A Language-Agent Approach to Formal Theorem-Proving

Amitayush Thakur, Yeming Wen, Swarat Chaudhuri

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

TL;DR: We give a large language model agent for formal theorem-proving that repeatedly queries GPT-4 and interacts with the underlying proof environment, and show that it offers state-of-the-art performance.

Abstract:

Language agents, which use a large language model (LLM) capable of in-context learning to interact with an external environment, have emerged as a promising approach to control tasks. We present a language-agent approach that offers state-of-the-art performance in formal theorem-proving. Our method, COPRA, uses a high-capacity, black-box LLM (GPT-4) as part of a policy for a stateful backtracking search. During the search, the policy can select proof tactics and retrieve lemmas and definitions from an external database. Each selected tactic is executed in the underlying proof framework, and the execution feedback is used to build the prompt for the next policy invocation. The search also tracks selected information from its history and uses it to reduce hallucinations and unnecessary LLM queries.

We evaluate COPRA on the miniF2F benchmark for Lean and a set of Coq tasks from the Compcert project. On these benchmarks, COPRA is significantly better than one-shot invocations of GPT-4, as well as state-of-the-art models fine-tuned on proof data, at finding correct proofs quickly.

Submission Number: 29