Mutation in Linked Data Structures

  • Ewen Maclean
  • Andrew Ireland
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6991)

Abstract

Separation logic was developed as an extension to Hoare logic with the aim of simplifying pointer program proofs. A key feature of the logic is that it focuses the reasoning effort on only those parts of the heap that are relevant to a program - so called local reasoning. Underpinning this local reasoning are the separating conjunction and separating implication operators. Here we present an automated reasoning technique called mutation that provides guidance for separation logic proofs. Specifically, given two heap structures specified within separation logic, mutation attempts to construct an equivalence proof using a difference reduction strategy. Pivotal to this strategy is a generalised decomposition operator which is essential when matching heap structures. We show how mutation provides an effective strategy for proving the functional correctness of iterative and recursive programs within the context of weakest precondition analysis. Currently, mutation is implemented as a proof plan within our CORE program verification system. CORE combines results from shape analysis with our work on invariant generation and proof planning. We present our results for mutation within the context of the CORE system.

Keywords

Core System Separation Logic Functional Correctness Recursive Program Loop Invariant 
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.
    Atkey, R.: Amortised resource analysis with separation logic. In: 19th European Symposium on Programming, pp. 85–103 (2010)Google Scholar
  2. 2.
    Berdine, J., Calcagno, C., O’Hearn, P.: 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
  3. 3.
    Berdine, J., Calcagno, C., O’Hearn, P.: Symbolic execution with separation logic. In: Yi, K. (ed.) APLAS 2005. LNCS, vol. 3780, pp. 52–68. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Bundy, A.: The use of explicit plans to guide inductive proofs. In: Lusk, R., Overbeek, R. (eds.) CADE 1988. LNCS, vol. 310, pp. 111–120. Springer, Heidelberg (1988)CrossRefGoogle Scholar
  5. 5.
    Bundy, A., Basin, D., Hutter, D., Ireland, A.: Rippling: Meta-level Guidance for Mathematical Reasoning. Cambridge University Press, Cambridge (2005)CrossRefMATHGoogle Scholar
  6. 6.
    Burstall, R.M.: Some techniques for proving correctness of programs. In: Machine Intelligence, vol. 7, pp. 23–50. Edinburgh University Press, Edinburgh (1972)Google Scholar
  7. 7.
    Distefano, D., Parkinson, M.J.: jstar: towards practical verification for java. In: Proceedings of the 23rd ACM SIGPLAN Conference on Object-Oriented Programming Systems Languages and Applications, OOPSLA 2008, pp. 213–226. ACM, New York (2008)Google Scholar
  8. 8.
    Dixon, L., Fleuriot, J.D.: IsaPlanner: A prototype proof planner in isabelle. In: Baader, F. (ed.) CADE 2003. LNCS (LNAI), vol. 2741, pp. 279–283. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  9. 9.
    Ireland, A., Maclean, E., Grov, G.: Verification and synthesis of functional correctness of pointer programs. Research Memo HW-MACS-TR-0087, School of Mathematical and Computer Sciences, Heriot-Watt University (2011)Google Scholar
  10. 10.
    Maclean, E., Ireland, A., Grov, G.: The core system: Animation and functional correctness of pointer programs, Under review as a ASE-11 Tool Demonstration paper (2011)Google Scholar
  11. 11.
    Nguyen, H.H., David, C., Qin, S., Chin, W.N.: Automated verification of shape and size properties via separation logic. In: Cook, B., Podelski, A. (eds.) VMCAI 2007. LNCS, vol. 4349, pp. 251–266. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  12. 12.
    Nipkow, T., Paulson, L.C., Wenzel, M.T.: Isabelle/HOL — A Proof Assistant for Higher-Order Logic. LNCS, vol. 2283. Springer, Heidelberg (2002)MATHGoogle Scholar
  13. 13.
    O’Hearn, P., Reynolds, J., Hongseok, Y.: 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
  14. 14.
    Reynolds, J.C.: Separation logic: A logic for shared mutable data structures. In: Logic in Computer Science, pp. 55–74. IEEE Computer Society, Los Alamitos (2002)Google Scholar
  15. 15.
    Tuerk, T.: A formalisation of smallfoot in HOL. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol. 5674, pp. 469–484. Springer, Heidelberg (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Ewen Maclean
    • 1
  • Andrew Ireland
    • 1
  1. 1.School of Mathematical and Computer SciencesHeriot-Watt UniversityEdinburghUK

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