arXiv subjects

Lihan Xie

Publications and source records attributed to Lihan Xie.

4 recordsLinked to original sources

arXiv2026

Verifiable Auto-Formalization of Mathematics Using a Relaxed Natural Formal Language

Auto-formalization aims to translate informal mathematical content into formal languages that can be processed by theorem provers. However, directly targeting existing theorem provers requires LLMs to bridge a substantial representational gap between informal mathematical writing and formal proof languages. This gap also makes semantic consistency difficult to evaluate. We address these difficulties by introducing a Relaxed Natural Formal Language (Relaxed NFL) as an intermediate target for auto-formalization. The Relaxed NFL is designed to remain close to informal mathematical writing: it preserves the usual structure of informal reasoning and allows partially specified expressions and propositions, without requiring their precise interpretation to be fixed at the auto-formalization stage. The remaining ambiguity and implicitness inherited from informal reasoning are resolved during a later elaboration stage, which transforms Relaxed NFL proofs into Core Natural Formal Language (Core NFL) proofs with formally defined semantics. The elaboration procedure combines rule-based transformations with LLM-generated heuristics, while maintaining verifiability through explicit constraints on each transformation step. The Core NFL is then used to generate proof gaps, namely verification conditions that must hold for the formalized proof to be correct. These gaps are discharged by LLM-generated proof scripts written in a domain-specific tactic language, which provides commands for invoking theorem libraries and domain-specific solvers implemented as part of our system.

cs.LO↗

arXiv2026

QCP: A Practical Separation Logic-based C Program Verification Tool

As software systems increase in size and complexity dramatically, ensuring their correctness, security, and reliability becomes an increasingly formidable challenge. Despite significant advancements in verification techniques and tools, their practical application to complex, real-world systems is often hindered by critical gaps in both automation and expressiveness. To address these difficulties, this paper presents \textbf{Qualified C Programming Verifier (QCP)}, a novel verification tool that integrates annotation-based automatic verification with interactive proving using Rocq. QCP employs symbolic execution and a separation logic entailment solver to automatically discharge many verification obligations, while deferring more complex obligations to Rocq for manual proof. Furthermore, QCP includes a VS Code extension designed to enhance proof efficiency and support a deeper understanding of both the program behavior and verification outcomes.

cs.PL↗

arXiv2025

Stellis: A Strategy Language for Purifying Separation Logic Entailments

Automatically proving separation logic entailments is a fundamental challenge in verification. While rule-based methods rely on separation logic rules (lemmas) for automation, these rule statements are insufficient for describing automation strategies, which usually involve the alignment and elimination of corresponding memory layouts in specific scenarios. To overcome this limitation, we propose Stellis, a strategy language for purifying separation logic entailments, i.e., removing all spatial formulas to reduce the entailment to a simpler pure entailment. Stellis features a powerful matching mechanism and a flexible action description, enabling the straightforward encoding of a wide range of strategies. To ensure strategy soundness, we introduce an algorithm that generates a soundness condition for each strategy, thereby reducing the soundness of each strategy to the correctness of its soundness condition. Furthermore, based on a mechanized reduction soundness theorem, our prototype implementation generates correctness proofs for the overall automation. We evaluate our system on a benchmark of 229 entailments collected from verification of standard linked data structures and the memory module of a microkernel, and the evaluation results demonstrate that, with such flexibility and convenience provided, our system is also highly effective, which automatically purifies 95.6% (219 out of 229) of the entailments using 5 libraries with 98 strategies.

cs.SE↗

arXiv2024

A Natural Formalized Proof Language

Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof languages adopted by traditional theorem provers were not intended to represent natural language proofs. Therefore, they are not well-suited for the aforementioned tasks and proof-checking work for educational purposes. In this paper, we design a proof language and its corresponding abstract syntax tree and implement a proof checking tool for it. This language can be easily converted from natural language, thus providing a rich corpus of formal proof. Additionally, it supports the handling of issues in informal proofs through static analysis, and enhances the expressive power of the language by introducing the structure of partial proofs. This design combines the expressiveness of natural language and the accuracy of formal language, resulting in an improved mathematical proof language.

cs.PL↗