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Generic Proof Scores for Generate & Check Method in CafeOBJ 

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Logic, Rewriting, and Concurrency

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9200))

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Abstract

Generic proof scores for the generate & check method in CafeOBJ are described. The generic proof scores codify the generate & check method as parameterized modules in the CafeOBJ language independently of specific systems to which the method applies. Basic proof scores for a specific system can be obtained by instantiating the formal parameter modules of the parameterized modules with the actual specification modules of the specific system. The effectiveness of the generic proof scores is demonstrated by applying them to a couple of non-trivial examples.

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Notes

  1. 1.

    \({(T_{\varSigma })}_{{\small {\mathtt{{State}}}}}/\!({\small {\mathtt{{=}}}}_E)_{\small {\mathtt{{State}}}}\) is better to be understood as \(T_{\varSigma }/\!{\small {\mathtt{{=}}}}_E\), for usually the sort State can only be understood together with other related sorts like Bool, Nat, Queue, etc.

  2. 2.

    We may need some \( Data \) for specifying a predicate on a transition system like “the agent with the name N is working” where N is \( Data \).

  3. 3.

    See [10] for a more precise definition.

  4. 4.

    The file genCheck.cafe on the web page contains the seven parameterized modules. The files exState.cafe, genCases.cafe, pnat.cafe and predCj.cafe are used in genCheck.cafe. Note that each file without suffix “abp-” or “qlock-” in its name is not depend on QLOCK or ABP and generic for the generate & check method.

  5. 5.

    The module GENcases is in the file genCases.cafe on the web page.

  6. 6.

    These equations are in the file qlock-genStTerm.cafe on the web page.

  7. 7.

    The module PREDcj is in the file predCj.cafe on the web page.

  8. 8.

    The modules INV-1v, INV-2v are in the file genCheck.cafe on the web page.

  9. 9.

    The modules VALIDq, G&C-Tv, INV-3q are in the file genCheck.cafe on the web page.

  10. 10.

    The modules EX-STATE, PCJ-EX-STATE are in the file exState.cafe on the web page.

  11. 11.

    The modules PQ-1q, PQ-2q, PQ-3v, PQ-4v are in the file genCheck.cafe on the web page.

  12. 12.

    The specifications explained in this section are in the file qlock-sys.cafe on the web page.

  13. 13.

    The file qlock-sys-ex.cafe on the web page contains the translated tyc and ex rules.

  14. 14.

    The modules in this section is in the file qlock-prop.cafe unless otherwise stated.

  15. 15.

    The module PNAT* is in the file qlock-natQuSet.cafe on the web page.

  16. 16.

    The base modules Q-INV-1v, Q-INV-2v, Q-INV-3q, and Q-PQ-1q, Q-PQ-2q, Q-PQ-3v, Q-PQ-4v are in the file qlock-genCheck.cafe on the web page.

  17. 17.

    The module Q-INV-1-genCheck is in the file qlock-inv-1-ps.cafe on the web.

  18. 18.

    The module Q-INV-2-genCheck is in the file qlock-inv-2-ps.cafe on the web page.

  19. 19.

    The module Q-INV-3-genCheck is in the file qlock-inv-3-ps.cafe on the web page.

  20. 20.

    The module GENstTerm is in the file qlock-genStTerm.cafe on the web page.

  21. 21.

    The module CONSTandLITL is in the file qlock-constAndLitl.cafe on the web page.

  22. 22.

    The module FACTtbu is in the file qlock-factTbu.cafe on the web page.

  23. 23.

    You can see the proof score using Generate&Check-T2 in the file qlock-inv-3-ps. cafe on the web page.

  24. 24.

    The module Q-PQ-1-genCheck is in the file qlock-pq-1-ps.cafe on the web page.

  25. 25.

    The module Q-PQ-2-genCheck is in the file qlock-pq-2-ps.cafe on the web page.

  26. 26.

    The module Q-PQ-3-genCheck is in the file qlock-pq-3-ps.cafe on the web page.

  27. 27.

    The module Q-PQ-4-genCheck is in the file qlock-pq-4-ps.cafe on the web page.

  28. 28.

    You can see the expanded term after the eof in the file qlocik-pq-3-ps.cafe on the web page.

  29. 29.

    The base modules ABP-INV-1v, ABP-INV-2v, ABP-INV-3q are in the file abp- genCheck.cafe on the web page.

  30. 30.

    You can see the similarity by looking into the files abp-genCheck.cafe and qlock-genCheck.cafe on the web page.

  31. 31.

    Examples of CITP usage (i.e. :goal and :ctf) can be found in file abp-factTbu-ps. cafe on the web page.

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Acknowledgments

It is a great pleasure for the author (KF) to have the chance to prepare this paper for the Festschrift in honor of Professor Jos\(\acute{\mathrm {e}}\) Meseguer who has originated the rewriting logic and been leading the development of the area. The work reported in this paper is based on that development.

Comments from anonymous reviewers help to improve the quality of the paper and are appreciated.

This work was supported in part by Grant-in-Aid for Scientific Research (S) 23220002 from Japan Society for the Promotion of Science (JSPS).

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  1. Research Center for Software Verification (RCSV), Japan Advanced Institute of Science and Technology (JAIST), 1-1 Asahidai, Nomi, Ishikawa, 923-1292, Japan

    Kokichi Futatsugi

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Correspondence to Kokichi Futatsugi .

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  1. Universidad Complutense de Madrid, Madrid, Spain

    Narciso Martí-Oliet

  2. University of Oslo, Oslo, Norway

    Peter Csaba Ölveczky

  3. SRI International, Menlo Park, California, USA

    Carolyn Talcott

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Futatsugi, K. (2015). Generic Proof Scores for Generate & Check Method in CafeOBJ . In: Martí-Oliet, N., Ölveczky, P., Talcott, C. (eds) Logic, Rewriting, and Concurrency. Lecture Notes in Computer Science(), vol 9200. Springer, Cham. https://doi.org/10.1007/978-3-319-23165-5_14

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  • DOI: https://doi.org/10.1007/978-3-319-23165-5_14

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