research-article

Inductive invariant generation via abductive inference

Authors:

Ken McMillanAuthors Info & Claims

OOPSLA '13: Proceedings of the 2013 ACM SIGPLAN international conference on Object oriented programming systems languages & applications

Pages 443 - 456

https://doi.org/10.1145/2509136.2509511

Published: 29 October 2013 Publication History

Abstract

This paper presents a new method for generating inductive loop invariants that are expressible as boolean combinations of linear integer constraints. The key idea underlying our technique is to perform a backtracking search that combines Hoare-style verification condition generation with a logical abduction procedure based on quantifier elimination to speculate candidate invariants. Starting with true, our method iteratively strengthens loop invariants until they are inductive and strong enough to verify the program. A key feature of our technique is that it is lazy: It only infers those invariants that are necessary for verifying program correctness. Furthermore, our technique can infer arbitrary boolean combinations (including disjunctions) of linear invariants. We have implemented the proposed approach in a tool called HOLA. Our experiments demonstrate that HOLA can infer interesting invariants that are beyond the reach of existing state-of-the-art invariant generation tools.

References

[1]

Cousot, P., Halbwachs, N.: Automatic Discovery of Linear Restraints among Variables of a Program. In: POPL, ACM (1978) 84--96.

Digital Library

[2]

Miné, A.: The octagon abstract domain. Higher-Order and Symbolic Computation 19(1) (2006) 31--100.

Digital Library

[3]

Cousot, P., Cousot, R.: Systematic design of program analysis frameworks. In: POPL, ACM (1979) 269--282.

Digital Library

[4]

Karr, M.: Affine relationships among variables of a program. A. I. (1976) 133--151.

[5]

Gupta, A., Rybalchenko, A.: Invgen: An efficient invariant generator. In: Computer Aided Verification, Springer (2009) 634--640.

Digital Library

[6]

Colón, M., Sankaranarayanan, S., Sipma, H.: Linear invariant generation using non-linear constraint solving. In: Computer Aided Verification, Springer (2003) 420--432.

[7]

Henzinger, T., Jhala, R., Majumdar, R., Sutre, G.: Software verification with BLAST. In: International conference on Model checking software. (2003) 235--239.

Digital Library

[8]

Ball, T., Rajamani, S.: The slam toolkit. In: Computer aided verification, Springer (2001) 260--264.

[9]

McMillan, K.: Lazy annotation for program testing and verification. In: Computer Aided Verification, Springer (2010) 104--118.

Digital Library

[10]

Henzinger, T., Jhala, R., Majumdar, R., McMillan, K.: Abstractions from proofs. ACM SIGPLAN Notices 39(1) (2004) 232--244.

Digital Library

[11]

McMillan, K.: Interpolation and sat-based model checking. In: Computer Aided Verification, Springer (2003) 1--13.

[12]

Flanagan, C., Leino, K. R. M., Lillibridge, M., Nelson, G., Saxe, J. B., Stata, R.: Extended static checking for java. In: Proceedings of the ACM SIGPLAN 2002 Conference on Programming language design and implementation. PLDI '02, New York, NY, USA, ACM (2002) 234--245.

Digital Library

[13]

Leino, K.: Dafny: An automatic program verifier for functional correctness. In: Logic for Programming, Artificial Intelligence, and Reasoning, Springer (2010) 348--370.

Digital Library

[14]

Barnett, M., yuh Evan Chang, B., Deline, R., Jacobs, B., Leino, K. R.: Boogie: A modular reusable verifier for object-oriented programs. In: Formal Methods for Components and Objects: 4th International Symposium, FMCO 2005, volume 4111 of Lecture Notes in Computer Science, Springer (2006) 364--387.

Digital Library

[15]

Peirce, C.: Collected papers of Charles Sanders Peirce. Belknap Press (1932).

[16]

Dillig, I., Dillig, T., McMillan, K., Aiken, A.: Minimum satisfying assignments for SMT, CAV (2012).

Digital Library

[17]

Cooper, D.: Theorem proving in arithmetic without multiplication. Machine Intelligence 7(91-99) (1972) 300.

[18]

Dillig, I., Dillig, T., Aiken, A.: SAIL: Static Analysis Intermediate Language. Stanford University Technical Report.

[19]

Dillig, I., Dillig, T., Aiken, A.: Small formulas for large programs: On-line constraint simplification in scalable static analysis. SAS (2011).

Digital Library

[20]

Dillig, I., Dillig, T., Aiken, A.: Cuts from Proofs: A Complete and Practical Technique for Solving Linear Inequalities over Integers. In: CAV. (2009).

Digital Library

[21]

Jeannet, B.: Interproc analyzer for recursive programs with numerical variables. http://pop-art.inrialpes.fr/interproc/interprocweb.cgi.

[22]

Bradley, A.: Understanding IC3. Theory and Applications of Satisfiability Testing - SAT 2012 (2012) 1--14.

Digital Library

[23]

Gulwani, S., Srivastava, S., Venkatesan, R.: Program analysis as constraint solving. In: PLDI. Volume 43., ACM (2008) 281--292.

Digital Library

[24]

Jhala, R., McMillan, K.: A practical and complete approach to predicate refinement. Tools and Algorithms for the Construction and Analysis of Systems (2006) 459--473.

Digital Library

[25]

Sharma, R., Nori, A., Aiken, A.: Interpolants as classifiers. In: Computer Aided Verification, Springer (2012) 71--87.

Digital Library

[26]

Gulavani, B., Rajamani, S.: Counterexample driven refinement for abstract interpretation. Tools and Algorithms for the Construction and Analysis of Systems (2006) 474--488.

Digital Library

[27]

Gulwani, S., Jojic, N.: Program verification as probabilistic inference. In: ACM SIGPLAN Notices. Volume 42., ACM (2007) 277--289.

Digital Library

[28]

Gulavani, B., Chakraborty, S., Nori, A., Rajamani, S.: Automatically refining abstract interpretations. TACAS (2008) 443--458.

Digital Library

[29]

Beyer, D., Henzinger, T. A., Majumdar, R., Rybalchenko, A.: Path invariants. In: Proceedings of the 2007 ACM SIGPLAN conference on Programming language design and implementation. PLDI '07, New York, NY, USA, ACM (2007) 300--309.

Digital Library

[30]

Bradley, A. R., Manna, Z.: Property-directed incremental invariant generation. Form. Asp. Comput. 20(4-5) (June 2008) 379--405.

[31]

Gulavani, B. S., Henzinger, T. A., Kannan, Y., Nori, A. V., Rajamani, S. K.: Synergy: a new algorithm for property checking. In: Proceedings of the 14th ACM SIGSOFT international symposium on Foundations of software engineering. SIGSOFT '06/FSE-14, New York, NY, USA, ACM (2006) 117--127.

Digital Library

[32]

http://pub.ist.ac.at/agupta/invgen/: InvGen tool.

[33]

http://www.nec-labs.com/research/system/systems_SAV-website/benchmarks.php: NECLABS NECLA verification benchmarks.

[34]

Laviron, V., Logozzo, F.: Subpolyhedra: A (more) scalable approach to infer linear inequalities. In: Verification, Model Checking, and Abstract Interpretation, Springer (2009) 229--244.

Digital Library

[35]

Clarke, E., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement for symbolic model checking. J. ACM 50(5) (September 2003) 752--794.

Digital Library

[36]

Gulwani, S., Srivastava, S., Venkatesan, R.: Constraint-based invariant inference over predicate abstraction. In: Verification, Model Checking, and Abstract Interpretation, Springer (2009) 120--135.

Digital Library

[37]

Flanagan, C., Leino, K.: Houdini, an annotation assistant for esc/java. FME 2001: Formal Methods for Increasing Software Productivity (2001) 500--517.

Digital Library

[38]

Ernst, M., Perkins, J., Guo, P., McCamant, S., Pacheco, C., Tschantz, M., Xiao, C.: The Daikon system for dynamic detection of likely invariants. Science of Computer Programming 69(1-3) (2007) 35--45.

Digital Library

[39]

McMillan, K.: Lazy abstraction with interpolants. In: Computer Aided Verification, Springer (2006) 123--136.

Digital Library

[40]

Păsăreanu, C. S., Visser, W.: Verification of java programs using symbolic execution and invariant generation. In: SPIN Workshop on Model Checking Software. Springer (2004) 164--181.

[41]

Bradley, A.: Sat-based model checking without unrolling. In: Verification, Model Checking, and Abstract Interpretation, Springer (2011) 70--87.

Digital Library

[42]

Somenzi, F., Bradley, A.: IC3: where monolithic and incremental meet. In: Proceedings of the International Conference on Formal Methods in Computer-Aided Design, FMCAD Inc (2011) 3--8.

Digital Library

[43]

Calcagno, C., Distefano, D., O'Hearn, P., Yang, H.: Compositional shape analysis by means of bi-abduction. POPL 44(1) (2009) 289--300.

Digital Library

[44]

Giacobazzi, R.: Abductive analysis of modular logic programs. In: Proceedings of the 1994 International Symposium on Logic programming, Citeseer (1994) 377--391.

Digital Library

[45]

Gulwani, S., McCloskey, B., Tiwari, A.: Lifting abstract interpreters to quantified logical domains. In: POPL, ACM (2008) 235--246.

Digital Library

[46]

Calcagno, C., Distefano, D., Vafeiadis, V.: Bi-abductive resource invariant synthesis. In: Proceedings of the 7th Asian Symposium on Programming Languages and Systems. APLAS '09, Berlin, Heidelberg, Springer-Verlag (2009) 259--274.

Digital Library

[47]

Dillig, I., Dillig, T., Aiken, A.: Automated error diagnosis using abductive inference. In: Proceedings of the 33rd ACM SIGPLAN conference on Programming Language Design and Implementation. PLDI '12, New York, NY, USA, ACM (2012) 181--192.

Digital Library

[48]

Li, B., Dillig, I., Dillig, T.,McMillan, K., Sagiv, M.: Synthesis of circular compositional program proofs via abduction. In: Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems. TACAS'13, Springer-Verlag (2013) 370--384.

Digital Library

[49]

Gulwani, S., Musuvathi, M.: Cover Algorithms. In: ESOP. (2008) 193--207.

Digital Library

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Nagy SKim JReps TD’Antoni L(2024)Automating Unrealizability Logic: Hoare-Style Proof Synthesis for Infinite Sets of ProgramsProceedings of the ACM on Programming Languages10.1145/36897158:OOPSLA2(113-139)Online publication date: 8-Oct-2024
https://dl.acm.org/doi/10.1145/3689715
Wang ZPailoor SPrakash AWang YDillig I(2024)From Batch to Stream: Automatic Generation of Online AlgorithmsProceedings of the ACM on Programming Languages10.1145/36564188:PLDI(1014-1039)Online publication date: 20-Jun-2024
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Sellami YGirol GRecoules FCouroussé DBardin S(2024)Inference of Robust Reachability ConstraintsProceedings of the ACM on Programming Languages10.1145/36329338:POPL(2731-2760)Online publication date: 5-Jan-2024
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Index Terms

Inductive invariant generation via abductive inference
1. Theory of computation
  1. Logic
  2. Semantics and reasoning
    1. Program reasoning

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cover image ACM Conferences

OOPSLA '13: Proceedings of the 2013 ACM SIGPLAN international conference on Object oriented programming systems languages & applications

October 2013

904 pages

ISBN:9781450323741

DOI:10.1145/2509136

Co-chair:
Antony Hosking
Purdue University, USA
,
General Chair:
Patrick Eugster
Purdue University, USA
,
Program Chair:
Cristina V. Lopes
University of California, Irvine, USA

ACM SIGPLAN Notices Volume 48, Issue 10
OOPSLA '13
October 2013
867 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/2544173
Editor:
Mark W. Bailey
Hamilton College, Clinton, NY
Issue’s Table of Contents

Copyright © 2013 ACM.

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Published: 29 October 2013

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SPLASH '13: Conference on Systems, Programming, and Applications: Software for Humanity

October 29 - 31, 2013

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Cited By

Nagy SKim JReps TD’Antoni L(2024)Automating Unrealizability Logic: Hoare-Style Proof Synthesis for Infinite Sets of ProgramsProceedings of the ACM on Programming Languages10.1145/36897158:OOPSLA2(113-139)Online publication date: 8-Oct-2024
https://dl.acm.org/doi/10.1145/3689715
Wang ZPailoor SPrakash AWang YDillig I(2024)From Batch to Stream: Automatic Generation of Online AlgorithmsProceedings of the ACM on Programming Languages10.1145/36564188:PLDI(1014-1039)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656418
Sellami YGirol GRecoules FCouroussé DBardin S(2024)Inference of Robust Reachability ConstraintsProceedings of the ACM on Programming Languages10.1145/36329338:POPL(2731-2760)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632933
Pailoor SWang YDillig I(2024)Semantic Code Refactoring for Abstract Data TypesProceedings of the ACM on Programming Languages10.1145/36328708:POPL(816-847)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632870
Wen CCao JSu JXu ZQin SHe MLi HCheung STian C(2024)Enchanting Program Specification Synthesis by Large Language Models Using Static Analysis and Program VerificationComputer Aided Verification10.1007/978-3-031-65630-9_16(302-328)Online publication date: 25-Jul-2024
https://doi.org/10.1007/978-3-031-65630-9_16
Yu SWang TWang JJust RFraser G(2023)Loop Invariant Inference through SMT Solving Enhanced Reinforcement LearningProceedings of the 32nd ACM SIGSOFT International Symposium on Software Testing and Analysis10.1145/3597926.3598047(175-187)Online publication date: 12-Jul-2023
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Yao PKe JSun JFu HWu RRen K(2023)Demystifying Template-Based Invariant Generation for Bit-Vector Programs2023 38th IEEE/ACM International Conference on Automated Software Engineering (ASE)10.1109/ASE56229.2023.00069(673-685)Online publication date: 11-Sep-2023
https://doi.org/10.1109/ASE56229.2023.00069
Dimovski A(2023)Generalized Program Sketching by Abstract Interpretation and Logical AbductionStatic Analysis10.1007/978-3-031-44245-2_11(212-230)Online publication date: 22-Oct-2023
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Schröder MPotanin A(2022)Grammar Inference for Ad Hoc ParsersCompanion Proceedings of the 2022 ACM SIGPLAN International Conference on Systems, Programming, Languages, and Applications: Software for Humanity10.1145/3563768.3565550(38-42)Online publication date: 29-Nov-2022
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Liu HFu HYu ZSong JLi G(2022)Scalable linear invariant generation with Farkas’ lemmaProceedings of the ACM on Programming Languages10.1145/35632956:OOPSLA2(204-232)Online publication date: 31-Oct-2022
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