Reasoning About Vectors Using an SMT Theory of Sequences

Ying Sheng; Andres Nötzli; Andrew Reynolds; Yoni Zohar; David Dill; Wolfgang Grieskamp; Junkil Park; Shaz Qadeer; Clark Barrett; Cesare Tinelli

doi:10.1007/978-3-031-10769-6_9

Reasoning About Vectors Using an SMT Theory of Sequences

Ying Sheng, Andres Nötzli, Andrew Reynolds, Yoni Zohar, David Dill, Wolfgang Grieskamp, Junkil Park, Shaz Qadeer, Clark Barrett, Cesare Tinelli

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

Dynamic arrays, also referred to as vectors, are fundamental data structures used in many programs. Modeling their semantics efficiently is crucial when reasoning about such programs. The theory of arrays is widely supported but is not ideal, because the number of elements is fixed (determined by its index sort) and cannot be adjusted, which is a problem, given that the length of vectors often plays an important role when reasoning about vector programs. In this paper, we propose reasoning about vectors using a theory of sequences. We introduce the theory, propose a basic calculus adapted from one for the theory of strings, and extend it to efficiently handle common vector operations. We prove that our calculus is sound and show how to construct a model when it terminates with a saturated configuration. Finally, we describe an implementation of the calculus in cvc5 and demonstrate its efficacy by evaluating it on verification conditions for smart contracts and benchmarks derived from existing array benchmarks.

Original language	English
Title of host publication	Automated Reasoning - 11th International Joint Conference, IJCAR 2022, Proceedings
Editors	Jasmin Blanchette, Laura Kovács, Dirk Pattinson
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	125-143
Number of pages	19
ISBN (Print)	9783031107689
DOIs	https://doi.org/10.1007/978-3-031-10769-6_9
State	Published - 2022
Event	11th International Joint Conference on Automated Reasoning, IJCAR 2022, part of the Federated Logic Conference, FLoC 2022 - Haifa, Israel Duration: 8 Aug 2022 → 10 Aug 2022

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	13385 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	11th International Joint Conference on Automated Reasoning, IJCAR 2022, part of the Federated Logic Conference, FLoC 2022
Country/Territory	Israel
City	Haifa
Period	8/08/22 → 10/08/22

Bibliographical note

Publisher Copyright:
© 2022, The Author(s).

Funding

This work was funded in part by the Stanford Center for Blockchain Research, NSF-BSF grant numbers 2110397 (NSF) and 2020704 (BSF), and Meta Novi. Part of the work was done when the first author was an intern at Meta Novi.

Funders	Funder number
NSF-BSF	2020704, 2110397
Stanford Center for Blockchain Research
Bloom's Syndrome Foundation

Access to Document

10.1007/978-3-031-10769-6_9

Cite this

Sheng, Y., Nötzli, A., Reynolds, A., Zohar, Y., Dill, D., Grieskamp, W., Park, J., Qadeer, S., Barrett, C., & Tinelli, C. (2022). Reasoning About Vectors Using an SMT Theory of Sequences. In J. Blanchette, L. Kovács, & D. Pattinson (Eds.), Automated Reasoning - 11th International Joint Conference, IJCAR 2022, Proceedings (pp. 125-143). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13385 LNAI). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-10769-6_9

Sheng, Ying ; Nötzli, Andres ; Reynolds, Andrew et al. / Reasoning About Vectors Using an SMT Theory of Sequences. Automated Reasoning - 11th International Joint Conference, IJCAR 2022, Proceedings. editor / Jasmin Blanchette ; Laura Kovács ; Dirk Pattinson. Springer Science and Business Media Deutschland GmbH, 2022. pp. 125-143 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Sheng, Y, Nötzli, A, Reynolds, A, Zohar, Y, Dill, D, Grieskamp, W, Park, J, Qadeer, S, Barrett, C & Tinelli, C 2022, Reasoning About Vectors Using an SMT Theory of Sequences. in J Blanchette, L Kovács & D Pattinson (eds), Automated Reasoning - 11th International Joint Conference, IJCAR 2022, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13385 LNAI, Springer Science and Business Media Deutschland GmbH, pp. 125-143, 11th International Joint Conference on Automated Reasoning, IJCAR 2022, part of the Federated Logic Conference, FLoC 2022, Haifa, Israel, 8/08/22. https://doi.org/10.1007/978-3-031-10769-6_9

Reasoning About Vectors Using an SMT Theory of Sequences. / Sheng, Ying; Nötzli, Andres; Reynolds, Andrew et al.
Automated Reasoning - 11th International Joint Conference, IJCAR 2022, Proceedings. ed. / Jasmin Blanchette; Laura Kovács; Dirk Pattinson. Springer Science and Business Media Deutschland GmbH, 2022. p. 125-143 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13385 LNAI).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Park, Junkil

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AU - Barrett, Clark

AU - Tinelli, Cesare

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Sheng Y, Nötzli A, Reynolds A, Zohar Y, Dill D, Grieskamp W et al. Reasoning About Vectors Using an SMT Theory of Sequences. In Blanchette J, Kovács L, Pattinson D, editors, Automated Reasoning - 11th International Joint Conference, IJCAR 2022, Proceedings. Springer Science and Business Media Deutschland GmbH. 2022. p. 125-143. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-10769-6_9

Reasoning About Vectors Using an SMT Theory of Sequences

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