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Partial completion of equational theories

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Abstract

In this paper, the notion of partial completion of equational theories is proposed, which is a procedure to construct a confluent term rewriting system from an equational theory without requirement of termination condition. A partial completion algorithm is presented with a brief description of its application in a program development system.

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References

  1. Knuth D E, Bendix P B. Simple word problems in universal algebras. In Computational Problems in Abstract Algebra, Leech J (ed.), Pergamon Press, 1970, pp. 263–297.

  2. Huet G, Oppen D C. Equations and rewrite rules: A survey. InFormal Language Theory: Perspectives and Open Problems, Book R V (ed.), Academic Press, 1980, pp. 349–405.

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

    Article  MATH  MathSciNet  Google Scholar 

  4. Hullet J. A catalogue of canonical term rewriting systems. Tech. Rep. CSL-113, SRI International, Menlo Park, California, 1980.

    Google Scholar 

  5. Dershowitz N, Jouannaud J-P. Rewrite systems. InHandbook of Theoretical Computer Science B: Formal Methods and Semantics, Leeuwen J Van (ed.), North-Holland, 1990, pp. 243–320.

  6. Guttag J V, Horowitz E, Musser D R. Abstract data types and software validation.Communications of ACM, 1978, 21(12): 1048–1064.

    Article  MATH  MathSciNet  Google Scholar 

  7. Goguen J, Meseguer J. Equality, type module and generics for logic programming. InLogic Programming Symposium. Sweden, 1984, pp. 22–26.

  8. Peterson G. A technique for establishing completeness results in theorem proving with equality.SIAM J. Comp., 1986, 15:4.

    Google Scholar 

  9. Jouannaud J-P. Church-Rosser computations with equational term rewriting system.LNCS 159, 1988, pp. 85–97.

  10. Peterson G E, Stickel M E. Complete sets of reductions for some equational theories.Journal of ACM, 1981, 28(2): 233–264.

    Article  MATH  MathSciNet  Google Scholar 

  11. Jouannaud J-P, Kirchner H. Completion of a set of rules modulo a set of equations.SIAM J. Comp., 1986, 15(4): 1155–1194.

    Article  MATH  MathSciNet  Google Scholar 

  12. Bachmair L, Dershowitz N. Completion for rewriting modulo a congruence.Theoretical Computer Science 69, 1989, pp. 33–52.

    MathSciNet  Google Scholar 

  13. Hsiang J. Refutational theorem proving using term-rewriting systems.Artificial Intelligence, 1985, 25: 255–300.

    Article  MATH  MathSciNet  Google Scholar 

  14. Musser D R. On proving inductive properties of abstract data type. InProceedings of 7th POPL Conference, 1980.

  15. Huet G, Hullot J M. Proofs by induction in equational theories with constructors.Journal of Computer Science and System 25, 1980.

  16. Jounnaud J-P, Kounalis E. Automatic proofs by induction in theories without constructors.Information and Computation, 82, 1989, pp. 42–53.

    Google Scholar 

  17. Huet G. Confluent reductions: Abstract properties and applications to term rewriting systems.Journal of ACM, 1980, 27(4): 797–821.

    Article  MATH  MathSciNet  Google Scholar 

  18. Klop J W. Combinatory reduction systems [dissertation]. Amsterdam: Math Centrum, 1980.

    MATH  Google Scholar 

  19. Toyama Y. On the Church-Rosser property for the direct sum of term rewriting systems.Journal of ACM, 1987, 34(1): 128–143.

    Article  MathSciNet  Google Scholar 

  20. Lin Kai, Sun Yongqiang. Semi-regular term rewriting system and its confluence.Journal of Software, 1992, 3(4): 1–11. (in Chinese)

    MathSciNet  Google Scholar 

  21. Lin Kai, Sun Yongqiang. Semi-linear term rewriting system and its confluence. InSelected Scientific Papers 2, Shanghai Jiao Tong University, 1991. (in Chinese)

  22. Lin Kai, Sun Yongqiang. The confluence of semi-linear term rewriting systems with local confluence. Technical Report, Shanghai Jiao Tong University, 1992. (in Chinese)

  23. Lin Kai, Sun Yongqiang. Pseudo-linear term rewriting system and its confluence. Technical Report, Shanghai Jiao Tong University, 1993. (in Chinese)

  24. Lin Kai, Sun Yongqiang. Relative pseudo-linear term rewriting system and its confluence. InFundamental Research of Intelligent Computers, Tsinghua University Press, 1994, pp. 474–482. (in Chinese)

  25. Lin Kai, Sun Yongqiang. Compressed path ordering and the structure measure of term rewriting systems.Journal of Software, 1993 4(2). (in Chinese)

  26. Dershowitz N. Termination of rewriting.Journal of Symbolic Computation, 1987, 3(1): 69–116.

    Article  MATH  MathSciNet  Google Scholar 

  27. Sun Yongqiang, Lin Kai, Shen Li. The design and implementation of a program development system based on rewriting method.ACM SIGPLAN Notices, 1997, 32(2): 27–34.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Shanghai Jiao Tong University, 200030, Shanghai, P.R. China

    Sun Yongqiang, Lin Kai & Lu Chaojun

Authors
  1. Sun Yongqiang
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  2. Lin Kai
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  3. Lu Chaojun
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Corresponding author

Correspondence to Sun Yongqiang.

Additional information

SUN Yongqiang was born in 1931. He is a professor and Ph.D. advisor in the Department of Computer Science and Engineering of Shanghai Jiao Tong University. His interests lie in new type programming languages, theoretical computer science, parallel and distributed systems.

LIN Kai was born in 1962. He received the M.S. degree in 1987, and is now with University of California at San Diego. His interests lie in rewriting theory and techniques.

LU Chaojun was born in 1964. He received the Ph.D. degree in 1995, and now is an associate professor in the Department of Computer Science and Engineering of Shanghai Jiao Tong University. His interests lie in rewriting techniques and database systems.

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Sun, Y., Lin, K. & Lu, C. Partial completion of equational theories. J. Comput. Sci. & Technol. 15, 552–559 (2000). https://doi.org/10.1007/BF02948837

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  • DOI: https://doi.org/10.1007/BF02948837

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