Reasoning About Vectors using an SMT Theory of Sequences

• Main Authors: Sheng, Ying, Nötzli, Andres, Reynolds, Andrew, Zohar, Yoni, Dill, David, Grieskamp, Wolfgang, Park, Junkil, Qadeer, Shaz, Barrett, Clark, Tinelli, Cesare
• Format: Journal Article
• Language: English
• Published: 17-05-2022
• Subjects: Computer Science - Logic in Computer Science
• DOI: 10.48550/arxiv.2205.08095

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.