Automated Program Refinement: Guide and Verify Code Large Language Model with Refinement Calculus

Recently, the rise of code-centric Large Language Models (LLMs) has reshaped the software engineering world with low-barrier tools like Copilot that can easily generate code. However, there is no correctness guarantee for the code generated by LLMs, which suffer from the hallucination problem, and their output is fraught with risks. Besides, the end-to-end process from specification to code through LLMs is a non-transparent and uncontrolled black box. This opacity makes it difficult for users to understand and trust the generated code. Addressing these challenges is both necessary and critical. In contrast, program refinement transforms high-level specification statements into executable code while preserving correctness. Traditional tools for program refinement are primarily designed for formal methods experts and lack automation and extensibility. We apply program refinement to guide LLM and validate the LLM-generated code while transforming refinement into a more accessible and flexible framework. To initiate this vision, we propose Refine4LLM, an approach that aims to: (1) Formally refine the specifications, (2) Automatically prompt and guide the LLM using refinement calculus, (3) Interact with the LLM to generate the code, (4) Verify that the generated code satisfies the constraints, thus guaranteeing its correctness, (5) Learn and build more advanced refinement laws to extend the refinement calculus. We evaluated Refine4LLM against the state-of-the-art baselines on program refinement and LLMs benchmarks. The experiment results show that Refine4LLM can efficiently generate more robust code and reduce the time for refinement and verification.