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Variable Side Conditions and Greatest Relations in Algebraic Separation Logic

  • Han-Hing Dang
  • Peter Höfner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6663)

Abstract

When reasoning within separation logic, it is often necessary to provide side conditions for inference rules. These side conditions usually contain information about variables and their use, and are given within a meta-language, i.e., the side conditions cannot be encoded in separation logic itself. In this paper we discuss different possibilities how side conditions of variables—occurring e.g. in the ordinary or the hypothetical frame rule—can be characterised using algebraic separation logic. We also study greatest relations; a concept used in the soundness proof of the hypothetical frame rule. We provide one and only one level of abstraction for the logic, the side conditions and the greatest relations.

Keywords

Inference Rule Information Hiding Side Condition Proof Rule Separation Logic 
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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References

  1. 1.
    Berdine, J., Calcagno, C., O’Hearn, P.W.: Smallfoot: Modular Automatic Assertion Checking with Separation Logic. In: de Boer, F.S., Bonsangue, M.M., Graf, S., de Roever, W.-P. (eds.) FMCO 2005. LNCS, vol. 4111, pp. 115–137. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  2. 2.
    Birkhoff, G.: Lattice Theory, Colloquium Publications, 3rd edn., vol. XXV. American Mathematical Society, Providence (1967)Google Scholar
  3. 3.
    Bornat, R., Calcagno, C., Yang, H.: Variables as resource in separation logic. Electronic Notes in Theoretical Computer Science 155, 247–276 (2006)CrossRefzbMATHGoogle Scholar
  4. 4.
    Dang, H.H., Höfner, P., Möller, B.: Towards algebraic separation logic. In: Berghammer, R., Jaoua, A.M., Möller, B. (eds.) RelMiCS 2009. LNCS, vol. 5827, pp. 59–72. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. 5.
    Dang, H.H., Höfner, P., Möller, B.: Algebraic Separation Logic. Tech. Rep. 2010-06, Institute of Computer Science, University of Augsburg (2010)Google Scholar
  6. 6.
    Dang, H.H., Höfner, P., Möller, B.: Algebraic Separation Logic. J. Logic and Algebraic Programming (accepted, 2011)Google Scholar
  7. 7.
    Kozen, D.: On Hoare logic, Kleene algebra, and types. In: Gärdenfors, P., Woleński, J., Kijania-Placek, K. (eds.) The Scope of Logic, Methodology, and Philosophy of Science: Volume One of the 11th Int. Congress Logic, Methodology and Philosophy of Science, Studies in Epistemology, Logic, Methodology, and Philosophy of Science, vol. 315, pp. 119–133. Kluwer, Dordrecht (2002)Google Scholar
  8. 8.
    O’Hearn, P.W., Reynolds, J.C., Yang, H.: Local reasoning about programs that alter data structures. In: Fribourg, L. (ed.) CSL 2001 and EACSL 2001. LNCS, vol. 2142, pp. 1–19. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  9. 9.
    O’Hearn, P.W., Reynolds, J.C., Yang, H.: Separation and information hiding. ACM Trans. Program. Lang. Syst. 31(3), 1–50 (2009)CrossRefzbMATHGoogle Scholar
  10. 10.
    Parkinson, M., Bornat, R., Calcagno, C.: Variables as Resource in Hoare logics. In: Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science, pp. 137–146. IEEE Computer Society, Los Alamitos (2006)Google Scholar
  11. 11.
    Reynolds, J.C.: An introduction to separation logic. In: Broy, M. (ed.) Engineering Methods and Tools for Software Safety and Security, pp. 285–310. IOS Press, Amsterdam (2009)Google Scholar
  12. 12.
    Schmidt, G., Ströhlein, T.: Relations and Graphs: Discrete Mathematics for Computer Scientists. Springer, Heidelberg (1993)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Han-Hing Dang
    • 1
  • Peter Höfner
    • 1
  1. 1.Institut für InformatikUniversität AugsburgAugsburgGermany

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