops in Computing, pages 141--167. SpringerVerlag, 1994.

....set theory and sorted first order This work is supported by the Deutsche Forschungsgemeinschaft within the Schwerpunktprojekt Deduktion. y baar mathematik.hu berlin.de z dahn mathematik.hu berlin.de 1 predicate logic. Many concepts in Z can be easily translated into other logical languages [3]. A library of well known mathematical theorems called Mathematical Toolkit is an integral part of Z. It is comfortable to use these theorems formally in a proof for our purpose. The separation of the Mathematical Toolkit and the structured character of Z specification turn out to be very ....

J. Bowen and M. J. C. Gordon. Z and hol. http://gruffle.comlab.ox.ac.uk/archive/z.html.

....of a state oriented method such as B, VDM, or Z into a general specification language integrated with a proof checker such as HOL or PVS can be made in different ways and for different purposes. In the context of HOL, Gordon proposes in [15] a shallow embedding of the Hoare logic in HOL, and in [7] Bowen and Gordon propose a shallow embedding of Z in HOL. The motivation is to provide mechanical support for the notation by using the HOL system. More recently, Chartier has formalized the abstract machine notation of B in Isabelle HOL [9] by using a deep embedding. One of the aims of ....

J.P. Bowen and M.J.C. Gordon. Z and HOL. In Jonathan P. Bowen and J. Anthony Hall, editors, Z User Workshop, Cambridge 1994, pages 141-- 167, London, June 1994. Workshops in Computing, Springer-Verlag.

....an assessment of the approach is given. 2 Z and IOSS We have chosen the specification language Z because it has gained considerable popularity in industry and comes equipped not only with a methodology [PST91] but also with some tool support, e.g. for type checking [Spi92a] and theorem proving [BG94]. Z is designed to specify state based systems which is in good accordance with the reality of safety critical systems. An undeniable deficiency of Z is the fact that neither time nor complex control structures can be specified. The author s synthesis system IOSS supports the development of ....

J. Bowen and M. Gordon. Z and HOL. In Z User Workshop, Workshops in Computing, pages 141--167. Springer-Verlag, 1994.

....to realistic industrial scale languages) Of the five tools in the survey, only four provided any support for verification: 1. ProofPower: an embedding of the Z language in HOL[105] 2. Zola: a purpose built system[104] 3. CADiZ: a purpose built system[106] 4. Z HOL: another embedding of Z in HOL[107, 108]. 2 For a survey of current tool support for Z, the interested reader is referred to a report by Martin[103] Examining the systems which have been specifically designed for reasoning about Z specifications, we noted that the proof support in CADiZ was in the early stages of development and ....

....method of representing that meaning. Another way of distinguishing these embeddings is to label them as syntactic embeddings (deep) and semantic embeddings (shallow) Details of the specific issues and tradeoffs involved in embedding Z in other logics can be found in a paper by Bowen and Gordon[107]. The two embeddings of Z in HOL represent a deep (ProofPower) and a shallow (Z HOL) embedding. Z in HOL is quite unusual for a shallow embedding of one logic in another, in that it maintains a table of reverse translations, so that results of tactic applications are as far as possible returned to ....

J.P. Bowen and M.J.C. Gordon. Z and HOL. In J.P. Bowen and J.A. Hall, editors, Z User Workshop, Workshops in Computing, pages 141-- 167, Cambridge, UK, 1994. Springer-Verlag.

....there are the direct implementations. For Z, these include the tool Balzac [Harwood 91, Jordan 91] Second, there are the embeddings in other logics and in logical frameworks. Most such implementations of Z have been shallow rather than deep embeddings, including ProofPower [Jones 92] Z in HOL [Bowen Gordon 94] and Z in LEGO [Maharaj 90] The distinction between shallow and deep is not always clear cut, but in principle, the deeper the embedding, the more properties of the language can be proven in the embedding. Deep embeddings of Z in logical frameworks include Jigsaw [Martin 94] and our system ....

J.P. Bowen and M.J.C. Gordon. Z and HOL. In J.P. Bowen and J.A. Hall, editors, Z User Workshop, Cambridge 1994, Workshops in Computing, pages 141--167. Springer-Verlag, 1994.

....and reliability concludes the paper. 2 Z and IOSS We have chosen the specification language Z because it has gained considerable popularity in industry and comes equipped not only with a methodology [PST91] but also with some tool support, e.g. for type checking [Spi92a] and theorem proving [BG94]. Z is designed to specify state based systems which is in good accordance with the reality of safety critical systems. An undeniable deficiency of Z is the fact that neither time nor complex control structures can be specified. The author s synthesis system IOSS [HSZ95b] supports the development ....

J. Bowen and M. Gordon. Z and HOL. In Z User Workshop, Workshops in Computing, pages 141--167. Springer-Verlag, 1994.

No context found.

J. P.Bowen and M. J. C. Gordon. Z and HOL. In Bowen and Hall [22], pages 141--167.

.... proceedings have been published by Springer Verlag in the Workshops in Computing series (e.g. 11] In particular, Mike Gordon, the technical contact at the UniversityofCambridge, and Jim Woodcock of Oxford University are giving invited talks on mechanising Z using the HOL theorem prover [7] and on the use of Z to specify the UK MoD 00 56 draft standard [38] Other presentations are from Oxford University [14] Praxis [20,22] the UniversityofWarsaw (concerning work on the Duration Calculus associated with via the Technical University of Denmark) 17] and the UniversityofYork ....

....for both Z and VDM. One further Z User Meeting is planned during the lifetime of the Working Group, at the University of Limerick, Ireland, 7 8 September 1995. ProCoS WG encourages interaction between various formal methods communities suchas those associated with Z, VDM, HOL, etc. e.g. see [7]. Several partners are involved with Formal Methods Europe and its associated FME Symposia and FACS Europe newsletter. We maintain contact particularly via Martyn Thomas, Chairman of both Praxis (a site) and FME. Paper and electronic dissemination A postal mailing list and an electronic ....

J. P.Bowen and M. J. C. Gordon. Z and HOL. In Bowen and Hall [8].

....update the RAM contents. Such a specification could be of use to a microprocessor designer, acting as the specification of the processor to be implemented. More recently we haveinvestigated the embedding of Z within HOL which enables the efficient mechanisation of proofs about Z specifications [10]. 7 Compiler Specification A compiler can be specified as a relation defined recursively over the syntax of commands and expressions. qSn1 n2 ROM The relation is true if the instruction store ROM contains the compiled code for the process q starting at location n1 up to (but not including) ....

....way.Further work to unify the approaches at different levels of abstraction is certainly required. For example, both HOL andZwere used on the project but the use of HOL was prevalent because of the desire to mechanise proofs. There is now more support for the mechanisation of proofs in Z [10]sowere the project to have started today, more use of Z mighthave been possible with the same goals of mechanisation in mind. Whilst the project has now formally finished, further collaborativework on the support of Z using HOL has continued [10] and the related ProCoS project continues to ....

[Article contains additional citation context not shown here]

J.P.Bowen and M.J.C. Gordon. Z and HOL. In J.P.Bowen and J.A. Hall, editors, Z User Workshop, Cambridge 1994,Workshops in Computing, pages 141--167. Springer-Verlag, 1994.

....Z. Perhaps motivated by the ProofPower approach, much attention has focused recently on tailoring various generic theorem provers for use with model based specification languages such as Z. An implementation in OBJ [41] seems to be too slow, but particular successes have been reported with HOL [12] and EVES [52] We expect that in the future more emphasis will be placed on IFDSEs (In tegrated Formal Development Support Environments) which will support most stages of formal development. Such toolkits will be integrated in that, like IPSEs (Integrated Programming Support Environments) they ....

Bowen, J.P. & Gordon, M.J.C.: Z and HOL. In [13], pp 141--167.

....update the RAM contents. Such a specification could be of use to a microprocessor designer, acting as the specification of the processor to be implemented. More recently we have investigated the embedding of Z within HOL which enables the efficient mechanisation of proofs about Z specifications [10]. Jonathan P. Bowen et al. 13 7 Compiler Specification A compiler can be specified as a relation defined recursively over the syntax of commands and expressions. C p q S n1 n2 ROM The relation is true if the instruction store ROM contains the compiled code for the process q starting at ....

....way. Further work to unify the approaches at different levels of abstraction is certainly required. For example, both HOL and Z were used on the project but the use of HOL was prevalent because of the desire to mechanise proofs. There is now more support for the mechanisation of proofs in Z [10] so were the project to have started today, more use of Z might have been possible with the same goals of mechanisation in mind. Whilst the safemos project has now formally finished, further collaborative work on the support of Z using HOL has continued [10] and the related ProCoS project ....

[Article contains additional citation context not shown here]

J.P. Bowen and M.J.C. Gordon. Z and HOL. In J.P. Bowen and J.A. Hall, editors, Z User Workshop, Cambridge 1994, Workshops in Computing, pages 141--167. Springer-Verlag, 1994.

....Z. Perhaps motivated by the ProofPower approach, much attention has focused recently on tailoring various generic theorem provers for use with model based specification languages such as Z. An implementation in OBJ [40] seems to be too slow, but particular successes have been reported with HOL [11] and EVES [51] We expect that in the future more emphasis will be placed on IFDSEs (Integrated Formal Development Support Environments) which will support most stages of formal development, from initial functional specifications, through design specifications and refinement and will also provide ....

Bowen, J.P. & Gordon, M.J.C.: Z and HOL. In [12], pp 141--167.

....the VDM Toolbox from IFAD) and Z [62] e.g. Balzac Zola from Imperial Software Technology, and ProofPower from ICL) Quite a lot of interest has also focused lately on tailoring theorem provers for use with specific methods. For example, theorem provers for Z have been developed in EVES [61] HOL [11], and OBJ [48] Each of these three levels is useful in itself. One must determine, however, whether the additional cost (in time, effort, manpower, tool support, etc. is justified before embarking on full formal development and machine checked proofs. For systems where the highest integrity is ....

....written correctly in the first place The possibility of combining Cleanroom techniques and formal methods has been investigated [53] Sometimes it is possible to combine different formal methods together usefully and effectively. For example, HOL [35] has been used to provide tool support for Z [11]. This allows the more readable Z notation to have the benefit of mechanical proof checking by HOL, thus increasing confidence in the development. The management of a project using formal methods must be more technically aware than is perhaps normally the case. The use of a formal approach means ....

Bowen, J.P. & Gordon, M.J.C.: Z and HOL. In [12], pp 141--167.

No context found.

J.P.Bowen and M.J.C. Gordon. Z and HOL. In J.P. Bowen and J.A. Hall, editors, Z User Workshop, Cambridge 1994, Workshops in Computing, pages 141--167. Springer-Verlag, 1994.

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