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Automated Cyclic Entailment Proofs in Separation Logic

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Automated Deduction – CADE-23 (CADE 2011)

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Abstract

We present a general automated proof procedure, based upon cyclic proof, for inductive entailments in separation logic. Our procedure has been implemented via a deep embedding of cyclic proofs in the HOL Light theorem prover. Experiments show that our mechanism is able to prove a number of non-trivial entailments involving inductive predicates.

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References

  1. Aczel, P.: An introduction to inductive definitions. In: Barwise, J. (ed.) Handbook of Mathematical Logic, pp. 739–782. North-Holland, Amsterdam (1977)

    Chapter  Google Scholar 

  2. Brotherston, J.: Sequent Calculus Proof Systems for Inductive Definitions. PhD thesis, University of Edinburgh (November 2006)

    Google Scholar 

  3. Brotherston, J.: Formalised inductive reasoning in the logic of bunched implications. In: Riis Nielson, H., Filé, G. (eds.) SAS 2007. LNCS, vol. 4634, pp. 87–103. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  4. Brotherston, J., Bornat, R., Calcagno, C.: Cyclic proofs of program termination in separation logic. In: Proceedings of POPL-35, pp. 101–112. ACM, New York (2008)

    Google Scholar 

  5. Brotherston, J., Kanovich, M.: Undecidability of propositional separation logic and its neighbours. In: Proceedings of LICS-25, pp. 137–146. IEEE, New York (2010)

    Google Scholar 

  6. Brotherston, J., Simpson, A.: Sequent calculi for induction and infinite descent. Journal of Logic and Computation (2010)

    Google Scholar 

  7. Bundy, A.: The automation of proof by mathematical induction. In: Handbook of Automated Reasoning, vol. I, ch. 13, pp. 845–911. Elsevier Science, Amsterdam (2001)

    Chapter  Google Scholar 

  8. Calcagno, C., Distefano, D., O’Hearn, P., Yang, H.: Compositional shape analysis by means of bi-abduction. In: Proceedings of POPL-36, pp. 289–300 (2009)

    Google Scholar 

  9. Calcagno, C., O’Hearn, P., Yang, H.: Local action and abstract separation logic. In: Proceedings of LICS-22, pp. 366–378. IEEE, Los Alamitos (2007)

    Google Scholar 

  10. Evan Chang, B.-Y., Rival, X.: Relational inductive shape analysis. In: POPL 2008, pp. 247–260 (2008)

    Google Scholar 

  11. Chang, B.-Y.E., Rival, X., Necula, G.C.: Shape analysis with structural invariant checkers. In: Riis Nielson, H., Filé, G. (eds.) SAS 2007. LNCS, vol. 4634, pp. 384–401. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  12. Distefano, D., O’Hearn, P., Yang, H.: A local shape analysis based on separation logic. In: Hermanns, H. (ed.) TACAS 2006. LNCS, vol. 3920, pp. 287–302. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  13. Distefano, D., Parkinson, M.: jStar: Towards practical verification for Java. In: Proceedings of OOPSLA, pp. 213–226. ACM, New York (2008)

    Google Scholar 

  14. Dixon, L., Fleuriot, J.D.: Higher order rippling in isaPlanner. In: Slind, K., Bunker, A., Gopalakrishnan, G.C. (eds.) TPHOLs 2004. LNCS, vol. 3223, pp. 83–98. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  15. Harrison, J.: HOL light: An overview. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol. 5674, pp. 60–66. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  16. Martin-Löf, P.: Haupstatz for the intuitionistic theory of iterated inductive definitions. In: Proc. Second Scandinavian Logic Symposium, pp. 179–216 (1971)

    Google Scholar 

  17. Nguyen, H.H., Chin, W.-N.: Enhancing program verification with lemmas. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 355–369. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  18. Nguyen, H.H., David, C., Qin, S.C., 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)

    Chapter  Google Scholar 

  19. Reynolds, J.C.: Separation logic: A logic for shared mutable data structures. In: Proceedings of 17th LICS (2002)

    Google Scholar 

  20. 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)

    Chapter  Google Scholar 

  21. Voicu, R., Li, M.: Descente infinie proofs in Coq. In: Proceedings of the 1st Coq Workshop, Technische Universität München (2009)

    Google Scholar 

  22. Wirth, C.-P.: Descente Infinie + Deduction. Logic Journal of the IGPL 12(1), 1–96 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  23. Yang, H., Lee, O., Berdine, J., Calcagno, C., Cook, B., Distefano, D., O’Hearn, P.W.: Scalable shape analysis for systems code. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 385–398. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

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Brotherston, J., Distefano, D., Petersen, R.L. (2011). Automated Cyclic Entailment Proofs in Separation Logic. In: Bjørner, N., Sofronie-Stokkermans, V. (eds) Automated Deduction – CADE-23. CADE 2011. Lecture Notes in Computer Science(), vol 6803. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22438-6_12

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  • DOI: https://doi.org/10.1007/978-3-642-22438-6_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22437-9

  • Online ISBN: 978-3-642-22438-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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