CSI – A Confluence Tool

  • Harald Zankl
  • Bertram Felgenhauer
  • Aart Middeldorp
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6803)

Abstract

This paper describes a new confluence tool for term rewrite systems. Due to its modular design, the few techniques implemented so far can be combined flexibly. Methods developed for termination analysis are adapted to prove and disprove confluence. Preliminary experimental results show the potential of our tool.

Keywords

term rewriting confluence automation 

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References

  1. 1.
    Aoto, T.: Automated confluence proof by decreasing diagrams based on rule-labelling. In: Lynch, C. (ed.) RTA 2010. LIPIcs, vol. 6, pp. 7–16. Schloss Dagstuhl, Dagstuhl (2010)Google Scholar
  2. 2.
    Aoto, T., Yoshida, J., Toyama, Y.: Proving confluence of term rewriting systems automatically. In: Treinen, R. (ed.) RTA 2009. LNCS, vol. 5595, pp. 93–102. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)CrossRefMATHGoogle Scholar
  4. 4.
    Contejean, E., Courtieu, P., Forest, J., Pons, O., Urbain, X.: Automated certified proofs with CiME3. In: Schmidt-Schauß, M. (ed.) RTA 2011. LIPIcs, vol. 10, pp. 21–30. Schloss Dagstuhl, Dagstuhl (2011)Google Scholar
  5. 5.
    Felgenhauer, B., Zankl, H., Middeldorp, A.: Proving confluence with layer systems (2011); submitted for publicationGoogle Scholar
  6. 6.
    Genet, T.: Decidable approximations of sets of descendants and sets of normal forms. In: Nipkow, T. (ed.) RTA 1998. LNCS, vol. 1379, pp. 151–165. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  7. 7.
    Giesl, J., Thiemann, R., Schneider-Kamp, P.: Proving and disproving termination of higher-order functions. In: Gramlich, B. (ed.) FroCoS 2005. LNCS (LNAI), vol. 3717, pp. 216–231. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Huet, G.: Confluent reductions: Abstract properties and applications to term rewriting systems. JACM 27(4), 797–821 (1980)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Knuth, D., Bendix, P.: Simple word problems in universal algebras. In: Leech, J. (ed.) Computational Problems in Abstract Algebra, pp. 263–297. Pergamon Press, Oxford (1970)CrossRefGoogle Scholar
  10. 10.
    Korp, M., Middeldorp, A.: Match-bounds revisited. I&C 207(11), 1259–1283 (2009)MATHMathSciNetGoogle Scholar
  11. 11.
    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)CrossRefGoogle Scholar
  12. 12.
    van Oostrom, V.: Confluence by decreasing diagrams. TCS 126(2), 259–280 (1994)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    van Oostrom, V.: Developing developments. TCS 175(1), 159–181 (1997)CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    van Oostrom, V.: Confluence by decreasing diagrams. In: Voronkov, A. (ed.) RTA 2008. LNCS, vol. 5117, pp. 306–320. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  15. 15.
    Terese: Term Rewriting Systems, vol. 55. Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge (2003)Google Scholar
  16. 16.
    Tiwari, A.: Deciding confluence of certain term rewriting systems in polynomial time. In: LICS 2002, pp. 447–457 (2002)Google Scholar
  17. 17.
    Zankl, H., Felgenhauer, B., Middeldorp, A.: Labelings for decreasing diagrams. In: Schmidt-Schauß, M. (ed.) RTA 2011. LIPIcs, vol. 10, pp. 377–392. Schloss Dagstuhl, Dagstuhl (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Harald Zankl
    • 1
  • Bertram Felgenhauer
    • 1
  • Aart Middeldorp
    • 1
  1. 1.Institute of Computer ScienceUniversity of InnsbruckInnsbruckAustria

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