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On proving properties of completion strategies

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 488))

Abstract

We develop methods for proving the fairness and correctness properties of rule based completion strategies by means of process logic. The concepts of these properties are formulated generally within process logic and then concretized to rewrite system theory based on transition rules. We develop in parallel the notions of success and failure of a completion strategy, necessary to support the proves of the cited properties. Finally we show the necessity of another property, called justice, in the analysis of completion strategies.

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References

  1. L. Bachmair. Proof methods for equational theories. PhD thesis, University of Illinois, Urbana Champaign, Illinois, 1987.

    Google Scholar 

  2. L. Bachmair, N. Dershowitz, and J. Hsiang. Orderings for equational proofs. In Proceedings 1st IEEE Symposium on Logic in Computer Science, Cambridge, MA, pages 346–357, June 1986.

    Google Scholar 

  3. N. Dershowitz and J.-P. Jouannaud. Rewrite systems. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science B: Formal Methods and Semantics, chapter 6. North-Holland, Amsterdam, 1990.

    Google Scholar 

  4. M.J. Fischer and R.E. Ladner. Propositional dynamic logic of regular programs. Journal of Computer and System Science, 18:194–211, 1979.

    Google Scholar 

  5. N. Francez. Fairness. Springer Verlag, 1986.

    Google Scholar 

  6. D. Gabbay, A. Pnueli, S. Shelah, and J. Stavi. On the temporal analysis of fairness. In Proceedings of the 7th ACM Symposium on POPL, Las Vegas, pages 163–173, January 1980.

    Google Scholar 

  7. M. Hermann. On proving properties of completion strategies. Research report 90-R-149, Centre de Recherche en Informatique de Nancy, 1990.

    Google Scholar 

  8. D. Harel, D. Kozen, and R. Parikh. Process logic: Expressiveness, decidability, completeness. Journal of Computer and System Science, 25:144–170, 1982.

    Google Scholar 

  9. J.Y. Halpern and J.H. Reif. The propositional dynamic logic of deterministic, well-structured programs. Theoretical Computer Science, 27:127–165, 1983.

    Google Scholar 

  10. G. Huet. A complete proof of correctness of the Knuth-Bendix completion algorithm. Journal of Computer and System Science, 23(1):11–21, August 1981.

    Google Scholar 

  11. D.E. Knuth and P.B. Bendix. Simple word problems in universal algebras. In J. Leech, editor, Computational Problems in Abstract Algebra, pages 263–297. Pergamon Press, Oxford, 1970.

    Google Scholar 

  12. F. Kröger. Temporal logic of programs, volume 8 of EATCS Monographs on Theoretical Computer Science. Springer Verlag, 1987.

    Google Scholar 

  13. Z. Manna and A. Pnueli. How to cook a temporal proof system for your pet language. In Proceedings of the 10th ACM POPL Symposium, Austin, TX, pages 141–154, 1983.

    Google Scholar 

  14. J.P. Queille and J. Sifakis. Fairness and related properties in transition systems — A temporal logic to deal with fairness. Acta Informatica, 19:195–220, 1983.

    Google Scholar 

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Ronald V. Book

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© 1991 Springer-Verlag Berlin Heidelberg

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Hermann, M. (1991). On proving properties of completion strategies. In: Book, R.V. (eds) Rewriting Techniques and Applications. RTA 1991. Lecture Notes in Computer Science, vol 488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53904-2_113

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  • DOI: https://doi.org/10.1007/3-540-53904-2_113

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53904-9

  • Online ISBN: 978-3-540-46383-2

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