Compositional entailment checking for a fragment of separation logic
We present a decision procedure for checking entailment between separation logic formulas with inductive predicates specifying complex data structures corresponding to finite nesting of various kinds of singly linked lists: acyclic or cyclic, nested lists, skip lists, etc. The decision procedure is...
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| Published in | Formal methods in system design Vol. 51; no. 3; pp. 575 - 607 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.12.2017
Springer Nature B.V Springer Verlag |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0925-9856 1572-8102 1572-8102 |
| DOI | 10.1007/s10703-017-0289-4 |
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| Abstract | We present a decision procedure for checking entailment between separation logic formulas with inductive predicates specifying complex data structures corresponding to finite nesting of various kinds of singly linked lists: acyclic or cyclic, nested lists, skip lists, etc. The decision procedure is compositional in the sense that it reduces the problem of checking entailment between two arbitrary formulas to the problem of checking entailment between a formula and an atom. Subsequently, in case the atom is a predicate, we reduce the entailment to testing membership of a tree derived from the formula in the language of a tree automaton derived from the predicate. The procedure is later also extended to doubly linked lists. We implemented this decision procedure and tested it successfully on verification conditions obtained from programs using both singly and doubly linked nested lists as well as skip lists. |
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| AbstractList | We present a decision procedure for checking entailment between separation logic formulas with inductive predicates specifying complex data structures corresponding to finite nesting of various kinds of singly linked lists: acyclic or cyclic, nested lists, skip lists, etc. The decision procedure is compositional in the sense that it reduces the problem of checking entailment between two arbitrary formulas to the problem of checking entailment between a formula and an atom. Subsequently, in case the atom is a predicate, we reduce the entailment to testing membership of a tree derived from the formula in the language of a tree automaton derived from the predicate. The procedure is later also extended to doubly linked lists. We implemented this decision procedure and tested it successfully on verification conditions obtained from programs using both singly and doubly linked nested lists as well as skip lists. |
| Author | Vojnar, Tomáš Lengál, Ondřej Sighireanu, Mihaela Enea, Constantin |
| Author_xml | – sequence: 1 givenname: Constantin surname: Enea fullname: Enea, Constantin organization: IRIF, University Paris Diderot and CNRS – sequence: 2 givenname: Ondřej orcidid: 0000-0002-3038-5875 surname: Lengál fullname: Lengál, Ondřej email: lengal@fit.vutbr.cz organization: FIT, IT4I Centre of Excellence, Brno University of Technology – sequence: 3 givenname: Mihaela surname: Sighireanu fullname: Sighireanu, Mihaela organization: IRIF, University Paris Diderot and CNRS – sequence: 4 givenname: Tomáš surname: Vojnar fullname: Vojnar, Tomáš organization: FIT, IT4I Centre of Excellence, Brno University of Technology |
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| Keywords | Separation logic Decision procedure Tree automata Program analysis |
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| References | Enea C, Saveluc V, Sighireanu M (2013) Compositional invariant checking for overlaid and nested linked lists. In: Proceedings of ESOP’13, volume 7792 of LNCS, pp 129–148. Springer Piskac R, Wies T, Zufferey D (2014) Automating separation logic with trees and data. In: Proceedings of CAV’14, volume 8559 of LNCS, pp 711–728. Springer Qiu X, Garg P, Stefanescu A, Madhusudan P (2013) Natural proofs for structure, data, and separation. In: Proceedings of PLDI’13, pp 231–242. ACM Gu X, Chen T, Wu Z (2016) A complete decision procedure for linearly compositional separation logic with data constraints. In: Proceedings of IJCAR’16, volume 9706 of LNCS, pp 532–549. Springer Brotherston J, Fuhs C, Gorogiannis N, Pérez JN (2014) A decision procedure for satisfiability in separation logic with inductive predicates. In: Proceedings of CSL-LICS’14, pp 25:1–25:10. ACM Lengál O, Šimáček J, Vojnar T (2012) Vata: a library for efficient manipulation of non-deterministic tree automata. In: Proceedings of TACAS’12, volume 7214 of LNCS, pp 79–94. Springer Reynolds JC (2002) Separation logic: a logic for shared mutable data structures. In: Proceedings of LICS’02, pp 55–74. IEEE Sighireanu M, Cok D (2014) Report on SL-COMP’14. JSAT 1. http://smtcomp.sourceforge.net/2014/results-SLCOMP2.shtml Ishtiaq S, O’Hearn PW (2001) BI as an assertion language for mutable data structures. In: Proceedings of POPL’01, pp 14–26. ACM Pérez JN, Rybalchenko A (2013) Separation logic modulo theories. In: Proceedings of APLAS’13, volume 8301 of LNCS, pp 90–106. Springer Berdine J, Calcagno C, O’Hearn PW (2006) Smallfoot: modular automatic assertion checking with separation logic. In: Proceedings of FMCO’05, volume 4111 of LNCS, pp 115–137. Springer Enea C, Lengál O, Sighireanu M, Vojnar T (2014) Compositional entailment checking for a fragment of separation logic. In: Proceedings of APLAS’14, volume 8858 of LNCS, pp 314–333. Springer Pérez JN, Rybalchenko A (2011) Separation logic + superposition calculus = heap theorem prover. In: Proceedings of PLDI’11, pp 556–566. ACM Iosif R, Rogalewicz A, Šimáček J (2013) The tree width of separation logic with recursive definitions. In: Proceedings of CADE’13, volume 7898 of LNCS, pp 21–38. Springer Le QL, Sun J, Chin W-N (2016) Satisfiability modulo heap-based programs. In: Proceedings of CAV’16, volume 9779 of LNCS, pp 382–404. Springer Piskac R, Wies T, Zufferey D (2013) Automating separation logic using SMT. In: Proceedings of CAV’13, volume 8044 of LNCS, pp 773–789. Springer Brotherston J, Gorogiannis N, Petersen RL (2012) A generic cyclic theorem prover. In: Proceedings of APLAS’12, volume 7705 of LNCS, pp 350–367. Springer Iosif R, Rogalewicz A, Vojnar T (2014) Deciding entailments in inductive separation logic with tree automata. In: Proceedings of ATVA’14, volume 8837 of LNCS, pp 201–218. Springer Calcagno C, Yang H, O’Hearn PW (2001) Computability and complexity results for a spatial assertion language for data structures. In: Proceedings of FSTTCS’01, volume 2245 of LNCS, pp 108–119. Springer Berdine J, Calcagno C, Cook B, Distefano D, O’Hearn PW, Wies T, Yang H (2007) Shape analysis for composite data structures. In: Proceedings of CAV’07, volume 4590 of LNCS, pp 178–192. Springer Enea C, Lengál O, Sighireanu M, Vojnar T (2014) Spen. https://www.irif.fr/~sighirea/spen GaifmanHOn local and non-local propertiesStud Logic Found Math198210710513510.1016/S0049-237X(08)71879-20518.03008 Enea C, Sighireanu M, Wu Z (2015) On automated lemma generation for separation logic with inductive definitions. In: ATVA’15, volume 9364 of LNCS, pp 80–96. Springer ChinW-NDavidCHuuHNShengchaoQAutomated verification of shape, size and bag properties via user-defined predicates in separation logicSci Comput Program20127791006103610.1016/j.scico.2010.07.0041243.68148 Cook B, Haase C, Ouaknine J, Parkinson MJ, Worrell J (2011) Tractable reasoning in a fragment of separation logic. In: Proceedings of CONCUR’11, volume 6901 of LNCS, pp 235–249. Springer Berdine J, Calcagno C, O’Hearn PW (2005) A decidable fragment of separation logic. In: Proceedings of FSTTCS’04, volume 3328 of LNCS, pp 97–109. Springer 289_CR1 289_CR2 H Gaifman (289_CR13) 1982; 107 289_CR9 289_CR25 289_CR26 289_CR23 289_CR8 289_CR24 289_CR5 289_CR21 289_CR6 289_CR22 289_CR3 289_CR4 289_CR20 289_CR18 289_CR19 289_CR16 289_CR17 W-N Chin (289_CR7) 2012; 77 289_CR14 289_CR15 289_CR12 289_CR10 289_CR11 |
| References_xml | – reference: ChinW-NDavidCHuuHNShengchaoQAutomated verification of shape, size and bag properties via user-defined predicates in separation logicSci Comput Program20127791006103610.1016/j.scico.2010.07.0041243.68148 – reference: Iosif R, Rogalewicz A, Šimáček J (2013) The tree width of separation logic with recursive definitions. In: Proceedings of CADE’13, volume 7898 of LNCS, pp 21–38. Springer – reference: Calcagno C, Yang H, O’Hearn PW (2001) Computability and complexity results for a spatial assertion language for data structures. In: Proceedings of FSTTCS’01, volume 2245 of LNCS, pp 108–119. Springer – reference: Berdine J, Calcagno C, O’Hearn PW (2006) Smallfoot: modular automatic assertion checking with separation logic. In: Proceedings of FMCO’05, volume 4111 of LNCS, pp 115–137. Springer – reference: Enea C, Lengál O, Sighireanu M, Vojnar T (2014) Spen. https://www.irif.fr/~sighirea/spen – reference: Enea C, Sighireanu M, Wu Z (2015) On automated lemma generation for separation logic with inductive definitions. In: ATVA’15, volume 9364 of LNCS, pp 80–96. Springer – reference: Cook B, Haase C, Ouaknine J, Parkinson MJ, Worrell J (2011) Tractable reasoning in a fragment of separation logic. In: Proceedings of CONCUR’11, volume 6901 of LNCS, pp 235–249. Springer – reference: Sighireanu M, Cok D (2014) Report on SL-COMP’14. JSAT 1. http://smtcomp.sourceforge.net/2014/results-SLCOMP2.shtml – reference: Le QL, Sun J, Chin W-N (2016) Satisfiability modulo heap-based programs. In: Proceedings of CAV’16, volume 9779 of LNCS, pp 382–404. Springer – reference: Berdine J, Calcagno C, O’Hearn PW (2005) A decidable fragment of separation logic. In: Proceedings of FSTTCS’04, volume 3328 of LNCS, pp 97–109. Springer – reference: Gu X, Chen T, Wu Z (2016) A complete decision procedure for linearly compositional separation logic with data constraints. In: Proceedings of IJCAR’16, volume 9706 of LNCS, pp 532–549. Springer – reference: Berdine J, Calcagno C, Cook B, Distefano D, O’Hearn PW, Wies T, Yang H (2007) Shape analysis for composite data structures. In: Proceedings of CAV’07, volume 4590 of LNCS, pp 178–192. Springer – reference: Enea C, Lengál O, Sighireanu M, Vojnar T (2014) Compositional entailment checking for a fragment of separation logic. In: Proceedings of APLAS’14, volume 8858 of LNCS, pp 314–333. Springer – reference: Piskac R, Wies T, Zufferey D (2013) Automating separation logic using SMT. In: Proceedings of CAV’13, volume 8044 of LNCS, pp 773–789. Springer – reference: Lengál O, Šimáček J, Vojnar T (2012) Vata: a library for efficient manipulation of non-deterministic tree automata. In: Proceedings of TACAS’12, volume 7214 of LNCS, pp 79–94. Springer – reference: Pérez JN, Rybalchenko A (2011) Separation logic + superposition calculus = heap theorem prover. In: Proceedings of PLDI’11, pp 556–566. ACM – reference: Enea C, Saveluc V, Sighireanu M (2013) Compositional invariant checking for overlaid and nested linked lists. In: Proceedings of ESOP’13, volume 7792 of LNCS, pp 129–148. Springer – reference: Ishtiaq S, O’Hearn PW (2001) BI as an assertion language for mutable data structures. In: Proceedings of POPL’01, pp 14–26. ACM – reference: Qiu X, Garg P, Stefanescu A, Madhusudan P (2013) Natural proofs for structure, data, and separation. In: Proceedings of PLDI’13, pp 231–242. ACM – reference: Iosif R, Rogalewicz A, Vojnar T (2014) Deciding entailments in inductive separation logic with tree automata. In: Proceedings of ATVA’14, volume 8837 of LNCS, pp 201–218. Springer – reference: GaifmanHOn local and non-local propertiesStud Logic Found Math198210710513510.1016/S0049-237X(08)71879-20518.03008 – reference: Brotherston J, Fuhs C, Gorogiannis N, Pérez JN (2014) A decision procedure for satisfiability in separation logic with inductive predicates. In: Proceedings of CSL-LICS’14, pp 25:1–25:10. ACM – reference: Piskac R, Wies T, Zufferey D (2014) Automating separation logic with trees and data. In: Proceedings of CAV’14, volume 8559 of LNCS, pp 711–728. Springer – reference: Brotherston J, Gorogiannis N, Petersen RL (2012) A generic cyclic theorem prover. In: Proceedings of APLAS’12, volume 7705 of LNCS, pp 350–367. Springer – reference: Pérez JN, Rybalchenko A (2013) Separation logic modulo theories. In: Proceedings of APLAS’13, volume 8301 of LNCS, pp 90–106. Springer – reference: Reynolds JC (2002) Separation logic: a logic for shared mutable data structures. In: Proceedings of LICS’02, pp 55–74. 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| Title | Compositional entailment checking for a fragment of separation logic |
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