Skip to main content
Springer Nature Link
Log in

Dynamic term rewriting calculus and its application to inductive equational reasoning

  • Conference paper
  • First Online:
Design and Implementation of Symbolic Computation Systems (DISCO 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 722))

  • 218 Accesses

Abstract

Dynamic Term Rewriting Calculus (DTRC) is a new computation model proposed by the authors for the purpose of formal description and verification of algorithms treating Term Rewriting Systems (TRSs). The computation of DTRC is basically term rewriting. The characteristic features of DTRC are dynamic change of rewriting rules during computation and hierarchical declaration of not only function symbols and variables but also rewriting rules. These features allow us to program meta-computation of TRSs in DTRC, i.e., we can implement in DTRC in a natural way those algorithms which manipulate TRSs as well as those procedures which verify such algorithms. We show here that we can use DTRC to represent the proof of an inductive theorem of an equational axiom system, i.e., we can translate the statements of base and induction steps in the proof of the inductive theorem into a DTRC term. The translation reduces the proof of the statements into the evaluation of the DTRC term.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Feng S., Sakabe T. and Inagaki Y.: “Dynamic Term Rewriting Calculus and its Application”, IEICE Technical Report, COMP 91-47, pp. 31–40, 1991. (in Japanese)

    Google Scholar 

  2. Feng S., Sakabe T. and Inagaki Y.: “Interpretation of Conditional Term Rewriting System by DTRC”, Proc. of 9th Conference of Japan Society for Software Science and Technology, pp. 313–316, September 1992

    Google Scholar 

  3. Feng S., Sakabe T. and Inagaki Y.: “Confluence and Termination of Dynamic Term Rewriting Calculus”, to be submitted.

    Google Scholar 

  4. Huet G. and Hullot J. M.: “Proofs by Induction in Equational Theories with Constructors”, Rapports de Recherch, INRIA,28(1980).

    Google Scholar 

  5. Huet G. and Lang B.: “Proving and applying program transformations expressed with second-order logic”, Acta Informatica, 11, pp. 31–55, 1978.

    Article  Google Scholar 

  6. Huet G. and Oppen D.: “Equations and rewrite rules: A survey”, In R. Book, ed., Formal Language Theory: Perspectives and Open Problems, pp. 349–405, Academic Press, New York, 1980.

    Google Scholar 

  7. Jouannaud J. P. and Kounalis E.: “Proof by induction in equational theories without constructors”, Proc. of 1st Symp. on Logic In Computer Science, pp. 358–366, Boston, USA, 1986

    Google Scholar 

  8. Klint P.: “A meta-environment for generating programming meta-environments”, In J. A. Bergstra and L. M. G. Feijs, eds., Algebraic Methods II: Theory, Tools, and Applications, pp. 105–124. LNCS 490, 1991.

    Google Scholar 

  9. Knuth D. E. and Bendix P.: “Simple word problems in universal algebra”, In J. Leech, ed., Computational Problems in Abstract Algebra, pp. 263–297. Oxford, Pergamon Press, 1970.

    Google Scholar 

  10. Kounalis E. and Rusinowitch M., “Mechanizing inductive reasoning”, Proc. Eighth National Conference on Artificial Intelligence, AAAI-90, pp. 240–245, July, 1990

    Google Scholar 

  11. Nadathur G. and Miller D.: “An overview of λ Prolog”, In K. Bowen and R. Kowalski,ed., Fifth International Conference and Symposium on Logic Programming, MIT Press, 1988.

    Google Scholar 

  12. Reddy U. S., “Term Rewriting Induction”, Proc. 10th International Conference on Automated Deduction, Kaiserslautern, FRG, LNCS 449, pp. 162–177, July 1990.

    Google Scholar 

  13. Sakai M., Sakabe T. and Inagaki Y.: “Cover Set Induction for Verifying Algebraic Specifications”, The transactions of the institute of electronics, information and communication engineers, Vol. J75-D-I No. 3, pp. 170–179, March 1992. (in Japanese)

    Google Scholar 

  14. Zhang H., Kapur K. and Krishnamoorthy M. S.: “A Mechanizable Induction Principle for Equational Specification”, Proc. of 9th International Conf. on Automated Deduction at Argonne,Illinois, USA, LNCS 310, pp. 162–181, May 1988.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Information Engineering, Faculty of Engineering, Nagoya University, Furo-cho, Chikusa-ku, 464-01, Nagoya, Japan

    Su Feng, Toshiki Sakabe & Yasuyoshi Inagaki

Authors
  1. Su Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Toshiki Sakabe
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yasuyoshi Inagaki
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Alfonso Miola

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Feng, S., Sakabe, T., Inagaki, Y. (1993). Dynamic term rewriting calculus and its application to inductive equational reasoning. In: Miola, A. (eds) Design and Implementation of Symbolic Computation Systems. DISCO 1993. Lecture Notes in Computer Science, vol 722. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013182

Download citation

  • DOI: https://doi.org/10.1007/BFb0013182

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57235-0

  • Online ISBN: 978-3-540-47985-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics