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Practical Tactics for Separation Logic

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Book cover Theorem Proving in Higher Order Logics (TPHOLs 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5674))

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Abstract

We present a comprehensive set of tactics that make it practical to use separation logic in a proof assistant. These tactics enable the verification of partial correctness properties of complex pointer-intensive programs. Our goal is to make separation logic as easy to use as the standard logic of a proof assistant. We have developed tactics for the simplification, rearranging, splitting, matching and rewriting of separation logic assertions as well as the discharging of a program verification condition using a separation logic description of the machine state. We have implemented our tactics in the Coq proof assistant, applying them to a deep embedding of Cminor, a C-like intermediate language used by Leroy’s verified CompCert compiler. We have used our tactics to verify the safety and completeness of a Cheney copying garbage collector written in Cminor. Our ideas should be applicable to other substructural logics and imperative languages.

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References

  1. Reynolds, J.C.: Separation logic: A logic for shared mutable data structures. In: LICS 2002, Washington, DC, USA, pp. 55–74. IEEE Computer Society, Los Alamitos (2002)

    Google Scholar 

  2. Girard, J.Y.: Linear logic. Theoretical Computer Science 50, 1–102 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  3. Birkedal, L., Torp-Smith, N., Reynolds, J.C.: Local reasoning about a copying garbage collector. In: POPL 2005, pp. 220–231. ACM Press, New York (2004)

    Google Scholar 

  4. McCreight, A., Shao, Z., Lin, C., Li, L.: A general framework for certifying gcs and their mutators. In: PLDI 2007, pp. 468–479. ACM, New York (2007)

    Google Scholar 

  5. The Coq Development Team: The Coq proof assistant, http://coq.inria.fr

  6. 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)

    Chapter  Google Scholar 

  7. Leroy, X.: Formal certification of a compiler back-end, or: programming a compiler with a proof assistant. In: POPL 2006, pp. 42–54. ACM Press, New York (2006)

    Google Scholar 

  8. Cheney, C.J.: A nonrecursive list compacting algorithm. Communications of the ACM 13(11), 677–678 (1970)

    Article  MATH  Google Scholar 

  9. Appel, A.W., Blazy, S.: Separation logic for small-step Cminor. In: Schneider, K., Brandt, J. (eds.) TPHOLs 2007. LNCS, vol. 4732, pp. 5–21. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  10. Paulin-Mohring, C.: Inductive definitions in the system Coq—rules and properties. In: Bezem, M., Groote, J.F. (eds.) TLCA 1993. LNCS, vol. 664. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  11. Wildmoser, M., Nipkow, T.: Certifying machine code safety: Shallow versus deep embedding. In: Slind, K., Bunker, A., Gopalakrishnan, G.C. (eds.) TPHOLs 2004. LNCS, vol. 3223, pp. 305–320. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  12. Appel, A.W.: Tactics for separation logic (January 2006), http://www.cs.princeton.edu/~appel/papers/septacs.pdf

  13. Marti, N., Affeldt, R., Yonezawa, A.: Formal verification of the heap manager of an os using separation logic. In: Liu, Z., He, J. (eds.) ICFEM 2006. LNCS, vol. 4260, pp. 400–419. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  14. Boutin, S.: Using reflection to build efficient and certified decision procedures. In: Ito, T., Abadi, M. (eds.) TACS 1997. LNCS, vol. 1281, pp. 515–529. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  15. Myreen, M.O., Slind, K., Gordon, M.J.C.: Machine-code verification for multiple architectures - an application of decompilation into logic. In: Proceedings of Formal Methods in Computer-Aided Design (FMCAD) (2008)

    Google Scholar 

  16. Hawblitzel, C., Petrank, E.: Automated verification of practical garbage collectors. In: POPL 2009, pp. 441–453. ACM, New York (2009)

    Google Scholar 

  17. Tuch, H., Klein, G., Norrish, M.: Types, bytes, and separation logic. In: POPL 2007, pp. 97–108. ACM, New York (2007)

    Google Scholar 

  18. Marti, N., Affeldt, R.: A certified verifier for a fragment of separation logic. In: 9th JSSST Workshop on Programming and Prog. Langs, PPL 2007 (2007)

    Google Scholar 

  19. Tuerk, T.: A separation logic framework in HOL. In: Otmane Ait Mohamed, C.M., Tahar, S. (eds.) TPHOLs 2008: Emerging Trends Proceedings, August 2008, pp. 116–122 (2008)

    Google Scholar 

  20. Calcagno, C., Distefano, D., O’Hearn, P., Yang, H.: Compositional shape analysis by means of bi-abduction. In: POPL 2009, pp. 289–300. ACM, New York (2009)

    Google Scholar 

  21. Mehta, F., Nipkow, T.: Proving pointer programs in higher-order logic. Inf. Comput. 199(1-2), 200–227 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  22. Bulwahn, L., Krauss, A., Haftmann, F., Erkök, L., Matthews, J.: Imperative functional programming with Isabelle/HOL. In: Mohamed, O.A., Muñoz, C., Tahar, S. (eds.) TPHOLs 2008. LNCS, vol. 5170, pp. 134–149. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  23. Filliâtre, J.C., Marché, C.: The Why/Krakatoa/Caduceus platform for deductive program verification. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 173–177. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Portland State University, USA

    Andrew McCreight

Authors
  1. Andrew McCreight
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Technische Universität München, Boltzmannstraße 3, 85748, Garching, Germany

    Stefan Berghofer , Tobias Nipkow , Christian Urban  & Makarius Wenzel , ,  & 

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McCreight, A. (2009). Practical Tactics for Separation Logic. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2009. Lecture Notes in Computer Science, vol 5674. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03359-9_24

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  • DOI: https://doi.org/10.1007/978-3-642-03359-9_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03358-2

  • Online ISBN: 978-3-642-03359-9

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