Skip to main content
SpringerLink
Log in

Transforming Conditional Rewrite Systems with Extra Variables into Unconditional Systems

  • Conference paper
Logic for Programming and Automated Reasoning (LPAR 1999)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1705))

Abstract

Deterministic conditional rewrite systems are interesting because they permit extra variables on the right-hand sides of the rules. If such a system is quasi-reductive, then it is terminating and has a computable rewrite relation. It will be shown that every deterministic CTRS R can be transformed into an unconditional TRS U(R) such that termination of U(R) implies quasi-reductivity of R. The main theorem states that quasi-reductivity of R implies innermost termination of U(R). These results have interesting applications in two different areas: modularity in term rewriting and termination proofs of well-moded logic programs.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. T. Arts and J. Giesl. Automatically proving termination where simplification orderings fail. In Proceedings of the 22nd International Colloquium on Trees in Algebra and Programming, volume 1214 of Lecture Notes in Computer Science, pages 261–272, Berlin, 1997. Springer-Verlag.

    Google Scholar 

  2. T. Arts and J. Giesl. Proving innermost normalisation automatically. In Proceedings of the 8th International Conference on Rewriting Techniques and Applications, volume 1232 of Lecture Notes in Computer Science, pages 157–172, Berlin, 1997. Springer-Verlag.

    Google Scholar 

  3. J. Avenhaus and C. Loría-Sáenz. On conditional rewrite systems with extra variables and deterministic logic programs. In Proceedings of the 5th International Conference on Logic Programming and Automated Reasoning, volume 822 of Lecture Notes in Artificial Intelligence, pages 215–229, Berlin, 1994. Springer-Verlag.

    Google Scholar 

  4. G. Aguzzi and U. Modigliani. Proving termination of logic programs by transforming them into equivalent term rewriting systems. In Proceedings of the 13th Conference on the Foundations of Software Technology and Theoretical Computer Science, volume 761 of Lecture Notes in Computer Science, pages 114–124, Berlin, 1993. Springer-Verlag.

    Google Scholar 

  5. T. Arts. Automatically Proving Termination and Innermost Normalisation of Term Rewriting Systems. PhD thesis, Utrecht University, 1997.

    Google Scholar 

  6. T. Arts and H. Zantema. Termination of logic programs via labelled term rewrite systems. In Proceedings of Computing Science in the Netherlands, pages 22–34, 1995.

    Google Scholar 

  7. T. Arts and H. Zantema. Termination of logic programs using semantic unification. In Proceedings of the 5th International Workshop on Logic Program Synthesis and Transformation, volume 1048 of Lecture Notes in Computer Science, pages 219–233, Berlin, 1996. Springer-Verlag.

    Google Scholar 

  8. H. Bertling and H. Ganzinger. Completion-time optimization of rewrite-time goal solving. In Proceedings of the 3rd International Conference on Rewriting Techniques and Applications, volume 355 of Lecture Notes in Computer Science, pages 45–58, Berlin, 1989. Springer-Verlag.

    Google Scholar 

  9. J.A. Bergstra and J.W. Klop. Conditional rewrite rules: Confluence and termination. Journal of Computer and System Sciences, 32(3):323–362, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  10. F. Baader and T. Nipkow. Term Rewriting and All That. Cambridge University Press, 1998.

    Google Scholar 

  11. N. Dershowitz, M. Okada, and G. Sivakumar. Canonical conditional rewrite systems. In Proceedings of the 9th Conference on Automated Deduction, volume 310 of Lecture Notes in Computer Science, pages 538-549, Berlin, 1988. Springer-Verlag.

    Chapter  Google Scholar 

  12. H. Ganzinger. Order-sorted completion: The many-sorted way. Theoretical Computer Science, 89:3–32, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  13. E. Giovannetti and C. Moiso. Notes on the elimination of conditions. In Proceedings of the 1st International Workshop on Conditional and Typed Rewriting Systems, volume 308 of Lecture Notes in Computer Science, pages 91–97, Berlin, 1988. Springer-Verlag.

    Google Scholar 

  14. B. Gramlich. Abstract relations between restricted termination and confluence properties of rewrite systems. Fundamenta Informaticae, 24:3–23, 1995.

    MATH  MathSciNet  Google Scholar 

  15. H. Ganzinger and U. Waldmann. Termination proofs of well-moded logic programs via conditional rewrite systems. In Proceedings of the 3rd International Workshop on Conditional Term Rewriting Systems, volume 656 of Lecture Notes in Computer Science, pages 113–127, Berlin, 1993. Springer-Verlag.

    Google Scholar 

  16. M. Hanus. The integration of functions into logic programming: Prom theory to practice. The Journal of Logic Programming, 19&20:583–628, 1994.

    Article  MathSciNet  Google Scholar 

  17. C. Hintermeier. How to transform canonical decreasing CTRSs into equivalent canonical TRSs. In Proceedings of the 4rd International Workshop on Conditional and Typed Rewriting Systems, volume 968 of Lecture Notes in Computer Science, pages 186–205, Berlin, 1995. Springer-Verlag.

    Google Scholar 

  18. T. Johnsson. Lambda lifting: Transforming programs to recursive functions. In Functional Programming Languages and Computer Architecture, volume 201 of Lecture Notes in Computer Science, pages 190–203, Berlin, 1985. Springer-Verlag.

    Google Scholar 

  19. M.R.K. Krishna Rao, D. Kapur, and R.K. Shyamasundar. A transformational methodology for proving termination of logic programs. In Proceedings of the 5th Workshop on Computer Science Logic, volume 626 of Lecture Notes in Computer Science, pages 213–226, Berlin, 1992. Springer-Verlag.

    Chapter  Google Scholar 

  20. M.R.K. Krishna Rao, D. Kapur, and R.K. Shyamasundar. Transformational methodology for proving termination of logic programs. The Journal of Logic Programming, 34(1):1–42, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  21. M. Marchiori. Logic programs as term rewriting systems. In Proceedings of the 4th International Conference on Algebraic and Logic Programming, volume 850 of Lecture Notes in Computer Science, pages 223–241, Berlin, 1994. Springer-Verlag.

    Google Scholar 

  22. M. Marchiori. Unravelings and ultra-properties. Technical Report 8, Dept. of Pure and Applied Mathematics, University of Padova, Italy, 1995.

    Google Scholar 

  23. M. Marchiori. Unravelings and ultra-properties. In Proceedings of the 5th International Conference on Algebraic and Logic Programming, volume 1139 of Lecture Notes in Computer Science, pages 107–121, Berlin, 1996. Springer-Verlag.

    Google Scholar 

  24. M. Marchiori. On the expressive power of rewriting. In Proceedings of the 17th International Conference on the Foundations of Software Technology and Theoretical Computer Science, volume 1346 of Lecture Notes in Computer Science, pages 88–102, Berlin, 1997. Springer-Verlag.

    Chapter  Google Scholar 

  25. E. Ohlebusch. Modular properties of composable term rewriting systems. Journal of Symbolic Computation, 20:1–41, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  26. F. van Raamsdonk. Translating logic programs into conditional rewriting systems. In Proceedings of the 14th International Conference on Logic Programming, pages 168–182. MIT Press, 1997.

    Google Scholar 

  27. D. de Schreye and S. Decorte. Termination of logic programs: The never-ending story. The Journal of Logic Programming, 19&20:199–260, 1994.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Technology, University of Bielefeld, P.O. Box 10 01 31, 33501, Bielefeld, Germany

    Enno Ohlebusch

Authors
  1. Enno Ohlebusch
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Max-Planck-Institut für Informatik, Im Stadtwald, D-66123, Saarbrücken, Germany

    Harald Ganzinger

  2. AT&T Labs Research, 180 Park Ave, Florham Park, NJ, 07932-0971, USA

    David McAllester

  3. Department of Computer Science, University of Manchester, Oxford Road, M13 9PL, Manchester, UK

    Andrei Voronkov

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ohlebusch, E. (1999). Transforming Conditional Rewrite Systems with Extra Variables into Unconditional Systems. In: Ganzinger, H., McAllester, D., Voronkov, A. (eds) Logic for Programming and Automated Reasoning. LPAR 1999. Lecture Notes in Computer Science(), vol 1705. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48242-3_8

Download citation

  • DOI: https://doi.org/10.1007/3-540-48242-3_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66492-5

  • Online ISBN: 978-3-540-48242-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation