Abstract
We propose a logic-based framework for automated reasoning about sequential programs manipulating singly-linked lists and arrays with unbounded data. We introduce the logic \(\textsf{SLAD}\), which allows combining shape constraints, written in a fragment of Separation Logic, with data and size constraints. We address the problem of checking the entailment between \(\textsf{SLAD}\) formulas, which is crucial in performing pre-post condition reasoning. Although this problem is undecidable in general for \(\textsf{SLAD}\), we propose a sound and powerful procedure that is able to solve this problem for a large class of formulas, beyond the capabilities of existing techniques and tools. We prove that this procedure is complete, i.e., it is actually a decision procedure for this problem, for an important fragment of \(\textsf{SLAD}\) including known decidable logics. We implemented this procedure and shown its preciseness and its efficiency on a significant benchmark of formulas.
This work has been partially supported by the French ANR project Veridyc.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Balaban, I., Pnueli, A., Zuck, L.D.: Shape Analysis of Single-Parent Heaps. In: Cook, B., Podelski, A. (eds.) VMCAI 2007. LNCS, vol. 4349, pp. 91–105. Springer, Heidelberg (2007)
Benedikt, M., Reps, T., Sagiv, M.: A Decidable Logic for Describing Linked Data Structures. In: Swierstra, S.D. (ed.) ESOP 1999. LNCS, vol. 1576, pp. 2–19. Springer, Heidelberg (1999)
Berdine, J., Calcagno, C., O’Hearn, P.W.: A Decidable Fragment of Separation Logic. In: Lodaya, K., Mahajan, M. (eds.) FSTTCS 2004. LNCS, vol. 3328, pp. 97–109. Springer, Heidelberg (2004)
Bouajjani, A., Drăgoi, C., Enea, C., Sighireanu, M.: A Logic-Based Framework for Reasoning about Composite Data Structures. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 178–195. Springer, Heidelberg (2009)
Bouajjani, A., Dragoi, C., Enea, C., Sighireanu, M.: Accurate invariant checking for programs manipulating lists and arrays with infinite data. Technical report, LIAFA (2011), http://www.liafa.univ-paris-diderot.fr/~cenea/SLAD.pdf
Bouajjani, A., Dragoi, C., Enea, C., Sighireanu, M.: On inter-procedural analysis of programs with lists and data. In: PLDI, pp. 578–589. ACM (2011)
Bouajjani, A., Drăgoi, C., Enea, C., Sighireanu, M.: Abstract Domains for Automated Reasoning about List-Manipulating Programs with Infinite Data. In: Kuncak, V., Rybalchenko, A. (eds.) VMCAI 2012. LNCS, vol. 7148, pp. 1–22. Springer, Heidelberg (2012)
Bradley, A.R., Manna, Z., Sipma, H.B.: What’s Decidable About Arrays? In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 427–442. Springer, Heidelberg (2005)
Cook, B., Haase, C., Ouaknine, J., Parkinson, M.J., Worrell, J.: Tractable Reasoning in a Fragment of Separation Logic. In: Katoen, J.-P., König, B. (eds.) CONCUR 2011. LNCS, vol. 6901, pp. 235–249. Springer, Heidelberg (2011)
de Moura, L., Bjørner, N.: Efficient E-Matching for SMT Solvers. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 183–198. Springer, Heidelberg (2007)
Ge, Y., de Moura, L.: Complete Instantiation for Quantified Formulas in Satisfiabiliby Modulo Theories. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 306–320. Springer, Heidelberg (2009)
Gulwani, S., McCloskey, B., Tiwari, A.: Lifting abstract interpreters to quantified logical domains. In: POPL, pp. 235–246. ACM (2008)
Habermehl, P., Iosif, R., Vojnar, T.: What Else Is Decidable about Integer Arrays? In: Amadio, R.M. (ed.) FOSSACS 2008. LNCS, vol. 4962, pp. 474–489. Springer, Heidelberg (2008)
Lahiri, S.K., Qadeer, S.: Back to the future: revisiting precise program verification using SMT solvers. In: POPL, pp. 171–182. ACM (2008)
Madhusudan, P., Parlato, G., Qiu, X.: Decidable logics combining heap structures and data d. In: POPL, pp. 283–294. ACM (2011)
Madhusudan, P., Qiu, X., Stefanescu, A.: Recursive proofs for inductive tree data-structures. In: POPL, pp. 123–136. ACM (2012)
Reynolds, J.C.: Separation logic: A logic for shared mutable data structures. In: LICS (2002)
Suter, P., Dotta, M., Kuncak, V.: Decision procedures for algebraic data types with abstractions. In: POPL, pp. 199–210. ACM (2010)
Wies, T., Muñiz, M., Kuncak, V.: An Efficient Decision Procedure for Imperative Tree Data Structures. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 476–491. Springer, Heidelberg (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bouajjani, A., Drăgoi, C., Enea, C., Sighireanu, M. (2012). Accurate Invariant Checking for Programs Manipulating Lists and Arrays with Infinite Data. In: Chakraborty, S., Mukund, M. (eds) Automated Technology for Verification and Analysis. ATVA 2012. Lecture Notes in Computer Science, vol 7561. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33386-6_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-33386-6_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33385-9
Online ISBN: 978-3-642-33386-6
eBook Packages: Computer ScienceComputer Science (R0)