arXiv subjects

Xiwei Wu

Publications and source records attributed to Xiwei Wu.

7 recordsLinked to original sources

arXiv2026

Neuro-Symbolic Generation and Validation of Memory-Aware Formal Function Specifications

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.

cs.SE↗

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↗

arXiv2025

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

Encode the $\forall\exists$ Relational Hoare Logic into Standard Hoare Logic

Verifying a real-world program's functional correctness can be decomposed into (1) a refinement proof showing that the program implements a more abstract high-level program and (2) an algorithm correctness proof at the high level. Relational Hoare logic serves as a powerful tool to establish refinement but often necessitates formalization beyond standard Hoare logic. Particularly in the nondeterministic setting, the $\forall\exists$ relational Hoare logic is required. Existing approaches encode this logic into a Hoare logic with ghost states and invariants, yet these extensions significantly increase formalization complexity and soundness proof overhead. This paper proposes a generic encoding theory that reduces the $\forall\exists$ relational Hoare logic to standard (unary) Hoare logic. Precisely, we propose to redefine the validity of relational Hoare triples while preserving the original proof rules and then encapsulate the $\forall\exists$ pattern within assertions. We have proved that the validity of encoded standard Hoare triples is equivalent to the validity of the desired relational Hoare triples. Moreover, the encoding theory demonstrates how common relational Hoare logic proof rules are indeed special cases of standard Hoare logic proof rules, and relational proof steps correspond to standard proof steps. Our theory enables standard Hoare logic to prove $\forall\exists$ relational properties by defining a predicate Exec, without requiring modifications to the logic framework or re-verification of soundness.

cs.PL↗

arXiv2024

Towards General Loop Invariant Generation: A Benchmark of Programs with Memory Manipulation

Program verification is vital for ensuring software reliability, especially in the context of increasingly complex systems. Loop invariants, remaining true before and after each iteration of loops, are crucial for this verification process. Traditional provers and machine learning based methods for generating loop invariants often require expert intervention or extensive labeled data, and typically only handle numerical property verification. These methods struggle with programs involving complex data structures and memory manipulations, limiting their applicability and automation capabilities. In this paper, we introduce a new benchmark named LIG-MM, specifically for programs with complex data structures and memory manipulations. We collect 312 programs from various sources, including daily programs from college homework, the international competition (SV-COMP), benchmarks from previous papers (SLING), and programs from real-world software systems (Linux Kernel, GlibC, LiteOS, and Zephyr). Based on LIG-MM, our findings indicate that previous methods, including GPT-4, fail to automate verification for these programs. Consequently, we propose a novel LLM-SE framework that coordinates LLM with symbolic execution, fine-tuned using self-supervised learning, to generate loop invariants. Experimental results on LIG-MM demonstrate that our LLM-SE outperforms state-of-the-art methods, offering a new direction toward automated program verification in real-world scenarios.

cs.PL↗

arXiv2024

A Coq Library of Sets for Teaching Denotational Semantics

Sets and relations are very useful concepts for defining denotational semantics. In the Coq proof assistant, curried functions to Prop are used to represent sets and relations, e.g. A -> Prop, A -> B -> Prop, A -> B -> C -> Prop, etc. Further, the membership relation can be encoded by function applications, e.g. X a represents a in X if X: A -> Prop. This is very convenient for developing formal definitions and proofs for professional users, but it makes propositions more difficult to read for non-professional users, e.g. students of a program semantics course. We develop a small Coq library of sets and relations so that standard math notations can be used when teaching denotational semantics of simple imperative languages. This library is developed using Coq's type class system. It brings about zero proof-term overhead comparing with the existing formalization of sets.

cs.PL↗

arXiv2021

Countability of Inductive Types Formalized in the Object-Logic Level

The set of integer number lists with finite length, and the set of binary trees with integer labels are both countably infinite. Many inductively defined types also have countably many elements. In this paper, we formalize the syntax of first order inductive definitions in Coq and prove them countable, under some side conditions. Instead of writing a proof generator in a meta language, we develop an axiom-free proof in the Coq object logic. In other words, our proof is a dependently typed Coq function from the syntax of the inductive definition to the countability of the type. Based on this proof, we provide a Coq tactic to automatically prove the countability of concrete inductive types. We also developed Coq libraries for countability and for the syntax of inductive definitions, which have value on their own.

cs.LO↗