research-article

Modular reasoning about heap paths via effectively propositional formulas

Authors:

Shachar Itzhaky,

Anindya Banerjee,

Aleksandar Nanevski,

Mooly SagivAuthors Info & Claims

ACM SIGPLAN Notices, Volume 49, Issue 1

Pages 385 - 396

https://doi.org/10.1145/2578855.2535854

Published: 08 January 2014 Publication History

Abstract

First order logic with transitive closure, and separation logic enable elegant interactive verification of heap-manipulating programs. However, undecidabilty results and high asymptotic complexity of checking validity preclude complete automatic verification of such programs, even when loop invariants and procedure contracts are specified as formulas in these logics. This paper tackles the problem of procedure-modular verification of reachability properties of heap-manipulating programs using efficient decision procedures that are complete: that is, a SAT solver must generate a counterexample whenever a program does not satisfy its specification. By (a) requiring each procedure modifies a fixed set of heap partitions and creates a bounded amount of heap sharing, and (b) restricting program contracts and loop invariants to use only deterministic paths in the heap, we show that heap reachability updates can be described in a simple manner. The restrictions force program specifications and verification conditions to lie within a fragment of first-order logic with transitive closure that is reducible to effectively propositional logic, and hence facilitate sound, complete and efficient verification. We implemented a tool atop Z3 and report on preliminary experiments that establish the correctness of several programs that manipulate linked data structures.

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References

[1]

M. F. Atig, A. Bouajjani, and S. Qadeer. Context-bounded analysis for concurrent programs with dynamic creation of threads. Logical Methods in Computer Science, 7(4), 2011.

[2]

M. Barnett, M. Fähndrich, K. R. M. Leino, P. Müller, W. Schulte, and H. Venter. Specification and verification: the spec# experience. Commun. ACM, 54(6):81--91, 2011.

Digital Library

[3]

C. Barrett, A. Stump, and C. Tinelli. SMTLIB: Satisfiability Modulo Theories Library, 2013. http://smtlib.cs.uiowa.edu/docs.html.

[4]

A. Bouajjani, C. Dragoi, C. Enea, and M. Sighireanu. Accurate invariant checking for programs manipulating lists and arrays with infinite data. In ATVA, pages 167--182, 2012.

Digital Library

[5]

G. Dong and J. Su. Incremental and decremental evaluation of transitive closure by first-order queries. Inf. & Comput., 120:101--106, 1995.

Digital Library

[6]

A. Gotsman, J. Berdine, and B. Cook. Interprocedural shape analysis with separated heap abstractions. In SAS, pages 240--260, 2006.

Digital Library

[7]

W. Hesse. Dynamic Computational Complexity. PhD thesis, UMass in Computer Science, June 2003.

Digital Library

[8]

N. Immerman. Descriptive complexity. Graduate texts in computer science. Springer, 1999.

[9]

S. S. Ishtiaq and P. W. O'Hearn. Bi as an assertion language for mutable data structures. In POPL, pages 14--26, 2001.

Digital Library

[10]

S. Itzhaky, A. Banerjee, N. Immerman, O. Lahav, A. Nanevski, and M. Sagiv. Modular reasoning about heap paths via effectively propositional formulas. Technical report, Tel Aviv University, 2013. http://www.cs.tau.ac.il/~shachar/dl/tr 2013b.pdf.

[11]

S. Itzhaky, A. Banerjee, N. Immerman, A. Nanevski, and M. Sagiv. Effectively-propositional reasoning about reachability in linked data structures. In CAV, pages 756--772, 2013.

Digital Library

[12]

S. Itzhaky, A. Banerjee, N. Immerman, A. Nanevski, and M. Sagiv. Effectively-propositional reasoning about reachability in linked data structures. Technical report, Tel Aviv University, 2013. http://www.cs.tau.ac.il/~shachar/dl/tr-2013.pdf.

[13]

S. K. Lahiri and S. Qadeer. Back to the future: revisiting precise program verification using smt solvers. In POPL, pages 171--182, 2008.

Digital Library

[14]

G. T. Leavens, A. L. Baker, and C. Ruby. Preliminary design of JML: a behavioral interface specification language for Java. ACM SIGSOFT Software Engineering Notes, 31(3):1--38, 2006.

Digital Library

[15]

P. Madhusudan, G. Parlato, and X. Qiu. Decidable logics combining heap structures and data. In POPL, pages 611--622. ACM, 2011.

Digital Library

[16]

N. Mitchell, E. Schonberg, and G. Sevitsky. Making sense of large heaps. In ECOOP, pages 77--97, 2009.

Digital Library

[17]

A. Møller and M. I. Schwartzbach. The pointer assertion logic engine. In PLDI, pages 221--231. ACM, 2001.

Digital Library

[18]

R. Piskac, L. M. de Moura, and N. Bjørner. Deciding effectively propositional logic using dpll and substitution sets. J. Autom. Reasoning, 44(4):401--424, 2010.

Digital Library

[19]

R. Piskac, T.Wies, and D. Zufferey. Automating separation logic using smt. In CAV, pages 773--789, 2013.

Digital Library

[20]

T. W. Reps, S. Sagiv, and G. Yorsh. Symbolic implementation of the best transformer. In VMCAI, pages 252--266, 2004.

[21]

N. Rinetzky, J. Bauer, T. W. Reps, S. Sagiv, and R. Wilhelm. A semantics for procedure local heaps and its abstractions. In POPL, pages 296--309, 2005.

Digital Library

[22]

N. Rinetzky, M. Sagiv, and E. Yahav. Interprocedural shape analysis for cutpoint-free programs. In SAS, pages 284--302, 2005.

Digital Library

[23]

X. Rival and B.-Y. E. Chang. Calling context abstraction with shapes. In POPL, pages 173--186, 2011.

Digital Library

[24]

R. E. Tarjan. Efficiency of a good but not linear set union algorithm. Journal of the ACM, 22(2):215--225, 1975.

Digital Library

[25]

J. Wing. The CMU Larch Project. 1995. URL http://www.cs.cmu.edu/afs/cs/project/larch/www/home.html.

[26]

G. Winskel. The Formal Semantics of Programming Languages: An Introduction. Foundations of Computing Series. Zone Books, U.S., 1993. ISBN 9780262731034.

Digital Library

[27]

H. Yang, O. Lee, J. Berdine, C. Calcagno, B. Cook, D. Distefano, and P. W. O'Hearn. Scalable shape analysis for systems code. In CAV, pages 385--398, 2008.

Digital Library

[28]

G. Yorsh, A. M. Rabinovich, M. Sagiv, A. Meyer, and A. Bouajjani. A logic of reachable patterns in linked data-structures. J. Log. Algebr. Program., 73(1-2):111--142, 2007.

[29]

K. Zee, V. Kuncak, and M. C. Rinard. Full functional verification of linked data structures. In PLDI, pages 349--361, 2008.

Digital Library

Cited By

Zhou ZDickerson RDelaware BJagannathan S(2021)Data-driven abductive inference of library specificationsProceedings of the ACM on Programming Languages10.1145/34854935:OOPSLA(1-29)Online publication date: 15-Oct-2021
https://dl.acm.org/doi/10.1145/3485493
Elad NPadon OShoham S(2024)An Infinite Needle in a Finite Haystack: Finding Infinite Counter-Models in Deductive VerificationProceedings of the ACM on Programming Languages10.1145/36328758:POPL(970-1000)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632875
Murali APeña LLöding CMadhusudan P(2023)A First-order Logic with FramesACM Transactions on Programming Languages and Systems10.1145/358305745:2(1-44)Online publication date: 15-May-2023
https://dl.acm.org/doi/10.1145/3583057
Show More Cited By

Index Terms

Modular reasoning about heap paths via effectively propositional formulas
1. Software and its engineering
  1. Software notations and tools
    1. Compilers
      1. Dynamic compilers
  2. Software organization and properties
    1. Contextual software domains
      1. Operating systems
        Memory management

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Published In

cover image ACM SIGPLAN Notices

ACM SIGPLAN Notices Volume 49, Issue 1

POPL '14

January 2014

661 pages

ISSN:0362-1340

EISSN:1558-1160

DOI:10.1145/2578855

Editor:
Mark W. Bailey
Hamilton College, Clinton, NY

Issue’s Table of Contents

POPL '14: Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
January 2014
702 pages
ISBN:9781450325448
DOI:10.1145/2535838
General Chair:
Suresh Jagannathan
Purdue University, USA
,
Program Chair:
Peter Sewell
University of Cambridge, UK

Copyright © 2014 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 08 January 2014

Published in SIGPLAN Volume 49, Issue 1

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Cited By

Zhou ZDickerson RDelaware BJagannathan S(2021)Data-driven abductive inference of library specificationsProceedings of the ACM on Programming Languages10.1145/34854935:OOPSLA(1-29)Online publication date: 15-Oct-2021
https://dl.acm.org/doi/10.1145/3485493
Elad NPadon OShoham S(2024)An Infinite Needle in a Finite Haystack: Finding Infinite Counter-Models in Deductive VerificationProceedings of the ACM on Programming Languages10.1145/36328758:POPL(970-1000)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632875
Murali APeña LLöding CMadhusudan P(2023)A First-order Logic with FramesACM Transactions on Programming Languages and Systems10.1145/358305745:2(1-44)Online publication date: 15-May-2023
https://dl.acm.org/doi/10.1145/3583057
Meyer RWies TWolff S(2022)A concurrent program logic with a future and historyProceedings of the ACM on Programming Languages10.1145/35633376:OOPSLA2(1378-1407)Online publication date: 31-Oct-2022
https://dl.acm.org/doi/10.1145/3563337
Mathur UMadhusudan PViswanathan M(2020)What’s Decidable About Program Verification Modulo Axioms?Tools and Algorithms for the Construction and Analysis of Systems10.1007/978-3-030-45237-7_10(158-177)Online publication date: 17-Apr-2020
https://doi.org/10.1007/978-3-030-45237-7_10
Murali APeña LLöding CMadhusudan P(2020)A First-Order Logic with FramesProgramming Languages and Systems10.1007/978-3-030-44914-8_19(515-543)Online publication date: 27-Apr-2020
https://dl.acm.org/doi/10.1007/978-3-030-44914-8_19
Ter-Gabrielyan ASummers AMüller P(2019)Modular verification of heap reachability properties in separation logicProceedings of the ACM on Programming Languages10.1145/33605473:OOPSLA(1-28)Online publication date: 10-Oct-2019
https://dl.acm.org/doi/10.1145/3360547
Malik VHruska MSchrammel PVojnar T(2018)Template-Based Verification of Heap-Manipulating Programs2018 Formal Methods in Computer Aided Design (FMCAD)10.23919/FMCAD.2018.8603009(1-9)Online publication date: Oct-2018
https://doi.org/10.23919/FMCAD.2018.8603009
Kaki GEaranky KSivaramakrishnan KJagannathan S(2018)Safe replication through bounded concurrency verificationProceedings of the ACM on Programming Languages10.1145/32765342:OOPSLA(1-27)Online publication date: 24-Oct-2018
https://dl.acm.org/doi/10.1145/3276534
McMillan KPadon O(2018)Deductive Verification in Decidable Fragments with IvyStatic Analysis10.1007/978-3-319-99725-4_4(43-55)Online publication date: 29-Aug-2018
https://doi.org/10.1007/978-3-319-99725-4_4
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