Alignment Completeness for Relational Hoare Logics

TL;DR

This paper introduces the concept of alignment completeness for relational Hoare logics, providing a framework to evaluate and guide the design of RHLs using automata and the inductive assertion method.

Contribution

It formalizes alignment completeness for RHLs, offering a new criterion to assess their expressiveness and guiding the development of more powerful relational verification tools.

Findings

Alignment completeness accounts for various rule sets in RHLs.

Provides a formal framework using product automata and inductive assertions.

Guides the design of RHLs for richer programming languages.

Abstract

Relational Hoare logics (RHL) provide rules for reasoning about relations between programs. Several RHLs include a rule we call sequential product that infers a relational correctness judgment from judgments of ordinary Hoare logic (HL). Other rules embody sensible patterns of reasoning and have been found useful in practice, but sequential product is relatively complete on its own (with HL). As a more satisfactory way to evaluate RHLs, a notion of alignment completeness is introduced, in terms of the inductive assertion method and product automata. Alignment completeness results are given to account for several different sets of rules. The notion may serve to guide the design of RHLs and relational verifiers for richer programming languages and alignment patterns.