On SMT Theory Design: The Case of Sequences

TL;DR

This paper analyzes the design choices of the SMT theory of sequences, proposing criteria to evaluate and standardize its variants to improve reasoning capabilities and consistency across tools.

Contribution

It introduces a set of theory design criteria and suggests specific changes to standardize the SMT theory of sequences.

Findings

Defined criteria for SMT theory design

Compared existing variants of the theory

Proposed standardization changes

Abstract

Choices in the semantics and the signature of a theory are integral in determining how the theory is used and how challenging it is to reason over it. Our interest in this paper lies in the SMT theory of sequences. Various versions of it exist in the literature and in state-of-the-art SMT solvers, but it has not yet been standardized in the SMT-LIB. We reflect on its existing variants, and we define a set of theory design criteria to help determine what makes one variant of a theory better than another. The criteria we define can be used to appraise theory proposals for other theories as well. Based on these criteria, we propose a series of changes to the SMT theory of sequences as a contribution to the discussion regarding its standardization.