Skip to main content

Nominal Confluence Tool

  • Conference paper
  • First Online:
Book cover Automated Reasoning (IJCAR 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9706))

Included in the following conference series:

Abstract

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.

This work is partially supported by JSPS KAKENHI (Nos. 15K00003, 16K00091).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
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

Notes

  1. 1.

    http://www.smlnj.org/

References

  1. Confluence competition. http://coco.nue.riec.tohoku.ac.jp/

  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)

    Chapter  Google Scholar 

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

    Book  MATH  Google Scholar 

  5. Cheney, J.: Equivariant unification. J. Autom. Reasoning 45, 267–300 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Fernández, M., Gabbay, M.J.: Nominal rewriting. Inform. Comput. 205, 917–965 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  9. Gabbay, M.J., Pitts, A.M.: A new approach to abstract syntax with variable binding. Formal Aspects Comput. 13, 341–363 (2002)

    Article  MATH  Google Scholar 

  10. Hirokawa, N., Klein, D.: Saigawa: a confluence tool. In: Proceedings of the 1st IWC, p. 49 (2012)

    Google Scholar 

  11. Kikuchi, K., Aoto, T., Toyama, Y.: Parallel closure theorem for left-linear nominal rewriting systems. http://www.nue.riec.tohoku.ac.jp/user/kentaro/cr-nominal/pct.pdf

  12. Klop, J.W., van Oostrom, V., van Raamsdonk, F.: Combinatory reduction systems: introduction and survey. Theoret. Comput. Sci. 121, 279–308 (1993)

    Article  MathSciNet  MATH  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. Mayr, R., Nipkow, T.: Higher-order rewrite systems and their confluence. Theoret. Comput. Sci. 192, 3–29 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  16. Pitts, A.M.: Nominal logic, a first order theory of names and binding. Inform. Comput. 186, 165–193 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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. 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. 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. Urban, C., Pitts, A.M., Gabbay, M.J.: Nominal unification. Theoret. Comput. Sci. 323, 473–497 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Takahito Aoto .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Aoto, T., Kikuchi, K. (2016). Nominal Confluence Tool. In: Olivetti, N., Tiwari, A. (eds) Automated Reasoning. IJCAR 2016. Lecture Notes in Computer Science(), vol 9706. Springer, Cham. https://doi.org/10.1007/978-3-319-40229-1_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-40229-1_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40228-4

  • Online ISBN: 978-3-319-40229-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics