Bingxu Xiao | Searcharxiv

arXiv2026

Understanding and Improving Automated Proof Synthesis for Interactive Theorem Provers

Formal verification using interactive theorem provers ensures high-quality software. However, writing proof scripts for interactive theorem provers is labor-intensive and requires deep expertise. Recent studies have leveraged deep learning to automate theorem proving by learning from manually written proof corpora. Nevertheless, these techniques still achieve limited success rates in proof synthesis. This paper investigates the theorems that current proof synthesis techniques are unable to prove and analyzes their characteristics. Through an in-depth analysis of the proven theorems, proof scripts, and the proof search process, we identify the limitations of existing tools and summarize the key factors influencing proof success rates. Our research provides valuable insights for the future optimization of automated proof tools. Based on our empirical study, we discover that tactic selections conforming to human expert proof patterns are more likely to lead to successful proofs. Inspired by this finding, we propose a pattern-guided tactic search (PGTS) method to heuristically enhance the search process of existing proof synthesis tools. Our evaluation experiments demonstrate that PGTS improves the number of theorems proved by existing proof synthesis tools by an average of 8.05\%, while also achieving an average 20\% increase in previously unproven theorems. Furthermore, PGTS enhances the capability of proof synthesis tools to prove complex theorems and generates more concise proof scripts.

cs.LO↗

arXiv2026

OODEval: Evaluating Large Language Models on Object-Oriented Design

Recent advances in large language models (LLMs) have driven extensive evaluations in software engineering. however, most prior work concentrates on code-level tasks, leaving software design capabilities underexplored. To fill this gap, we conduct a comprehensive empirical study evaluating 29 LLMs on object-oriented design (OOD) tasks. Owing to the lack of standardized benchmarks and metrics, we introduce OODEval, a manually constructed benchmark comprising 50 OOD tasks of varying difficulty, and OODEval-Human, the first human-rated OOD benchmark, which includes 940 undergraduate-submitted class diagrams evaluated by instructors. We further propose CLUE (Class Likeness Unified Evaluation), a unified metric set that assesses both global correctness and fine-grained design quality in class diagram generation. Using these benchmarks and metrics, we investigate five research questions: overall correctness, comparison with humans, model dimension analysis, task feature analysis, and bad case analysis. The results indicate that while LLMs achieve high syntactic accuracy, they exhibit substantial semantic deficiencies, particularly in method and relationship generation. Among the evaluated models, Qwen3-Coder-30B achieves the best overall performance, rivaling DeepSeek-R1 and GPT-4o, while Gemma3-4B-IT outperforms GPT-4o-Mini despite its smaller parameter scale. Although top-performing LLMs nearly match the average performance of undergraduates, they remain significantly below the level of the best human designers. Further analysis shows that parameter scale, code specialization, and instruction tuning strongly influence performance, whereas increased design complexity and lower requirement readability degrade it. Bad case analysis reveals common failure modes, including keyword misuse, missing classes or relationships, and omitted methods.

cs.SE↗