Qinxiang Cao

Xiwei Wu, Yueyang Feng, Xiaoyang Lu et al.

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.

Zhang Cheng, Jiyang Wu, Di Wang et al.

A desired but challenging property of compiler verification is compositionality, in the sense that the compilation correctness of a program can be deduced incrementally from that of its substructures ranging from statements, functions, and modules. This article proposes a novel compiler verification framework based on denotational semantics for better compositionality, compared to previous approaches based on small-step operational semantics and simulation theories. Our denotational semantics is defined by semantic functions that map a syntactic component to a semantic domain composed of multiple behavioral \emph{sets}, with compiler correctness established through behavior refinement between the semantic domains of the source and target programs. The main contributions of this article include proposing a denotational semantics for open modules, a novel semantic linking operator, and a refinement algebra that unifies various behavior refinements, making compiler verification structured and compositional. Furthermore, our formalization captures the full meaning of a program and bridges the gap between traditional power-domain-based denotational semantics and the practical needs of compiler verification. We apply our denotation-based framework to verify the front-end of CompCert and typical optimizations on simple prototypes of imperative languages. Our results demonstrate that the compositionality from sub-statements to statements, from functions to modules, and from modules to the whole program can be effectively achieved.

Liao Zhang, Tong Chen, Xiwei Wu et al.

Formal verification of memory-manipulating programs critically depends on precise function specifications that capture memory states written by experts. This requirement has become a major bottleneck as large language models (LLMs) increasingly generate low-level systems code whose correctness cannot be assumed. To enable scalable formal verification, we focus exclusively on function specification generation, deliberately avoiding the synthesis of complex loop invariants that are central to traditional verification pipelines. We propose a neuro-symbolic framework for automatically generating memory-aware formal function specifications for C programs from natural language problem descriptions and function signatures. The pipeline first produces candidate specifications via in-context learning, and then iteratively refines them using compiler diagnostics from symbolic provers and the verification toolchain. In particular, we validate candidate specifications by constructing a proof for the negation of the specification with concrete examples, enabling machine-checked rejection of plausible-but-incorrect specifications. To support systematic evaluation, we introduce LeetCode-C-Spec, a new benchmark of 200 C programming problems for generating memory-aware formal function specifications. Experiments show that iterative refinement substantially improves syntactic validity, while symbolic prover-based refutation significantly enhances correctness assessment by filtering false positives that LLM-only judges frequently accept. Our results demonstrate that combining neural generation with symbolic feedback provides an effective approach to formal specification synthesis for memory-safe systems software.

Zhicheng Hui, Lihan Xie, Xingzhi Qi et al.

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.

Qi Liu, Xinhao Zheng, Renqiu Xia et al.

As a seemingly self-explanatory task, problem-solving has been a significant component of science and engineering. However, a general yet concrete formulation of problem-solving itself is missing. With the recent development of AI-based problem-solving agents, the demand for process-level verifiability is rapidly increasing yet underexplored. To fill these gaps, we present a principled formulation of problem-solving as a deterministic Markov decision process; a novel framework, FPS (Formal Problem-Solving), which utilizes existing FTP (formal theorem proving) environments to perform process-verified problem-solving; and D-FPS (Deductive FPS), decoupling solving and answer verification for better human-alignment. The expressiveness, soundness and completeness of the frameworks are proven. We construct three benchmarks on problem-solving: FormalMath500, a formalization of a subset of the MATH500 benchmark; MiniF2F-Solving and PutnamBench-Solving, adaptations of FTP benchmarks MiniF2F and PutnamBench. For faithful, interpretable, and human-aligned evaluation, we propose RPE (Restricted Propositional Equivalence), a symbolic approach to determine the correctness of answers by formal verification. We evaluate four prevalent FTP models and two prompting methods as baselines, solving at most 23.77% of FormalMath500, 27.47% of MiniF2F-Solving, and 0.31% of PutnamBench-Solving.

Ting Long, Yutong Xie, Xianyu Chen et al.

Program representation, which aims at converting program source code into vectors with automatically extracted features, is a fundamental problem in programming language processing (PLP). Recent work tries to represent programs with neural networks based on source code structures. However, such methods often focus on the syntax and consider only one single perspective of programs, limiting the representation power of models. This paper proposes a multi-view graph (MVG) program representation method. MVG pays more attention to code semantics and simultaneously includes both data flow and control flow as multiple views. These views are then combined and processed by a graph neural network (GNN) to obtain a comprehensive program representation that covers various aspects. We thoroughly evaluate our proposed MVG approach in the context of algorithm detection, an important and challenging subfield of PLP. Specifically, we use a public dataset POJ-104 and also construct a new challenging dataset ALG-109 to test our method. In experiments, MVG outperforms previous methods significantly, demonstrating our model's strong capability of representing source code.