A Hoare Logic for Symmetry Properties

2025-08-30

AI Summary

Existing formal verification methods struggle to effectively validate correctness properties of programs characterized by symmetry. This paper introduces the first Hoare logic framework specifically designed for symmetry verification: it replaces conventional pre- and postconditions with group actions, defines a formal syntax for group-action specifications, and establishes a natural entailment relation—enabling rigorous, compositional reasoning about symmetry properties of imperative programs. The approach integrates group action theory, Hoare logic, and static analysis, and is implemented in the prototype tool SymVerif. Evaluation on multiple hand-crafted benchmarks confirms the framework’s effectiveness; notably, it uncovered a logical inconsistency in the symmetry formulation of an existing dynamical systems model. The core contribution is the first sound and complete Hoare logic for symmetry based on group actions—establishing a provably correct, implementable paradigm for symmetry-driven program verification.

Technology Category

• Knowledge Representation and Reasoning: Logic Programming
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Computer Vision: Visual Reasoning & Symbolic Representations

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Security and Privacy: Applications of cryptography
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Many natural program correctness properties can be stated in terms of symmetries, but existing formal methods have little support for reasoning about such properties. We consider how to formally verify a broad class of symmetry properties expressed in terms of group actions. To specify these properties, we design a syntax for group actions, supporting standard constructions and a natural notion of entailment. Then, we develop a Hoare-style logic for verifying symmetry properties of imperative programs, where group actions take the place of the typical pre- and post-condition assertions. Finally, we develop a prototype tool $mathsf{SymVerif}$, and use it to verify symmetry properties on a series of handcrafted benchmarks. Our tool uncovered an error in a model of a dynamical system described by citet{McLachlan_Quispel_2002}.

Problem

• Formally verifying symmetry properties using group actions
• Developing Hoare-style logic for imperative program symmetries
• Creating tool SymVerif to verify symmetry correctness benchmarks

Innovation

• Hoare-style logic for symmetry verification
• Group actions replace pre-post conditions
• Prototype tool SymVerif for benchmarks