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Combining decision procedures in the HOL system

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Higher Order Logic Theorem Proving and Its Applications (TPHOLs 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 971))

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Abstract

A HOL implementation of Nelson and Oppen's technique for combining decision procedures is described. The principal advantage of this technique is that the procedures for the component theories (e.g. linear arithmetic, lists, uninterpreted function symbols) remain separate. Equations between two variables are the only information that need be communicated between them. Thus, code for deciding the component theories can be reused in a combined procedure and the latter can easily be extended. In addition, efficiency techniques used in the component procedures can be retained in the combined procedure.

Research supported by the Engineering and Physical Sciences Research Council of Great Britain under grant GR/J42236.

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References

  1. C. M. Angelo, L. Claesen, and H. De Man. Reasoning about a class of linear systems of equations in HOL. In T. F. Melham and J. Camilleri, editors, Proceedings of the 7th International Workshop on Higher Order Logic Theorem Proving and Its Applications, volume 859 of Lecture Notes in Computer Science, pages 33–48, Valletta, Malta, September 1994. Springer-Verlag.

    Google Scholar 

  2. R. J. Boulton. Lazy techniques for fully expansive theorem proving. Formal Methods in System Design, 3(1/2):25–47, August 1993.

    Google Scholar 

  3. R. J. Boulton. Efficiency in a Fully-Expansive Theorem Prover. PhD thesis, University of Cambridge Computer Laboratory, New Museums Site, Pembroke Street, Cambridge CB2 3QG, U.K., May 1994. Technical Report 337.

    Google Scholar 

  4. D. Craigen, S. Kromodimoeljo, I. Meisels, W. Pase, and M. Saaltink. EVES: An overview. In S. Prehn and W. J. Toetenel, editors, VDM'91 Formal Software Development Methods, volume 551 of Lecture Notes in Computer Science, pages 389–405. Springer-Verlag, 1991.

    Google Scholar 

  5. L. Fribourg. A decision procedure for a subtheory of linear arithmetic with lists. Research Report LiTH-IDA-R-91-33, Department of Computer and Information Science, Linköping University, Linköping, Sweden, October 1991.

    Google Scholar 

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

    Google Scholar 

  7. J. Harrison. A HOL decision procedure for elementary real algebra. 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 426–436, Vancouver, B.C., Canada, August 1993. Springer-Verlag, 1994.

    Google Scholar 

  8. T. Käufl. Cooperation of decision procedures in a tableau-based theorem prover. Technical Report 19/89, University of Karlsruhe, Institut für Logik, Komplexität und Deduktionssysteme, 1989.

    Google Scholar 

  9. G. Nelson. Techniques for Program Verification. PhD thesis, Stanford University, 1980. Revised version: Technical Report CSL-81-10, Xerox PARC, June 1981.

    Google Scholar 

  10. G. Nelson and D. C. Oppen. Simplification by cooperating decision procedures. ACM Transactions on Programming Languages and Systems, 1(2):245–257, October 1979.

    Google Scholar 

  11. G. Nelson and D. C. Oppen. Fast decision procedures based on congruence closure. Journal of the ACM, 27(2):356–364, April 1980.

    Google Scholar 

  12. D. C. Oppen. Reasoning about recursively defined data structures. Journal of the ACM, 27(3):403–411, July 1980.

    Google Scholar 

  13. R. E. Shostak. On the SUP-INF method for proving Presburger formulae. Journal of the ACM, 24(4):529–543, October 1977.

    Google Scholar 

  14. R. Shostak. Deciding linear inequalities by computing loop residues. Technical report, Computer Science Laboratory, SRI International, Menlo Park, California, 1978.

    Google Scholar 

  15. R. E. Shostak. An algorithm for reasoning about equality. Communications of the ACM, 21(7):583–585, July 1978.

    Google Scholar 

  16. R. E. Shostak. A practical decision procedure for arithmetic with function symbols. Journal of the ACM, 26(2):351–360, April 1979.

    Google Scholar 

  17. R. E. Shostak. Deciding combinations of theories. Journal of the ACM, 31(1):1–12, January 1984.

    Google Scholar 

  18. K. Slind. Completion as a derived rule of inference. Research Report 90/409/33, Department of Computer Science, The University of Calgary, 2500 University Drive N.W., Calgary, Alberta, Canada T2N 1N4, 1990.

    Google Scholar 

  19. N. Shankar, S. Owre, and J. M. Rushby. The PVS Proof Checker: A Reference Manual. Computer Science Laboratory, SRI International, Menlo Park CA 94025, March 1993. Beta Release.

    Google Scholar 

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Authors and Affiliations

  1. Computer Laboratory, University of Cambridge, New Museums Site, Pembroke Street, CB2 3QG, Cambridge, UK

    Richard J. Boulton

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  1. Richard J. Boulton
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Editor information

E. Thomas Schubert Philip J. Windley James Alves-Foss

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© 1995 Springer-Verlag Berlin Heidelberg

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Boulton, R.J. (1995). Combining decision procedures in the HOL system. In: Thomas Schubert, E., Windley, P.J., Alves-Foss, J. (eds) Higher Order Logic Theorem Proving and Its Applications. TPHOLs 1995. Lecture Notes in Computer Science, vol 971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60275-5_58

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  • DOI: https://doi.org/10.1007/3-540-60275-5_58

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60275-0

  • Online ISBN: 978-3-540-44784-9

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