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A Certified Decision Procedure for Tree Shares

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Formal Methods and Software Engineering (ICFEM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10610))

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Abstract

We develop a certified decision procedure for reasoning about systems of equations over the “tree share” fractional permission model of Dockins et al. Fractional permissions can reason about shared ownership of resources, e.g. in a concurrent program. We imported our certified procedure into the HIP/SLEEK verification system and found bugs in both the previous, uncertified, decision procedure and HIP/SLEEK itself. In addition to being certified, our new procedure improves previous work by correctly handling negative clauses and enjoys better performance.

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Notes

  1. 1.

    This is the entailment checker for positive constraints from previous work [25].

References

  1. Appel, A.W., Dockins, R., Hobor, A., Beringer, L., Dodds, J., Stewart, G., Blazy, S., Leroy, X.: Program Logics for Certified Compilers. Cambridge University Press, New York (2014)

    Book  MATH  Google Scholar 

  2. Bengtson, J., Jensen, J.B., Birkedal, L.: Charge! - a framework for higher-order separation logic in Coq. In: ITP, pp. 315–331 (2012)

    Google Scholar 

  3. Bornat, R., Calcagno, C., O’Hearn, P., Parkinson, M.: Permission accounting in separation logic. In: POPL, pp. 259–270 (2005)

    Google Scholar 

  4. Boyland, J.T., Müller, P., Schwerhoff, M., Summers, A.J.: Constraint semantics for abstract read permissions. In: FTfJP, pp. 2:1–2:6 (2014)

    Google Scholar 

  5. Boyland, J.: Checking interference with fractional permissions. In: Cousot, R. (ed.) SAS 2003. LNCS, vol. 2694, pp. 55–72. Springer, Heidelberg (2003). doi:10.1007/3-540-44898-5_4

    Chapter  Google Scholar 

  6. Calcagno, C., O’Hearn, P.W., Yang, H.: Local action and abstract separation logic. In: LICS, pp. 366–378 (2007)

    Google Scholar 

  7. Chin, W.N., Le, T.C., Qin, S.: Automated verification of countdownlatch (2017)

    Google Scholar 

  8. Chlipala, A.: The bedrock structured programming system: combining generative metaprogramming and hoare logic in an extensible program verifier. In: ICFP, pp. 391–402 (2013)

    Google Scholar 

  9. Cormen, T.H., Stein, C., Rivest, R.L., Leiserson, C.E.: Introduction to Algorithms, 3 edn. MIT Press (2009)

    Google Scholar 

  10. de Moura, L., Bjørner, N.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008). doi:10.1007/978-3-540-78800-3_24

    Chapter  Google Scholar 

  11. Dinsdale-Young, T., da Rocha Pinto, P., Andersen, K.J., Birkedal, L.: Caper: Automatic verification for fine-grained concurrency. In: Yang, H. (ed.) ESOP 2017. LNCS, vol. 10201, pp. 420–447. Springer, Heidelberg (2017). doi:10.1007/978-3-662-54434-1_16

    Chapter  Google Scholar 

  12. Dinsdale-Young, T., Dodds, M., Gardner, P., Parkinson, M.J., Vafeiadis, V.: Concurrent abstract predicates. In: D’Hondt, T. (ed.) ECOOP 2010. LNCS, vol. 6183, pp. 504–528. Springer, Heidelberg (2010). doi:10.1007/978-3-642-14107-2_24

    Chapter  Google Scholar 

  13. Dockins, R., Hobor, A., Appel, A.W.: A Fresh Look at Separation Algebras and Share Accounting. In: Hu, Z. (ed.) APLAS 2009. LNCS, vol. 5904, pp. 161–177. Springer, Heidelberg (2009). doi:10.1007/978-3-642-10672-9_13

    Chapter  Google Scholar 

  14. Fiedor, J., Letko, Z., Lourenço, J., Vojnar, T.: Dynamic validation of contracts in concurrent code. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds.) EUROCAST 2015. LNCS, vol. 9520, pp. 555–564. Springer, Cham (2015). doi:10.1007/978-3-319-27340-2_69

    Chapter  Google Scholar 

  15. Gherghina, C.A.: Efficiently verifying programs with rich control flows. Ph.D. thesis, National University of Singapore (2012)

    Google Scholar 

  16. Hobor, A., Gherghina, C.: Barriers in concurrent separation logic. In: Barthe, G. (ed.) ESOP 2011. LNCS, vol. 6602, pp. 276–296. Springer, Heidelberg (2011). doi:10.1007/978-3-642-19718-5_15

    Chapter  Google Scholar 

  17. Hobor, A.: Oracle semantics. Ph.D. thesis, Princeton University, Department of Computer Science, Princeton, NJ, October 2008

    Google Scholar 

  18. Hobor, A., Appel, A.W., Nardelli, F.Z.: Oracle semantics for concurrent separation logic. In: Drossopoulou, S. (ed.) ESOP 2008. LNCS, vol. 4960, pp. 353–367. Springer, Heidelberg (2008). doi:10.1007/978-3-540-78739-6_27

    Chapter  Google Scholar 

  19. Hobor, A., Gherghina, C.: Barriers in concurrent separation logic: now with tool support!. Logical Methods Comput. Sci. 8(2), 1–36 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  20. Hoenicke, J., Majumdar, R., Podelski, A.: Thread modularity at many levels: a pearl in compositional verification. In: POPL, pp. 473–485 (2017)

    Google Scholar 

  21. Huisman, M., Mostowski, W.: A symbolic approach to permission accounting for concurrent reasoning. In: ISPDC, pp. 165–174 (2015)

    Google Scholar 

  22. Jung, R., Swasey, D., Sieczkowski, F., Svendsen, K., Turon, A., Birkedal, L., Dreyer, D.: Iris: monoids and invariants as an orthogonal basis for concurrent reasoning. In: POPL, pp. 637–650 (2015)

    Google Scholar 

  23. Křena, B., Letko, Z., Vojnar, T., Ur, S.: A platform for search-based testing of concurrent software. In: PADTAD, pp. 48–58 (2010)

    Google Scholar 

  24. Le, D.-K., Chin, W.-N., Teo, Y.M.: Threads as resource for concurrency verification. In: PEPM, pp. 73–84 (2015)

    Google Scholar 

  25. Le, X.B., Gherghina, C., Hobor, A.: Decision procedures over sophisticated fractional permissions. In: Jhala, R., Igarashi, A. (eds.) APLAS 2012. LNCS, vol. 7705, pp. 368–385. Springer, Heidelberg (2012). doi:10.1007/978-3-642-35182-2_26

    Chapter  Google Scholar 

  26. Le, X.-B., Hobor, A., Lin, A.W.: Decidability and complexity of tree shares formulas. In: FSTTCS (2016)

    Google Scholar 

  27. Le, X.-B., Nguyen, T.-T., Chin, W.-N., Hobor, A.: A certified decision procedure for tree shares (extended) (2017). http://www.comp.nus.edu.sg/~lxbach/certtool/

  28. Meng, W., He, F., Wang, B.-Y., Liu, Q.: Thread-modular model checking with iterative refinement. In: Goodloe, A.E., Person, S. (eds.) NFM 2012. LNCS, vol. 7226, pp. 237–251. Springer, Heidelberg (2012). doi:10.1007/978-3-642-28891-3_24

    Chapter  Google Scholar 

  29. Müller, P., Schwerhoff, M., Summers, A.J.: Viper: a verification infrastructure for permission-based reasoning. In: Jobstmann, B., Leino, K.R.M. (eds.) VMCAI 2016. LNCS, vol. 9583, pp. 41–62. Springer, Heidelberg (2016). doi:10.1007/978-3-662-49122-5_2

    Chapter  Google Scholar 

  30. 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). doi:10.1007/978-3-540-69738-1_18

    Chapter  Google Scholar 

  31. Parkinson, M.: Local reasoning for Java. Ph.D. thesis, University of Cambridge (2005)

    Google Scholar 

  32. Pippenger, N.: Pure versus impure LISP. In: POPL, pp. 104–109 (1996)

    Google Scholar 

  33. Sergey, I., Nanevski, A., Banerjee, A.: Mechanized verification of fine-grained concurrent programs. In: PLDI, pp. 77–87 (2015)

    Google Scholar 

  34. Svendsen, K., Birkedal, L.: Impredicative concurrent abstract predicates. In: Shao, Z. (ed.) ESOP 2014. LNCS, vol. 8410, pp. 149–168. Springer, Heidelberg (2014). doi:10.1007/978-3-642-54833-8_9

    Chapter  Google Scholar 

  35. Turon, A., Dreyer, D., Birkedal, L.: Unifying refinement and hoare-style reasoning in a logic for higher-order concurrency. In: ICFP, pp. 377–390 (2013)

    Google Scholar 

  36. Villard, J.: Heaps and Hops. Ph.D. thesis, Laboratoire Spécification et Vérification, École Normale Supérieure de Cachan, France, February 2011

    Google Scholar 

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Authors and Affiliations

  1. School of Computing, National University of Singapore, Singapore, Singapore

    Xuan-Bach Le, Thanh-Toan Nguyen, Wei-Ngan Chin & Aquinas Hobor

  2. Yale-NUS College, National University of Singapore, Singapore, Singapore

    Aquinas Hobor

Authors
  1. Xuan-Bach Le
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  2. Thanh-Toan Nguyen
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  3. Wei-Ngan Chin
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  4. Aquinas Hobor
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Corresponding author

Correspondence to Xuan-Bach Le .

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Editors and Affiliations

  1. Xidian University, Xi’an, China

    Zhenhua Duan

  2. University of Oxford, Oxford, United Kingdom

    Luke Ong

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Le, XB., Nguyen, TT., Chin, WN., Hobor, A. (2017). A Certified Decision Procedure for Tree Shares. In: Duan, Z., Ong, L. (eds) Formal Methods and Software Engineering. ICFEM 2017. Lecture Notes in Computer Science(), vol 10610. Springer, Cham. https://doi.org/10.1007/978-3-319-68690-5_14

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  • DOI: https://doi.org/10.1007/978-3-319-68690-5_14

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