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.

动态数组，也称为向量，是许多程序中使用的基本数据结构。在推理此类程序时，对其语义进行有效建模至关重要。数组理论得到了广泛的支持，但并不理想，因为元素的数量是固定的（由其索引排序决定）并且无法调整，这是一个问题，因为向量的长度在推理时通常起着重要作用矢量程序。在本文中，我们提出使用序列理论来推理向量。我们介绍了该理论，提出了一种改编自弦理论的基本微积分，并将其扩展以有效地处理常见的向量运算。我们证明我们的微积分是正确的，并展示了如何在模型以饱和配置终止时构建模型。最后，