An In-Context Learning Agent for Formal Theorem-Proving

Amitayush Thakur, George Tsoukalas, Yeming Wen, Jimmy Xin, Swarat Chaudhuri

Research Area: LMs and interactions, LMs with tools and code, LMs on diverse modalities and novel applications

Keywords: theorem proving, formal methods, large language models, agents

TL;DR: We present an LLM agent for formal theorem proving which capitalizes on rich error feedback from the proof environment and proof search history. Our agent conducts an in-context proof search and outperforms state-of-the-art fine-tuned methods.

Abstract: We present an in-context learning agent for formal theorem-proving in environments like Lean and Coq. Current state-of-the-art models for the problem are finetuned on environment-specific proof data. By contrast, our approach, called COPRA, repeatedly asks a high-capacity, general-purpose large language model (GPT-4) to propose tactic applications from within a stateful backtracking search. Proposed tactics are executed in the underlying proof environment. Feedback from the execution is used to build the prompt for the next model query, along with selected information from the search history and lemmas retrieved from an external database. We evaluate our implementation of COPRA on the miniF2F benchmark for Lean and a set of Coq tasks from the CompCert project. On these benchmarks, COPRA significantly outperforms few-shot invocations of GPT-4. It also compares favorably against finetuning-based approaches, outperforming REPROVER, a state-of-the-art finetuned approach for Lean, in terms of the pass@1 metric. Our code and data are available at https://github.com/trishullab/copra

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Submission Number: 1073