Abstract
Separation logic is a widely adopted formalism to verify programs manipulating dynamic data structures. Entailment checking of separation logic constitutes a crucial step for the verification of such programs. In general this problem is undecidable, hence only incomplete decision procedures are provided in most state-of-the-art tools. In this paper, we define a linearly compositional fragment of separation logic with inductive definitions, where traditional shape properties for linear data structures, as well as data constraints, e.g., the sortedness property and size constraints, can be specified in a unified framework. We provide complete decision procedures for both the satisfiability and the entailment problem, which are in NP and \(\mathrm{\varPi }^\mathrm{P}_3\) respectively.
Taolue Chen is partially supported by the ARC Discovery Project (DP160101652), the Singapore Ministry of Education AcRF Tier 2 grant (MOE2015-T2-1-137), and an oversea grant from the State Key Laboratory of Novel Software Technology, Nanjing Unviersity. Zhilin Wu is partially supported by the NSFC grants (No. 61100062, 61272135, 61472474, and 61572478).
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
References
Antonopoulos, T., Gorogiannis, N., Haase, C., Kanovich, M., Ouaknine, J.: Foundations for decision problems in separation logic with general inductive predicates. In: Muscholl, A. (ed.) FOSSACS 2014 (ETAPS). LNCS, vol. 8412, pp. 411–425. Springer, Heidelberg (2014)
Berdine, J., Calcagno, C., O’Hearn, P.W.: Symbolic execution with separation logic. In: Yi, K. (ed.) APLAS 2005. LNCS, vol. 3780, pp. 52–68. Springer, Heidelberg (2005)
Bouajjani, A., Drăgoi, C., Enea, C., Sighireanu, M.: Accurate invariant checking for programs manipulating lists and arrays with infinite data. In: Chakraborty, S., Mukund, M. (eds.) ATVA 2012. LNCS, vol. 7561, pp. 167–182. Springer, Heidelberg (2012)
Bozga, M., Iosif, R., Perarnau, S.: Quantitative separation logic and programs with lists. J. Autom. Reasoning 45(2), 131–156 (2010)
Brochenin, R., Demri, S., Lozes, É.: On the almighty wand. Inf. Comput. 211, 106–137 (2012)
Brotherston, J., Distefano, D., Petersen, R.L.: Automated cyclic entailment proofs in separation logic. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 131–146. Springer, Heidelberg (2011)
Brotherston, J., Fuhs, C., Perez, J.A.N., Gorogiannis, N.: A decision procedure for satisfiability in separation logic with inductive predicates. In: LICS (2014)
Calcagno, C., Distefano, D.: Infer: an automatic program verifier for memory safety of C programs. In: Bobaru, M., Havelund, K., Holzmann, G.J., Joshi, R. (eds.) NFM 2011. LNCS, vol. 6617, pp. 459–465. Springer, Heidelberg (2011)
Chin, W.-N., David, C., Nguyen, H.H., Qin, S.: Automated verification of shape, size and bag properties via user-defined predicates in separation logic. Sci. Comput. Program. 77(9), 1006–1036 (2012)
Chu, D., Jaffar, J., Trinh, M.: Automating proofs of data-structure properties in imperative programs. CoRR, abs/1407.6124 (2014)
Cook, B., Haase, C., Ouaknine, J., Parkinson, M., 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)
Demri, S., Deters, M.: Expressive completeness of separation logic with two variables and no separating conjunction. In: CSL-LICS, p. 37 (2014)
Enea, C., Lengál, O., Sighireanu, M., Vojnar, T.: Compositional entailment checking for a fragment of separation logic. In: Garrigue, J. (ed.) APLAS 2014. LNCS, vol. 8858, pp. 314–333. Springer, Heidelberg (2014)
Enea, C., Sighireanu, M., Wu, Z.: On automated lemma generation for separation logic with inductive definitions. ATVA 2015. LNCS, vol. 9364, pp. 80–96. Springer, Heidelberg (2015). doi:10.1007/978-3-319-24953-7_7
Hou, Z., Goré, R., Tiu, A.: Automated theorem proving for assertions in separation logic with all connectives. In: Felty, A.P., Middeldorp, A. (eds.) CADE-25. LNCS(LNAI), vol. 9195, pp. 501–516. Springer, Heidelberg (2015)
Iosif, R., Rogalewicz, A., Simacek, J.: The tree width of separation logic with recursive definitions. In: Bonacina, M.P. (ed.) CADE 2013. lncs, vol. 7898, pp. 21–38. Springer, Heidelberg (2013)
Iosif, R., Rogalewicz, A., Vojnar, T.: Deciding entailments in inductive separation logic with tree automata. In: Cassez, F., Raskin, J.-F. (eds.) ATVA 2014. LNCS, vol. 8837, pp. 201–218. Springer, Heidelberg (2014)
O’Hearn, P.W., Reynolds, J.C., Yang, H.: Local reasoning about programs that alter data structures. In: Fribourg, L. (ed.) CSL 2001 and EACSL 2001. LNCS, vol. 2142, p. 1. Springer, Heidelberg (2001)
Pek, E., Qiu, X., Madhusudan, P.: Natural proofs for data structure manipulation in C using separation logic. In: PLDI, pp. 440–451. ACM (2014)
Piskac, R., Wies, T., Zufferey, D.: Automating separation logic using SMT. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 773–789. Springer, Heidelberg (2013)
Piskac, R., Wies, T., Zufferey, D.: Automating separation logic with trees and data. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 711–728. Springer, Heidelberg (2014)
Piskac, R., Wies, T., Zufferey, D.: \({\sf {GRASShopper}}\) - complete heap verification with mixed specifications. In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014 (ETAPS). LNCS, vol. 8413, pp. 124–139. Springer, Heidelberg (2014)
Qiu, X., Garg, P., Stefănescu, A., Madhusudan, P.: Naturalproofs for structure, data, and separation. In: PLDI, pp. 231–242. ACM (2013)
Reynolds, J.C.: Separation logic: a logic for shared mutable datastructures. In: LICS, pp. 55–74. ACM (2002)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Gu, X., Chen, T., Wu, Z. (2016). A Complete Decision Procedure for Linearly Compositional Separation Logic with Data Constraints. In: Olivetti, N., Tiwari, A. (eds) Automated Reasoning. IJCAR 2016. Lecture Notes in Computer Science(), vol 9706. Springer, Cham. https://doi.org/10.1007/978-3-319-40229-1_36
Download citation
DOI: https://doi.org/10.1007/978-3-319-40229-1_36
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-40228-4
Online ISBN: 978-3-319-40229-1
eBook Packages: Computer ScienceComputer Science (R0)