Skip to main content
SpringerLink
Log in
Book cover

International Conference on Rewriting Techniques and Applications

RTA 1999: Rewriting Techniques and Applications pp 148–162Cite as

Theory Path Orderings

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1631))

Abstract

We introduce the notion of a theory path ordering (TPO), which simplifies the construction of term orderings for superposition theorem proving in algebraic theories. To achieve refutational completeness of such calculi we need total, E-compatible and E-antisymmetric simplification quasi-orderings. The construction of a TPO takes as its ingredients a status function for interpreted function symbols and a precedence that makes the interpreted function symbols minimal. The properties of the ordering then follow from related properties of the status function. Theory path orderings generalize associative path orderings.

This is a preview of subscription content, 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baader, F. (1997). Combination of compatible reduction orderings that are total on ground terms. In 12th Ann. IEEE Symp. on Logic in Computer Science, Warsaw, pp. 2–13. IEEE Computer Society Press.

    Google Scholar 

  2. Baader, F. and Nipkow, T. (1998). Term rewriting and all that. Cambridge University Press, Cambridge, UK.

    Google Scholar 

  3. Bachmair, L. and Plaisted, D. (1985). Termination orderings for associativecommutative rewriting systems. Journal of Symbolic Computation 1: 329–349.

    Article  MATH  MathSciNet  Google Scholar 

  4. Bachmair, L., Ganzinger, H. and Stuber, J. (1995). Combining algebra and universal algebra in first-order theorem proving: The case of commutative rings. In Proc. 10thWorkshop on Specification of Abstract Data Types, Santa Margherita, Italy, LNCS 906, pp. 1–29. Springer.

    Chapter  Google Scholar 

  5. Delor, C. and Puel, L. (1993). Extension of the associative path ordering to a chain of associative commutative symbols. In Proc. 5th Int. Conf. on Rewriting Techniques and Applications, Montreal, LNCS 690, pp. 389–404. Springer.

    Google Scholar 

  6. Dershowitz, N. and Hoot, C. (1995). Natural termination. Theoretical Computer Science 142: 179–207.

    Article  MATH  MathSciNet  Google Scholar 

  7. Dershowitz, N. and Jouannaud, J.-P. (1990). Rewrite systems. In J. van Leeuwen (ed.), Handbook of Theoretical Computer Science: Formal Models and Semantics, Vol. B, chapter 6, pp. 243–320. Elsevier/MIT Press.

    Google Scholar 

  8. Geser, A. (1996). An improved general path order. Applicable Algebra in Engineering, Communication and Computing 7: 469–511.

    Article  MATH  MathSciNet  Google Scholar 

  9. Kapur, D. and Sivakumar, G. (1997). A total ground path ordering for proving termination of AC-rewrite systems. In Proc. 8th Int. Conf. on Rewriting Techniques and Applications, Sitges, Spain, LNCS 1103, pp. 142–156. Springer.

    Google Scholar 

  10. e, C. (1996). Normalised rewriting: an alternative to rewriting modulo a set of equations. Journal of Symbolic Computation 21: 253–288.

    Article  MathSciNet  Google Scholar 

  11. Rubio, A. and Nieuwenhuis, R. (1995). A total AC-compatible ordering based on RPO. Theoretical Computer Science 142: 209–227.

    Article  MATH  MathSciNet  Google Scholar 

  12. Stuber, J. (1998a). Superposition theorem proving for abelian groups represented as integer modules. Theoretical Computer Science 208(1-2): 149–177.

    Article  MATH  MathSciNet  Google Scholar 

  13. Stuber, J. (1998b). Superposition theorem proving for commutative rings. In W. Bibel and P. H. Schmitt (eds), Automated Deduction-A Basis for Applications. Volume III. Applications, chapter 2, pp. 31–55. Kluwer, Dordrecht, The Netherlands.

    Google Scholar 

  14. Waldmann, U. (1998). Extending reduction orderings to ACU-compatible reduction orderings. Information Processing Letters 67(1): 43–49.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Jürgen Stuber

Authors
  1. Jürgen Stuber
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University at Albany — SUNY, Albany, NY, 12222, USA

    Paliath Narendran

  2. LORIA — INRIA Lorraine 615, rue du Jardin Botanique, F-54602, Villers les Nancy, Cedex, France

    Michael Rusinowitch

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Stuber, J. (1999). Theory Path Orderings. In: Narendran, P., Rusinowitch, M. (eds) Rewriting Techniques and Applications. RTA 1999. Lecture Notes in Computer Science, vol 1631. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48685-2_12

Download citation

  • DOI: https://doi.org/10.1007/3-540-48685-2_12

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66201-3

  • Online ISBN: 978-3-540-48685-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation