An SMT Theory for n-Indexed Sequences

TL;DR

This paper proposes an SMT theory of n-indexed sequences and explores different ways to represent and reason over n-indexed sequences using existing theories, as well as astailored calculi for the theory.

Abstract

The SMT (Satisfiability Modulo Theories) theory of arrays is well-established and widely used, with variousdecision procedures and extensions developed for it. However, recent works suggest that developing tailoredreasoning for some theories, such as sequences and strings, is more efficient than reasoning over them throughaxiomatization over the theory of arrays. In this paper, we are interested in reasoning over n-indexed sequences asthey are found in some programming languages, such as Ada. We propose an SMT theory of n-indexed sequencesand explore different ways to represent and reason over n-indexed sequences using existing theories, as well astailored calculi for the theory.

Figures (4)

• Figure 1: Common inference rules for the NS-BASE and NS-EXT calculi
• Figure 2: NS-BASE specific inference rules
• Figure 3: NS-EXT specific inference rules
• Figure 4: Number of solved goals by accumulated time in seconds on quantifier-free Seq benchmarks translated from the QF_AXSMT-LIB benchmarks

Theorems & Definitions (5)

• Definition 1: Bounds
• Definition 2: Extensionality
• Definition 3: Empty n-sequence
• Definition 4: Equivalence modulo relocation
• Definition 5: NSeq term normal form