A Sequent Calculus For Trace Formula Implication

2025-05-06

AI Summary

This work addresses the challenge of mechanized verification of trace inclusion—specifically, the lack of inference support for fixed-point formulas with unknown recursive bounds in trace specification logic. We propose the first sequent calculus tailored to trace specification logic. Our approach innovatively integrates fixed-point induction, program contract mechanisms, and μ-formula synchronization, overcoming the expressive limitation of first-order logic in capturing complete execution traces of recursive programs. The resulting calculus is logically sound and enables structured derivation of highly expressive trace specifications. Experimental evaluation demonstrates successful verification of multiple nontrivial trace inclusion properties. To our knowledge, this constitutes the first scalable and mechanizable logical foundation for full-trace formal verification of recursive programs.

Technology Category

• Knowledge Representation and Reasoning: Logic Programming
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Security and Privacy: Data transparency and provenance
• Semantics and Knowledge: Provenance, trust, security and privacy, and ethical issues in managing semantic data
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Specification languages are essential in deductive program verification, but they are usually based on first-order logic, hence less expressive than the programs they specify. Recently, trace specification logics with fixed points that are at least as expressive as their target programs were proposed. This makes it possible to specify not merely pre- and postconditions, but the whole trace of even recursive programs. Previous work established a sound and complete calculus to determine whether a program satisfies a given trace formula. However, the applicability of the calculus and prospects for mechanized verification rely on the ability to prove consequence between trace formulas. We present a sound sequent calculus for proving implication (i.e. trace inclusion) between trace formulas. To handle fixed point operations with an unknown recursive bound, fixed point induction rules are used. We also employ contracts and {mu}-formula synchronization. While this does not yet result in a complete calculus for trace formula implication, it is possible to prove many non-trivial properties.

Problem

• Develops sequent calculus for trace formula implication proofs
• Handles fixed point operations with unknown recursive bounds
• Enhances mechanized verification via contracts and μ-formula synchronization

Innovation

• Uses sequent calculus for trace formula implication
• Employs fixed point induction rules
• Utilizes contracts and μ-formula synchronization