Lazy Abstraction for Higher-Order Program Verification
Author: 
Taku TeraoAuthors Info & Claims
Taku TeraoAuthors Info & ClaimsArticle No.: 23, Pages 1 - 13
Abstract
This paper proposes a lazy abstraction algorithm for verification of functional programs. The feature of the lazy abstraction method is that the predicate abstraction and the model checking are fused, and that abstractions for unreachable configurations are pruned. We define an abstract semantics that characterizes the precision of the lazy abstraction algorithm, and prove the soundness of our verification method and the progress property of our abstraction refinement algorithm. We have implemented a prototype of our method, and confirmed through experiments that the total efficiency of verification is improved, compared with previous eager abstraction methods.
References
[1]
Broadbent, C.H., Carayol, A., Hague, M., Serre, O.: C-SHORe: a collapsible approach to higher-order verification. In: Proceedings of ICFP '13. pp. 13-24 (2013)
[2]
Broadbent, C.H., Kobayashi, N.: Saturation-based model checking of higher-order recursion schemes. In: Proceedings of CSL 2013. LIPIcs, vol. 23, pp. 129-148 (2013)
[3]
Champion, A., Chiba, T., Kobayashi, N., Sato, R.: Ice-based refinement type discovery for higher-order functional programs. In: Proceedings of TACAS '18 (To appear). LNCS, Springer (2018)
[4]
De Moura, L., Bjørner, N.: Z3: An efficient smt solver. In: Proceedings of TACAS '08. LNCS, vol. 4963, pp. 337--340. Springer (2008)
[5]
Henzinger, T.A., Jhala, R., Majumdar, R., Sutre, G.: Lazy abstraction. In: Proceedings of POPL. pp. 58--70. ACM (2002)
[6]
Kobayashi, N.: A practical linear time algorithm for trivial automata model checking of higher-order recursion schemes. In: Proceedings of FoSSaCS 2011. LNCS, vol. 6604, pp. 260--274. Springer (2011)
[7]
Kobayashi, N.: Model checking higher-order programs. Journal of the ACM 60(3) (2013)
[8]
Kobayashi, N.: HorSat2: A saturation-based higher-order model checker. A tool paper under submission. The tool is available at http://www-kb.is.s.u-tokyo.ac.jp/~koba/horsat2. (2015)
[9]
Kobayashi, N., Sato, R., Unno, H.: Predicate abstraction and CEGAR for higher-order model checking. In: Proceedings of PLDI '11. pp. 222--233. ACM (2011)
[10]
Neatherway, R.P., Ramsay, S.J., Ong, C.H.L.: A traversal-based algorithm for higher-order model checking. In: ACM SIGPLAN International Conference on Functional Programming (ICFP '12). pp. 353-364 (2012)
[11]
Ong, C.H.L.: On model-checking trees generated by higher-order recursion schemes. In: Proceedings of LICS '06. pp. 81--90. IEEE Computer Society Press (2006)
[12]
Ramsay, S.J., Neatherway, R.P., Ong, C.L.: A type-directed abstraction refinement approach to higher-order model checking. In: Proceedings of POPL '14. pp. 61--72. ACM (2014)
[13]
Rondon, P.M., Kawaguchi, M., Jhala, R.: Liquid types. In: PLDI 2008. pp. 159-169 (2008)
[14]
Sabry, A., Felleisen, M.: Reasoning about programs in continuation-passing style. LISP and Symbolic Computation 6(3), 289-360 (Nov 1993)
[15]
Sato, R., Unno, H., Kobayashi, N.: Towards a scalable software model checker for higher-order programs. In: Proceedings of PEPM '13. pp. 53--62. ACM (2013)
[16]
Shivers, O.: Control-Flow Analysis of Higher-Order Languages. Ph.D. thesis, Carnegie-Mellon University (May 1991)
[17]
Terao, T.: Lazy abstraction for higher-order program verification. http://www-kb.is.s.u-tokyo.ac.jp/~terao/papers/ppdp18.pdf (2018)
[18]
Terao, T., Tsukada, T., Kobayashi, N.: Higher-order model checking in direct style. In: Proceedings of APLAS '16. LNCS, vol. 10017, pp. 295--313. Springer (2016)
[19]
Terauchi, T.: Dependent types from counterexamples. In: Proceedings of POPL '10. pp. 119--130. ACM, New York, NY, USA (2010)
[20]
Unno, H., Kobayashi, N.: Dependent type inference with interpolants. In: Proceedings of PPDP '09. pp. 277--288. ACM, New York, NY, USA (2009)
[21]
Unno, H., Terauchi, T., Kobayashi, N.: Automating relatively complete verification of higher-order functional programs. In: Proceedings of POPL'13. pp. 75--86. ACM, New York, NY, USA (2013)
Index Terms
- Lazy Abstraction for Higher-Order Program Verification
Recommendations
Tool-supported program abstraction for finite-state verification
ICSE '01: Proceedings of the 23rd International Conference on Software EngineeringNumerous researchers have reported success in reasoning about properties of small programs using finite-state verification techniques. We believe, as do most researchers in this area, that in order to scale those initial successes to realistic programs, ...
Lazy abstraction
One approach to model checking software is based on the abstract-check-refine paradigm: build an abstract model, then check the desired property, and if the check fails, refine the model and start over. We introduce the concept of lazy abstraction to ...
Comments
Information & Contributors
Information
Published In
September 2018
306 pages
Copyright © 2018 ACM.
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]
In-Cooperation
- SIGPLAN: ACM Special Interest Group on Programming Languages
- Goethe University: Goethe University Frankfurt
Publisher
Association for Computing Machinery
New York, NY, United States
Publication History
Published: 03 September 2018
Check for updates
Qualifiers
- Research-article
- Research
- Refereed limited
Funding Sources
Conference
PPDP '18
PPDP '18: The 20th International Symposium on Principles and Practice of Declarative Programming
September 3 - 5, 2018
Frankfurt am Main, Germany
Acceptance Rates
PPDP '18 Paper Acceptance Rate 22 of 39 submissions, 56%;
Overall Acceptance Rate 230 of 486 submissions, 47%
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 54Total Downloads
- Downloads (Last 12 months)2
- Downloads (Last 6 weeks)1
Reflects downloads up to 22 Sep 2024
Other Metrics
Citations
Cited By
View allView Options
Get Access
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in