Reasoning About Vectors: Satisfiability Modulo a Theory of Sequences

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

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Article number32
JournalJournal of Automated Reasoning
Issue number3
StatePublished - Sep 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature B.V.


This work was funded in part by the Stanford Center for Blockchain Research, NSF-BSF Grant Numbers 2110397 (NSF) and 2020704 (BSF), ISF Grant Number 619/21, and Meta Novi. Part of the work was done when the first author was an intern at Meta Novi.

FundersFunder number
NSF-BSF2020704, 2110397
Stanford Center for Blockchain Research
United States-Israel Binational Science Foundation
Israel Science Foundation619/21


    • Decision Procedures
    • Satisfiability Modulo Theories
    • Sequences
    • Vectors


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