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Proving Confluence of Term Rewriting Systems via Persistency and Decreasing Diagrams

  • Conference paper
Rewriting and Typed Lambda Calculi (RTA 2014, TLCA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8560))

Abstract

The decreasing diagrams technique (van Oostrom, 1994) has been successfully used to prove confluence of rewrite systems in various ways; using rule-labelling (van Oostrom, 2008), it can also be applied directly to prove confluence of some linear term rewriting systems (TRSs) automatically. Some efforts for extending the rule-labelling are known, but non-left-linear TRSs are left beyond the scope. Two methods for automatically proving confluence of non-(left-)linear TRSs with the rule-labelling are given. The key idea of our methods is to combine the decreasing diagrams technique with persistency of confluence (Aoto & Toyama, 1997).

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References

  1. Aoto, T.: Automated confluence proof by decreasing diagrams based on rule-labelling. In: Proc. of 21st RTA. LIPIcs, vol. 6, pp. 7–16. Schloss Dagstuhl (2010)

    Google Scholar 

  2. Aoto, T., Toyama, Y.: Persistency of confluence. Journal of Universal Computer Science 3(11), 1134–1147 (1997)

    MATH  MathSciNet  Google Scholar 

  3. 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)

    Chapter  Google Scholar 

  4. Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press (1998)

    Google Scholar 

  5. Dutertre, B., de Moura, L.: The YICES SMT solver, http://yices.csl.sri.com/

  6. Gomi, H., Oyamaguchi, M., Ohta, Y.: On the Church-Rosser property of root-E-overlapping and strongly depth-preserving term rewriting systems. Transactions of IPSJ 39(4), 992–1005 (1998)

    MathSciNet  Google Scholar 

  7. Hirokawa, N., Klein, D.: Saigawa: A confluence tool. In: Proc. of 1st IWC, p. 49 (2012)

    Google Scholar 

  8. Hirokawa, N., Middeldorp, A.: Decreasing diagrams and relative termination. Journal of Automated Reasoning 47(4), 481–501 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  9. Huet, G.: Confluent reductions: Abstract properties and applications to term rewriting systems. Journal of the ACM 27(4), 797–821 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  10. Klein, D., Hirokawa, N.: Confluence of non-left-linear TRSs via relative termination. In: Bjørner, N., Voronkov, A. (eds.) LPAR-18 2012. LNCS, vol. 7180, pp. 258–273. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  11. van Oostrom, V.: Confluence by decreasing diagrams. Theoretical Computer Science 126(2), 259–280 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  12. van Oostrom, V.: Confluence by decreasing diagrams. In: Voronkov, A. (ed.) RTA 2008. LNCS, vol. 5117, pp. 306–320. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  13. Standard ML of New Jersey, http://www.sml.org/

  14. Suzuki, T., Aoto, T., Toyama, Y.: Confluence proofs of term rewriting systems based on persistency. Computer Software 30(3), 148–162 (2013) (in Japanese)

    Google Scholar 

  15. Toyama, Y.: Commutativity of term rewriting systems. In: Fuchi, K., Kott, L. (eds.) Programming of Future Generation Computers II, pp. 393–407. North-Holland, Amsterdam (1988)

    Google Scholar 

  16. Toyama, Y.: Membership conditional term rewriting systems. IEICE Transactions E72(11), 1224–1229 (1989)

    Google Scholar 

  17. Toyama, Y., Oyamaguchi, M.: Conditional linearization of non-duplicating term rewriting systems. IEICE Trans. Information and Systems E84-D(5), 439–447 (2001)

    Google Scholar 

  18. Zankl, H., Felgenhauer, B., Middeldorp, A.: CSI – A confluence tool. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 499–505. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  19. Zankl, H., Felgenhauer, B., Middeldorp, A.: Labelings for decreasing diagrams. In: Proc. of 22nd RTA. LIPIcs, vol. 10, pp. 377–392. Schloss Dagstuhl (2011)

    Google Scholar 

  20. Zantema, H.: Termination of term rewriting: interpretation and type elimination. Journal of Symbolic Computation 17, 23–50 (1994)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. RIEC, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577, Japan

    Takahito Aoto, Yoshihito Toyama & Kazumasa Uchida

Authors
  1. Takahito Aoto
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  2. Yoshihito Toyama
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  3. Kazumasa Uchida
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Editors and Affiliations

  1. Inria, 23 avenue d’Italie, CS 81321, 75214, Paris Cedex 13, France

    Gilles Dowek

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© 2014 Springer International Publishing Switzerland

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Aoto, T., Toyama, Y., Uchida, K. (2014). Proving Confluence of Term Rewriting Systems via Persistency and Decreasing Diagrams. In: Dowek, G. (eds) Rewriting and Typed Lambda Calculi. RTA TLCA 2014 2014. Lecture Notes in Computer Science, vol 8560. Springer, Cham. https://doi.org/10.1007/978-3-319-08918-8_4

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  • DOI: https://doi.org/10.1007/978-3-319-08918-8_4

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08917-1

  • Online ISBN: 978-3-319-08918-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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