Towards Algebraic Separation Logic

  • Han-Hing Dang
  • Peter Höfner
  • Bernhard Möller
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5827)


We present an algebraic approach to separation logic. In particular, we give algebraic characterisations for all constructs of separation logic. The algebraic view does not only yield new insights on separation logic but also shortens proofs and enables the use of automated theorem provers for verifying properties at a more abstract level.


  1. 1.
    Birkhoff, G.: Lattice Theory, 3rd edn., vol. XXV. American Mathematical Society, Colloquium Publications (1967)Google Scholar
  2. 2.
    Blyth, T., Janowitz, M.: Residuation Theory. Pergamon Press, Oxford (1972)zbMATHGoogle Scholar
  3. 3.
    Conway, J.H.: Regular Algebra and Finite Machines. Chapman & Hall, Boca Raton (1971)zbMATHGoogle Scholar
  4. 4.
    Dang, H.-H.: Algebraic aspects of separation logic. Technical Report 2009-01, Institut für Informatik (2009)Google Scholar
  5. 5.
    Dang, H.-H., Höfner, P., Möller, B.: Towards algebraic separation logic. Technical Report 2009-12, Institut für Informatik, Universität Augsburg (2009)Google Scholar
  6. 6.
    Desharnais, J., Möller, B.: Characterizing Determinacy in Kleene Algebras. Information Sciences 139, 253–273 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Dijkstra, E.: A discipline of programming. Prentice Hall, Englewood Cliffs (1976)zbMATHGoogle Scholar
  8. 8.
    Ehm, T.: Pointer Kleene algebra. In: Berghammer, R., Möller, B., Struth, G. (eds.) RelMiCS 2003. LNCS, vol. 3051, pp. 99–111. Springer, Heidelberg (2004)Google Scholar
  9. 9.
    Hoare, C.A.R.: An axiomatic basis for computer programming. Communications of the ACM 12(10), 576–580 (1969)zbMATHCrossRefGoogle Scholar
  10. 10.
    Höfner, P., Struth, G.: Automated reasoning in Kleene algebra. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 279–294. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Huntington, E.V.: Boolean algebra. A correction. Transaction of AMS 35, 557–558 (1933)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Huntington, E.V.: New sets of independent postulates for the algebra of logic. Transaction of AMS 35, 274–304 (1933)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Jónsson, B., Tarski, A.: Boolean algebras with operators, Part I. American Journal of Mathematics 73 (1951)Google Scholar
  14. 14.
    Möller, B.: Towards pointer algebra. Science of Computer Prog. 21(1), 57–90 (1993)zbMATHCrossRefGoogle Scholar
  15. 15.
    Möller, B.: Calculating with acyclic and cyclic lists. Information Sciences 119(3-4), 135–154 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    O’Hearn, P.: Resources, concurrency, and local reasoning. Theoretical Computer Science 375, 271–307 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    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
  18. 18.
    O’Hearn, P.W., Reynolds, J.C., Yang, H.: Separation and information hiding. ACM Trans. Program. Lang. Syst. 31(3), 1–50 (2009)CrossRefGoogle Scholar
  19. 19.
    Reynolds, J.C.: An introduction to separation logic. Proceedings Marktoberdorf Summer School (2008) (forthcoming)Google Scholar
  20. 20.
    Rosenthal, K.: Quantales and their applications. Pitman Research Notes in Mathematics Series 234 (1990)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

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

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