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E-unification algorithms for a class of confluent term rewriting systems

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Automata, Languages and Programming (ICALP 1986)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 226))

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Abstract

E-unification is the problem of unification in equational theories. The narrowing mechanism and term rewriting systems constitute a powerful tool for constructing complete and efficient unification algorithms for useful classes of equational theories. This has been shown for the case where term rewriting systems are confluent and noetherian. In this paper we show that extension of the application domain of narrowing to non-terminating term rewriting systems is possible, though difficult. Specifically, we show that the narrowing process, combined with ordinary unification, yields a complete unification algorithm for equational theories that can be described by a closed linear term rewriting system with the non-repetition property; this class allows non-terminating term rewriting systems. For some special forms of input terms, narrowing generates complete sets of E-unifiers without resorting to the non-repetition property.

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References

  1. Fay, M.J., “First-order unification in an equational theory,” in 4th Workshop on Automated Deduction, pp. 161–167, Austin, Texas, February, 1979.

    Google Scholar 

  2. Fribourg, L., “A superposition oriented theorem prover,” Tech. Report 11, L.I.T.P., 1983, To appear in Theoretical Compute Science, short version in Proc. IJCAI-83, pp. 923–925.

    Google Scholar 

  3. Fribourg, L., “SLOG: A logic programming language interpreter based on clausal superposition and rewriting,” in Proc. 1985 International Symposium on Logic Programming, pp. 172–184, Boston, Mass., July, 1985.

    Google Scholar 

  4. Hoffmann, C.M. and M. O'Donnell, “Programming with equations,” ACM TOPLAS, vol. 4, no. 1, pp. 83–112, January, 1982.

    Google Scholar 

  5. Hullot, J.M., “Canonical forms and unification,” in Proc. 5th Conference on Automated Deduction, pp 318–334, 1980.

    Google Scholar 

  6. Hussmann, H., “Unification in conditional-equational theories,” Tech. Report MIP 8502, Universitat Passau, January, 1985.

    Google Scholar 

  7. Knuth, D. and P. Bendix, “Simple word problems in universal algebras,” in Computational problems in abstract algebra, ed. J. Leech, pp. 163–279, Pergamon Press, 1970.

    Google Scholar 

  8. Jouannaud, J.P., C. Kirchner and H. Kirchner, “Incremental construction of unification algorithms in equational theories,” in Proc. 10th Colloquium on Automata, Languages and Programming, 1983.

    Google Scholar 

  9. Lankford, D.S., “Canonical inference,” Technical Report ATP-32, Department of Mathematics and Computer Science, University of Texas at Austin, December, 1975.

    Google Scholar 

  10. Plotkin, G., “Building-in equational theories,” in Machine Intelligence 7, pp. 73–90, Edinburgh University Press, 1972.

    Google Scholar 

  11. O'Donnell, M., “Computing in systems described by equations,” in Lecture notes in computer science, vol. 58, Springer-Verlag, New York, 1977.

    Google Scholar 

  12. Rety P, C. Kirchner, H. Kirchner and P. Lescanne, “NARROWER: a new algorithm and its application to logic programming,” in Proc. Rewriting Techniques and Applications, also in Lecture Notes in Computer Science 202, pp. 141–157, 1985.

    Google Scholar 

  13. Robinson, J.A., “A machine oriented logic based on the resolution,” in Journal of ACM, vol 12, no. 1 pp. 23–41, January, 1965.

    Google Scholar 

  14. Siekmann, J., “Universal unification,” in Proc. 7th International Conference on Automated Deduction, pp. 1–42, Napa, California, May, 1984.

    Google Scholar 

  15. Subrahmanyam, P.A. and Jia-Huai You, “FUNLOG: a computational model integrating logic programming and functional programming,” in Logic programming: relations, functions and equations, eds. D. DeGroot and G. Lindstrom, Prentice-Hall, 1986.

    Google Scholar 

  16. You, J.-H. and P.A. Subrahmanyam, “A class of term rewriting systems and unification,” unpublished manuscript, 1985.

    Google Scholar 

  17. You, J.-H. and P.A. Subrahmanyam, “Equational logic programming: an extension to equational programming,” in Proc. 13th POPL, pp. 209–218, St. Petersburg, Florida, January, 1986.

    Google Scholar 

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Laurent Kott

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© 1986 Springer-Verlag Berlin Heidelberg

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You, JH., Subrahmanyam, P.A. (1986). E-unification algorithms for a class of confluent term rewriting systems. In: Kott, L. (eds) Automata, Languages and Programming. ICALP 1986. Lecture Notes in Computer Science, vol 226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16761-7_95

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  • DOI: https://doi.org/10.1007/3-540-16761-7_95

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16761-7

  • Online ISBN: 978-3-540-39859-2

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