Showing Invariance Compositionally for a Process Algebra for Network Protocols

  • Timothy Bourke
  • Robert J. van Glabbeek
  • Peter Höfner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8558)


This paper presents the mechanization of a process algebra for Mobile Ad hoc Networks and Wireless Mesh Networks, and the development of a compositional framework for proving invariant properties. Mechanizing the core process algebra in Isabelle/HOL is relatively standard, but its layered structure necessitates special treatment. The control states of reactive processes, such as nodes in a network, are modelled by terms of the process algebra. We propose a technique based on these terms to streamline proofs of inductive invariance. This is not sufficient, however, to state and prove invariants that relate states across multiple processes (entire networks). To this end, we propose a novel compositional technique for lifting global invariants stated at the level of individual nodes to networks of nodes.


Open Invariant Sequential Process Wireless Mesh Network Process Algebra Control Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Bengtson, J., Parrow, J.: Psi-calculi in Isabelle. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol. 5674, pp. 99–114. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  2. 2.
    Blanchette, J.C., Böhme, S., Paulson, L.C.: Extending Sledgehammer with SMT solvers. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS (LNAI), vol. 6803, pp. 116–130. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  3. 3.
    Bourke, T.: Mechanization of the Algebra for Wireless Networks (AWN). In: Archive of Formal Proofs (2014),
  4. 4.
    Bourke, T., van Glabbeek, R.J., Höfner, P.: A mechanized proof of loop freedom of the (untimed) AODV routing protocol. See authors’ webpages (2014)Google Scholar
  5. 5.
    Chaudhuri, K., Doligez, D., Lamport, L., Merz, S.: Verifying safety properties with the TLA +  proof system. In: Giesl, J., Hähnle, R. (eds.) IJCAR 2010. LNCS, vol. 6173, pp. 142–148. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  6. 6.
    Fehnker, A., van Glabbeek, R.J., Höfner, P., McIver, A., Portmann, M., Tan, W.L.: A process algebra for wireless mesh networks used for modelling, verifying and analysing AODV. Technical Report 5513, NICTA (2013),
  7. 7.
    Feliachi, A., Gaudel, M.-C., Wolff, B.: Isabelle/Circus: A process specification and verification environment. In: Joshi, R., Müller, P., Podelski, A. (eds.) VSTTE 2012. LNCS, vol. 7152, pp. 243–260. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  8. 8.
    Fokkink, W., Groote, J.F., Reniers, M.: Process algebra needs proof methodology. EATCS Bulletin 82, 109–125 (2004)Google Scholar
  9. 9.
    Göthel, T., Glesner, S.: An approach for machine-assisted verification of Timed CSP specifications. Innovations in Systems and Software Engineering 6(3), 181–193 (2010)CrossRefGoogle Scholar
  10. 10.
    Heyd, B., Crégut, P.: A modular coding of UNITY in COQ. In: Goos, G., Hartmanis, J., van Leeuwen, J., von Wright, J., Grundy, J., Harrison, J. (eds.) TPHOLs 1996. LNCS, vol. 1125, pp. 251–266. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  11. 11.
    Hirschkoff, D.: A full formalisation of π-calculus theory in the Calculus of Constructions. In: Gunter, E.L., Felty, A.P. (eds.) TPHOLs 1997. LNCS, vol. 1275, pp. 153–169. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  12. 12.
    Kammüller, F., Wenzel, M., Paulson, L.C.: Locales - A sectioning concept for Isabelle. In: Bertot, Y., Dowek, G., Hirschowitz, A., Paulin, C., Théry, L. (eds.) TPHOLs 1999. LNCS, vol. 1690, pp. 149–165. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  13. 13.
    Manna, Z., Pnueli, A.: Temporal Verification of Reactive Systems: Safety. Springer (1995)Google Scholar
  14. 14.
    Müller, O.: A Verification Environment for I/O Automata Based on Formalized Meta-Theory. PhD thesis, TU München (1998)Google Scholar
  15. 15.
    Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)CrossRefzbMATHGoogle Scholar
  16. 16.
    Paulson, L.C.: The inductive approach to verifying cryptographic protocols. J. Computer Security 6(1-2), 85–128 (1998)Google Scholar
  17. 17.
    Perkins, C.E., Belding-Royer, E.M., Das, S.R.: Ad hoc on-demand distance vector (AODV) routing. RFC 3561 (Experimental), Network Working Group (2003)Google Scholar
  18. 18.
    de Roever, W.-P., de Boer, F., Hannemann, U., Hooman, J., Lakhnech, Y., Poel, M., Zwiers, J.: Concurrency Verification: Introduction to Compositional and Noncompositional Methods. Cambridge Tracts in Theor. Comp. Sci., vol. 54. CUP (2001)Google Scholar
  19. 19.
    Sutcliffe, G.: The TPTP problem library and associated infrastructure: The FOF and CNF parts, v3.5.0. J. Automated Reasoning 43(4), 337–362 (2009)CrossRefzbMATHGoogle Scholar
  20. 20.
    Tej, H., Wolff, B.: A corrected failure divergence model for CSP in Isabelle/HOL. In: Fitzgerald, J.S., Jones, C.B., Lucas, P. (eds.) FME 1997. LNCS, vol. 1313, pp. 318–337. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  21. 21.
    Wenzel, M.: Isabelle/jEdit – A prover IDE within the PIDE framework. In: Jeuring, J., Campbell, J.A., Carette, J., Dos Reis, G., Sojka, P., Wenzel, M., Sorge, V. (eds.) CICM 2012. LNCS, vol. 7362, pp. 468–471. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  22. 22.
    Wenzel, M.: Shared-memory multiprocessing for interactive theorem proving. In: Blazy, S., Paulin-Mohring, C., Pichardie, D. (eds.) ITP 2013. LNCS, vol. 7998, pp. 418–434. Springer, Heidelberg (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Timothy Bourke
    • 1
    • 2
  • Robert J. van Glabbeek
    • 3
    • 4
  • Peter Höfner
    • 3
    • 4
  1. 1.Inria Paris-RocquencourtFrance
  2. 2.Ecole normale supérieureParisFrance
  3. 3.NICTASydneyAustralia
  4. 4.Computer Science and EngineeringUNSWSydneyAustralia

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