Nominal Confluence Tool

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9706)


Nominal rewriting is a framework of higher-order rewriting introduced in (Fernández, Gabbay & Mackie, 2004; Fernández & Gabbay, 2007). Recently, (Suzuki et al., 2015) revisited confluence of nominal rewriting in the light of feasibility. We report on an implementation of a confluence tool for (non-closed) nominal rewriting, based on (Suzuki et al., 2015) and succeeding studies.


Confluence Nominal rewriting Automation Variable binding Higher-order rewriting 


  1. 1.
    Confluence competition.
  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.
    Ayala-Rincón, M., Fernández, M., Gabbay, M.J., Rocha-Oliveira, A.C.: Checking overlaps of nominal rewrite rules. In: Pre-proceedings of the 10th LSFA, pp. 199–214 (2015)Google Scholar
  4. 4.
    Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)CrossRefzbMATHGoogle Scholar
  5. 5.
    Cheney, J.: Equivariant unification. J. Autom. Reasoning 45, 267–300 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Fernández, M., Gabbay, M.J.: Nominal rewriting. Inform. Comput. 205, 917–965 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Fernández, M., Gabbay, M.J., Mackie, I.: Nominal rewriting systems. In: Proceedings of the 6th PPDP, pp. 108–119. ACM Press (2004)Google Scholar
  8. 8.
    Fernández, M., Rubio, A.: Nominal completion for rewrite systems with binders. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012, Part II. LNCS, vol. 7392, pp. 201–213. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  9. 9.
    Gabbay, M.J., Pitts, A.M.: A new approach to abstract syntax with variable binding. Formal Aspects Comput. 13, 341–363 (2002)CrossRefzbMATHGoogle Scholar
  10. 10.
    Hirokawa, N., Klein, D.: Saigawa: a confluence tool. In: Proceedings of the 1st IWC, p. 49 (2012)Google Scholar
  11. 11.
    Kikuchi, K., Aoto, T., Toyama, Y.: Parallel closure theorem for left-linear nominal rewriting systems.
  12. 12.
    Klop, J.W., van Oostrom, V., van Raamsdonk, F.: Combinatory reduction systems: introduction and survey. Theoret. Comput. Sci. 121, 279–308 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 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)CrossRefGoogle Scholar
  14. 14.
    Mayr, R., Nipkow, T.: Higher-order rewrite systems and their confluence. Theoret. Comput. Sci. 192, 3–29 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Parigot, M.: \(\lambda \mu \)-calculus: an algorithmic interpretation of classical natural deduction. In: Voronkov, A. (ed.) Logic Programming and Automated Reasoning. LNCS, vol. 624, pp. 190–201. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  16. 16.
    Pitts, A.M.: Nominal logic, a first order theory of names and binding. Inform. Comput. 186, 165–193 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Sternagel, T., Middeldorp, A.: Conditional confluence (system description). In: Dowek, G. (ed.) RTA-TLCA 2014. LNCS, vol. 8560, pp. 456–465. Springer, Heidelberg (2014)Google Scholar
  18. 18.
    Suzuki, T., Kikuchi, K., Aoto, T., Toyama, Y.: On confluence of nominal rewriting systems. In: Proceedings of the 16th PPL, in Japanese (2014)Google Scholar
  19. 19.
    Suzuki, T., Kikuchi, K., Aoto, T., Toyama, Y.: Confluence of orthogonal nominal rewriting systems revisited. In: Proceedings of the 26th RTA. LIPIcs, vol. 36, pp. 301–317 (2015)Google Scholar
  20. 20.
    Suzuki, T., Kikuchi, K., Aoto, T., Toyama, Y.: Critical pair analysis in nominal rewriting. In: Proceedings of the 7th SCSS. EPiC, vol. 39, pp. 156–168. EasyChair (2016)Google Scholar
  21. 21.
    Urban, C., Pitts, A.M., Gabbay, M.J.: Nominal unification. Theoret. Comput. Sci. 323, 473–497 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    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)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Faculty of EngineeringNiigata UniversityNiigataJapan
  2. 2.RIEC, Tohoku UniversitySendaiJapan

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