A Spatial Equational Logic for the Applied π-Calculus

  • Étienne Lozes
  • Jules Villard
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5201)


Spatial logics have been proposed to reason locally and modularly on algebraic models of distributed systems. In this paper we define the spatial equational logic AπL whose models are processes of the applied π-calculus. This extension of the π-calculus allows term manipulation and records communications as active substitutions in a frame, thus augmenting the underlying predefined equational theory. Our logic allows one to reason locally either on frames or on processes, thanks to static and dynamic spatial operators. We study the logical equivalences induced by various relevant fragments of AπL, and show in particular that the whole logic induces a coarser equivalence than structural congruence. We give characteristic formulae for some of these equivalences and for static equivalence. Going further into the exploration of AπL’s expressivity, we also show that it can eliminate standard term quantification.


Equational Theory Shift Function Separation Logic Evaluation Context Spatial Conjunction 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Reynolds, J.C.: Separation logic: A logic for shared mutable data structures. In: 17th IEEE Symposium on Logic in Computer Science (LICS 2002), pp. 55–74 (2002)Google Scholar
  2. 2.
    Ishtiaq, S., O’Hearn, P.W.: BI as an assertion language for mutable data structures. In: POPL 2001, pp. 14–26 (2001)Google Scholar
  3. 3.
    Gordon, A., Cardelli, L.: Anytime, anywhere: Modal logics for mobile ambients. In: Press, A. (ed.) POPL 2000, pp. 365–377 (2000)Google Scholar
  4. 4.
    Caires, L., Cardelli, L.: A spatial logic for concurrency (part I). Journal of Information and Computation 186(2) (2003)Google Scholar
  5. 5.
    Hirschkoff, D., Lozes, É., Sangiorgi, D.: Minimality results for spatial logics. In: Pandya, P.K., Radhakrishnan, J. (eds.) FSTTCS 2003. LNCS, vol. 2914, pp. 252–264. Springer, Heidelberg (2003)Google Scholar
  6. 6.
    Hirschkoff, D., Lozes, É., Sangiorgi, D.: On the expressiveness of the ambient logic. Logical Methods in Computer Science 2(2) (March 2006)Google Scholar
  7. 7.
    Hirschkoff, D.: An extensional spatial logic for mobile processes. In: Jin, H., Pan, Y., Xiao, N., Sun, J. (eds.) CONCUR 2002. LNCS, vol. 3252. Springer, Heidelberg (2004)Google Scholar
  8. 8.
    Abadi, M., Fournet, C.: Mobile values, new names, and secure communication. In: POPL 2001, pp. 104–115 (2001)Google Scholar
  9. 9.
    Milner, R., Parrow, J., Walker, D.: A calculus of mobile processes, i. Inf. Comput. 100(1), 1–40 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Dawar, A., Gardner, P., Ghelli, G.: Expressiveness and complexity of graph logic. Inf. Comput. 205(3), 263–310 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Calcagno, C., Gardner, P., Hague, M.: From separation logic to first-order logic. In: Sassone, V. (ed.) FOSSACS 2005. LNCS, vol. 3441, pp. 395–409. Springer, Heidelberg (2005)Google Scholar
  12. 12.
    Kuncak, V., Rinard, M.: On spatial conjunction as second-order logic. Technical report, MIT CSAIL (October 2004)Google Scholar
  13. 13.
    Hüttel, H., Pedersen, M.D.: A logical characterisation of static equivalence. Electron. Notes Theor. Comput. Sci. 173, 139–157 (2007)CrossRefGoogle Scholar
  14. 14.
    Sangiorgi, D.: Extensionality and intensionality of the ambient logics. In: POPL (2001)Google Scholar
  15. 15.
    Caires, L., Lozes, É.: Elimination of quantifiers and undecidability in spatial logics for concurrency. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 240–257. Springer, Heidelberg (2004)Google Scholar
  16. 16.
    Villard, J., Lozes, É., Treinen, R.: A spatial equational logic for the applied pi-calculus. Research Report LSV-08-10, LSV, ENS Cachan, France, 44 pages (March 2008)Google Scholar
  17. 17.
    Pym, D., Tofts, C.: A Calculus and logic of resources and processes. Formal Aspects of Computing 18(4), 495–517 (2006)zbMATHCrossRefGoogle Scholar
  18. 18.
    Mardare, R.: Observing distributed computation. a dynamic-epistemic approach. In: Mossakowski, T., Montanari, U., Haveraaen, M. (eds.) CALCO 2007. LNCS, vol. 4624, pp. 379–393. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  19. 19.
    Kramer, S.: Logical Concepts in Cryptography. PhD thesis, École Polytechnique Fédérale de Lausanne (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Étienne Lozes
    • 1
  • Jules Villard
    • 1
  1. 1.LSV, ENS CachanCNRS 61 av. du pdt WilsonCachanFrance

Personalised recommendations