Adaptive Proof Refinement with LLM-Guided Strategy Selection

TL;DR

This paper introduces Adapt, a proof refinement framework that uses an LLM-guided decision-maker to dynamically select strategies, significantly improving theorem proving success rates over fixed-strategy methods.

Contribution

The paper presents a novel adaptive proof refinement framework that dynamically chooses strategies using an LLM-guided decision-maker, enhancing proof success and generalizability across models.

Findings

Adapt outperforms baseline methods by proving 16.63% and 18.58% more theorems.

Adapt is effective across five different LLMs.

Ablation studies show the importance of each component and decision-maker design.

Abstract

Formal verification via theorem proving enables the expressive specification and rigorous proof of software correctness, but it is difficult to scale due to the significant manual effort and expertise required. While Large Language Models (LLMs) show potential in proof generation, they frequently produce incorrect proofs on the first attempt and require additional strategies for iterative refinement. However, existing approaches employ fixed refinement strategies and cannot dynamically choose an effective strategy based on the particular issues in a generated proof, which limits their performance. To overcome this limitation, we introduce Adapt, a novel proof refinement framework that leverages an LLM-guided decision-maker to dynamically select a suitable refinement strategy according to the state of the proof assistant and available context of an incorrect proof. We evaluate Adapt on two benchmarks against four existing methods and find that it significantly outperforms the best baseline on both by proving 16.63% and 18.58% more theorems, respectively. Furthermore, we demonstrate Adapt's generalizability by evaluating it across five different LLMs. We also conduct ablation studies to measure the contribution of each component and compare the trade-offs of alternative decision-maker designs.