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Elements of mathematical analysis in PVS

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1125))

Abstract

This paper presents the formalization of some elements of mathematical analysis using the PVS verification system. Our main motivation was to extend the existing PVS libraries and provide means of modelling and reasoning about hybrid systems. The paper focuses on several important aspects of PVS including recent extensions of the type system and discusses their merits and effectiveness. We conclude by a brief comparison with similar developments using other theorem provers.

Work partially funded by EPSRC Grant No GR/H11471 under DTI Project No IED/1/9013

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References

  1. J. Crow, S. Owre, J. Rushby, N. Shankar, and M. Srivas. A tutorial introduction to PVS. In WIFT'95 Workshop on Industrial-Strength Formal Specification Techniques, April 1995.

    Google Scholar 

  2. B. Dutertre. Coherent Requirements of the SafeFM Case Study. Technical Report SafeFM-050-RH-2, SafeFM project, September 1995.

    Google Scholar 

  3. W. M. Farmer, J. D. Guttman, and F. J. Thayer. Little theories. In D. Kapur, editor, Automated Deduction—CADE-11, volume 607 of Lecture Notes in Computer Science, pages 567–581. Springer-Verlag, 1992.

    Google Scholar 

  4. W. M. Farmer, J. D. Guttman, and F. J. Thayer. Imps: An Interactive Mathematical Proof System. Journal of Automated Reasoning, 11:213–248, 1993.

    Article  MATH  Google Scholar 

  5. W. M. Farmer, J. D. Guttman, and F. J. Thayer. The Imps user's manual. Technical Report M-93B138, The Mitre Corporation, 1993.

    Google Scholar 

  6. W. M. Farmer and F. J. Thayer. Two computer-supported proofs in metric space topology. Notices of the American Mathematical Society, 38:1133–1138, 1991.

    Google Scholar 

  7. M.J.C. Gordon and T.F. Melham. Introduction to HOL. A theorem proving environment for higher order logic. Cambridge University Press, 1993.

    Google Scholar 

  8. J. Harrison. Constructing the real numbers in HOL. Formal Methods in System Design, 4(1/2):35–59, July 1994.

    Article  Google Scholar 

  9. J. Harrison. Floating point verification in HOL. In E. T. Schubert, P. J. Windley, and J. Alves-Foss, editors, Proceedings of the 8th International Workshop on Higher Order Logic Theorem Proving and Its Applications, volume 971 of Lecture Notes in Computer Science, pages 186–199. Springer-Verlag, 1995.

    Google Scholar 

  10. J. Harrison and L. Théry. Extending the HOL theorem prover with a computer algebra system to reason about the reals. In J. J. Joyce and C.-J. H. Seger, editors, Proceedings of the 6th International Workshop on Higher Order Logic Theorem Proving and its Applications (HUG'93), volume 780 of Lecture Notes in Computer Science, pages 174–184. Springer-Verlag, 1993.

    Google Scholar 

  11. J. Hooman. Correctness of Real Time Systems by Construction. In Formal Techniques in Real-Time and Fault-Tolerant Systems, pages 19–40. Springer-Verlag, LNCS 863, September 1994.

    Google Scholar 

  12. D. Jamsek, R. W. Butler, S. Owre, and C. M. Holloway. PVS finite sets library, 1995. Part of the standard PVS distribution.

    Google Scholar 

  13. S. Lang. Analysis I. Addison-Wesley, 1968.

    Google Scholar 

  14. S. P. Miller and M. Srivas. Formal Verification of the AAMP5 Microprocessor: A Case Study in the Industrial Use of Formal Methods. In WIFT'95 Workshop on Industrial-Strength Formal Specification Techniques, April 1995.

    Google Scholar 

  15. S. Owre, J. Rushby, N. Shankar, and F. von Henke. Formal verification for fault-tolerant architectures: Prolegomena to the design of PVS. IEEE Transactions on Software Engineering, 21(2):107–125, February 1995.

    Article  Google Scholar 

  16. S. Owre and N. Shankar. The Formal Semantics of PVS. Technical report, Computer Science Lab., SRI International, June 1995.

    Google Scholar 

  17. S. Owre, N. Shankar, and J. M. Rushby. The PVS Specification Language. Computer Science Lab., SRI International, April 1993.

    Google Scholar 

  18. N. Shankar, S. Owre, and J. M. Rushby. The PVS Proof Checker: A reference Manual. Computer Science Lab., SRI International, March 1993.

    Google Scholar 

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Authors

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Gerhard Goos Juris Hartmanis Jan van Leeuwen Joakim von Wright Jim Grundy John Harrison

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© 1996 Springer-Verlag Berlin Heidelberg

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Dutertre, B. (1996). Elements of mathematical analysis in PVS. In: Goos, G., Hartmanis, J., van Leeuwen, J., von Wright, J., Grundy, J., Harrison, J. (eds) Theorem Proving in Higher Order Logics. TPHOLs 1996. Lecture Notes in Computer Science, vol 1125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105402

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  • DOI: https://doi.org/10.1007/BFb0105402

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61587-3

  • Online ISBN: 978-3-540-70641-0

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