Journal of Computer Science and Technology

, Volume 20, Issue 4, pp 496–513 | Cite as

Mechanizing Weakly Ground Termination Proving of Term Rewriting Systems by Structural and Cover-Set Inductions

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Abstract

The paper presents three formal proving methods for generalized weakly ground terminating property, i.e., weakly terminating property in a restricted domain of a term rewriting system, one with structural induction, one with cover-set induction, and the third without induction, and describes their mechanization based on a meta-computation model for term rewriting systems—dynamic term rewriting calculus. The methods can be applied to non-terminating, non-confluent and/or non-left-linear term rewriting systems. They can do “forward proving” by applying propositions in the proof, as well as “backward proving” by discovering lemmas during the proof.

Keywords

automated formal proving cover-set induction dynamic term rewriting calculus term rewriting system weakly ground termination 

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References

  1. 1.
    Heut G, Lankford D S. On the uniform halting problem for term rewriting systems. Technical Report 283, Laboria, France, 1978.Google Scholar
  2. 2.
    Middeldorp A, Zantema H. Simple termination of rewrite systems. Theoretical Computer Science, 1997, 175: 127–158.CrossRefMathSciNetGoogle Scholar
  3. 3.
    Toyama Y. How to prove equivalence of term rewriting systems without induction. Theoretical Computer Science, 1991, 90: 369–390.CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Feng S. An inductive proving method for weakly ground termination of term rewriting systems. Computer Science, 2001, 28(7): 105–108. (in Chinese)Google Scholar
  5. 5.
    Zhang H, Kapur K, Krishnamoorthy M S. A mechanizable induction principle for equational specification. In Proc. 9th Int. Conf. Automated Deduction at Argonne, Illinois, USA, Lecture Notes in Computer Science 310, May 1988, pp.162–181.Google Scholar
  6. 6.
    Sakai M, Sakabe T, Inagaki Y. Cover set induction for verifying algebraic specifications. The Transaction of the Institute of Electronics, Information and Communication Engineers, 1992, J75-D-I(3): 170–179. (in Japanese)Google Scholar
  7. 7.
    Feng S, Sakabe T, Inagaki Y. Mechanizing explicit inductive equational reasoning by DTRC. IEICE Trans. Information and Systems, 1995, E78-D(2): 113–121.Google Scholar
  8. 8.
    Feng S, Cao S, Liu S. Mechanizing weak termination proving of term rewriting systems by induction. In Proc. Sixth Int. Conf. Young Computer Scientists, Oct. 2001, Hangzhou, P.R. China, pp.15–19.Google Scholar
  9. 9.
    Feng S, Sakabe T, Inagaki Y. Confluence property of simple frames in dynamic term rewriting calculus. IEICE Trans. Information and Systems, 1997, E80-D(6): 625–645.Google Scholar
  10. 10.
    Huet G. Confluent reductions: Abstract properties and applications to term rewriting systems. J. ACM, 1980, 27: 797–821.CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Feng S. Equivalence proving of term rewriting systems by induction. Computer Science, 2000, 27(8): 5–7. (in Chinese)Google Scholar
  12. 12.
    Gramlich B. Abstract relations between restricted termination and confluence properties of rewrite systems. Fundamentae Informaticae (special issue on term rewriting systems), 1995, 24: 3–23.MATHMathSciNetGoogle Scholar
  13. 13.
    A Serebrenik, D De Schreye. On Termination of Meta-programs. In Logic for Programming, AI, and Reasoning, Proceedings, Nieuwenhuis R, Voronkov A (eds.), Lecture Notes in Computer Science 2250, 2001, pp.517–530.Google Scholar
  14. 14.
    Brauburger J, Giesl J. Termination analysis for partial functions. In Proc. the Third International Static Analysis Symposium (SAS'96), Aachen, Germany, Lecture Notes in Computer Science 1145, 1996, pp.113–127.Google Scholar
  15. 15.
    Giesl J. Termination of nested and mutually recursive algorithms. Journal of Automated Reasoning, 1997, 19: 1–29.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of Computer ScienceBeijing Normal UniversityBeijingP.R. China

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