Skip to main content
SpringerLink
Log in

AC Completion with Termination Tools

  • Conference paper
Automated Deduction – CADE-23 (CADE 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6803))

Included in the following conference series:

Abstract

We present masco tt, a tool for Knuth-Bendix completion modulo the theory of associative and commutative operators. In contrast to classical completion tools, masco tt does not rely on a fixed AC-compatible reduction order. Instead, a suitable order is implicitly constructed during a deduction by collecting all oriented rules in a similar fashion as done in the tool Slothrop. This allows for convergent systems which cannot be completed using standard orders. We outline the underlying inference system and comment on implementation details such as the use of multi-completion, term indexing techniques, and critical pair criteria.

The first author is supported by a DOC-fFORTE fellowship of the Austrian Academy of Sciences.

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. Alarcón, B., Gutiérrez, R., Lucas, S., Navarro-Marset, R.: Proving termination properties with mu-term. In: Johnson, M., Pavlovic, D. (eds.) AMAST 2010. LNCS, vol. 6486, pp. 201–208. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  2. Alarcón, B., Lucas, S., Meseguer, J.: A dependency pair framework for A ∨ C-termination. In: Ölveczky, P.C. (ed.) WRLA 2010. LNCS, vol. 6381, pp. 35–51. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  3. Bachmair, L.: Canonical Equational Proofs. Progress in Theoretical Computer Science. Birkhäuser (1991)

    Google Scholar 

  4. Bachmair, L., Chen, T., Ramakrishnan, I.V.: Associative-commutative discrimination nets. In: Gaudel, M.-C., Jouannaud, J.-P. (eds.) TAPSOFT 1993. LNCS, vol. 668, pp. 61–74. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  5. Ben Cherifa, A., Lescanne, P.: Termination of rewriting systems by polynomial interpretations and its implementation. SCP 9(2), 137–159 (1987)

    MATH  MathSciNet  Google Scholar 

  6. Contejean, E., Marché, C.: CiME: Completion modulo E. In: Ganzinger, H. (ed.) RTA 1996. LNCS, vol. 1103, pp. 416–419. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  7. Endrullis, J., Waldmann, J., Zantema, H.: Matrix interpretations for proving termination of term rewriting. JAR 40(2-3), 195–220 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  8. Fortenbacher, A.: An algebraic approach to unification under associativity and commutativity. JSC 3(3), 217–229 (1987)

    MATH  MathSciNet  Google Scholar 

  9. Gehrke, W.: Detailed catalogue of canonical term rewrite systems generated automatically. Technical report, RISC Linz (1992)

    Google Scholar 

  10. Giesl, J., Kapur, D.: Dependency pairs for equational rewriting. In: Middeldorp, A. (ed.) RTA 2001. LNCS, vol. 2051, pp. 93–108. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  11. Giesl, J., Schneider-Kamp, P., Thiemann, R.: AProVE 1.2: Automatic Termination Proofs in the Dependency Pair Framework. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 281–286. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  12. Kapur, D., Musser, D.R., Narendran, P.: Only prime superpositions need be considered in the Knuth-Bendix completion procedure. JSC 6(1), 19–36 (1988)

    MATH  MathSciNet  Google Scholar 

  13. Korp, M., Sternagel, C., Zankl, H., Middeldorp, A.: Tyrolean Termination Tool 2. In: Treinen, R. (ed.) RTA 2009. LNCS, vol. 5595, pp. 295–304. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  14. Kurihara, M., Kondo, H.: Completion for multiple reduction orderings. JAR 23(1), 25–42 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  15. Kusakari, K.: AC-Termination and Dependency Pairs of Term Rewriting Systems. PhD thesis, JAIST (2000)

    Google Scholar 

  16. Lincoln, P., Christian, J.: Adventures in associative-commutative unification. JSC 8, 393–416 (1989)

    MATH  MathSciNet  Google Scholar 

  17. Marché, C., Urbain, X.: Modular and incremental proofs of AC-termination. JSC 38(1), 873–897 (2004)

    MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  19. Sato, H., Winkler, S., Kurihara, M., Middeldorp, A.: Multi-completion with termination tools (system description). In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 306–312. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  20. Wehrman, I., Stump, A., Westbrook, E. M.: slothrop: Knuth-Bendix completion with a modern termination checker. In: Pfenning, F. (ed.) RTA 2006. LNCS, vol. 4098, pp. 287–296. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  21. Winkler, S., Sato, H., Middeldorp, A., Kurihara, M.: Optimizing mkbTT (system description). In: Proc. 21st RTA. LIPIcs, vol. 6, pp. 373–384 (2010)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computer Science, University of Innsbruck, Austria

    Sarah Winkler & Aart Middeldorp

Authors
  1. Sarah Winkler
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Aart Middeldorp
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Microsoft Research, One Microsoft Way, 98052-6399, Redmond, WA, USA

    Nikolaj Bjørner

  2. Max-Planck-Institut für Informatik, Campus E 1.4, 66123, Saarbrücken, Germany

    Viorica Sofronie-Stokkermans

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Winkler, S., Middeldorp, A. (2011). AC Completion with Termination Tools. In: Bjørner, N., Sofronie-Stokkermans, V. (eds) Automated Deduction – CADE-23. CADE 2011. Lecture Notes in Computer Science(), vol 6803. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22438-6_37

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-22438-6_37

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22437-9

  • Online ISBN: 978-3-642-22438-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation