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Using the rippling heuristic in set membership proofs

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Book cover ZUM '97: The Z Formal Specification Notation (ZUM 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1212))

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Abstract

We demonstrate how the rippling heuristic [Bundy et al 93], originally developed for inductive proofs, can be used to automate set membership proofs. Set membership proofs occur frequently as subgoals in Z proofs, and automating these goals would lift a significant burden of the proof off of users of proof tools. The approach is promising and is being integrated into the proof tool Z-in-Isabelle [Kraan & Baumann 95a].

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References

  1. D. Basin and T. Walsh. Difference matching. In Deepak Kapur, editor, 11th Conference on Automated Deduction, pages 295–309, Saratoga Springs, NY, USA, June 1992. Published as Springer Lecture Notes in Artificial Intelligence, No 607.

    Google Scholar 

  2. D. Basin and T. Walsh. Difference unification. In Proceedings of the 13th IJCAI. International Joint Conference on Artificial Intelligence, 1993. Also available as Technical Report MPI-I-92-247, Max-Planck-Institut für Informatik.

    Google Scholar 

  3. David Basin and Toby Walsh. A calculus for and termination of rippling. Journal of Automated Reasoning, 16(1/2):147–180, 1996.

    Google Scholar 

  4. S. M. Brien and J. E. Nicholls. Z base standard. Technical Monograph PRG-107, Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford, UK, November 1992. Accepted for ISO standardization, ISO/IEC JTC1/SC22.

    Google Scholar 

  5. A. Bundy. The use of explicit plans to guide inductive proofs. In R. Lusk and R. Overbeek, editors, 9th Conference on Automated Deduction, pages 111–120. Springer-Verlag, 1988. Longer version available from Edinburgh as DAI Research Paper No. 349.

    Google Scholar 

  6. A. Bundy, F. van Harmelen, C. Horn, and A. Smaill. The Oyster-Clam system. In M.E. Stickel, editor, 10th International Conference on Automated Deduction, pages 647–648. Springer-Verlag, 1990. Lecture Notes in Artificial Intelligence No. 449. Also available from Edinburgh as DAI Research Paper 507.

    Google Scholar 

  7. A. Bundy, A. Stevens, F. van Harmelen, A. Ireland, and A. Smaill. Rippling: A heuristic for guiding inductive proofs. Artificial Intelligence, 62:185–253, 1993. Also available from Edinburgh as DAI Research Paper No. 567.

    Google Scholar 

  8. I. Kraan and P. Baumann. Implementing Z in Isabelle. In J.P. Bowen and M.G. Hinchey, editors, Proceedings of ZUM'95: The Z Formal Specification Notation, Lecture Notes in Computer Science 967, pages 355–373. Springer-Verlag, 1995.

    Google Scholar 

  9. I. Kraan and P. Baumann. Logical frameworks as a basis for verification tools: A case study. In Proceedings of the Tenth Knowledge-Based Software Engineering Conference, 1995.

    Google Scholar 

  10. S. Negrete-Yankelevich. Proof Planning with Logic Presentations. Unpublished PhD thesis, Department of Artificial Inte lligence, University of Edinburgh, 1996.

    Google Scholar 

  11. B.L. Richards, I. Kraan, A. Smaill, and G.A. Wiggins. Mollusc: a general proof development shell for sequent-based logics. In A. Bundy, editor, 12th Conference on Automated Deduction, pages 826–30. Springer-Verlag, 1994. Lecture Notes in Artificial Intelligence, vol 814; Also available from Edinburgh as DAI Research paper 723.

    Google Scholar 

  12. J. M. Spivey. The Z Notation: A Reference Manual. Series in Computer Science. Prentice Hall International, 2nd edition, 1992.

    Google Scholar 

  13. T. Walsh, A. Nunes, and A. Bundy. The use of proof plans to sum series. In D. Kapur, editor, 11th Conference on Automated Deduction, pages 325–339. Springer Verlag, 1992. Lecture Notes in Computer Science No. 607. Also available from Edinburgh as DAI Research Paper 563.

    Google Scholar 

  14. Tetsuya Yoshida, Alan Bundy, Ian Green, Toby Walsh, and David Basin. Coloured rippling: An extension of a theorem proving heuristic. Technical Report TBA, Dept. of Artificial Intelligence, Edinburgh, 1994.

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University of Zürich, Switzerland

    Ina Kraan

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  1. Ina Kraan
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Jonathan P. Bowen Michael G. Hinchey David Till

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© 1997 Springer-Verlag Berlin Heidelberg

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Kraan, I. (1997). Using the rippling heuristic in set membership proofs. In: Bowen, J.P., Hinchey, M.G., Till, D. (eds) ZUM '97: The Z Formal Specification Notation. ZUM 1997. Lecture Notes in Computer Science, vol 1212. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027288

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  • DOI: https://doi.org/10.1007/BFb0027288

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62717-3

  • Online ISBN: 978-3-540-68490-9

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