Baldur: Whole-Proof Generation and Repair with Large Language Models
PROCEEDINGS OF THE 31ST ACM JOINT MEETING EUROPEAN SOFTWARE ENGINEERING CONFERENCE AND SYMPOSIUM ON THE FOUNDATIONS OF SOFTWARE ENGINEERING, ESEC/FSE 2023(2023)
Abstract
Formally verifying software is a highly desirable but labor-intensive task. Recent work has developed methods to automate formal verification using proof assistants, such as Coq and Isabelle/HOL, e.g., by training a model to predict one proof step at a time and using that model to search through the space of possible proofs. This paper introduces a new method to automate formal verification: We use large language models, trained on natural language and code and fine-tuned on proofs, to generate whole proofs at once. We then demonstrate that a model fine-tuned to repair generated proofs further increasing proving power. This paper: (1) Demonstrates that whole-proof generation using transformers is possible and is as effective but more efficient than search-based techniques. (2) Demonstrates that giving the learned model additional context, such as a prior failed proof attempt and the ensuing error message, results in proof repair that further improves automated proof generation. (3) Establishes, together with prior work, a new state of the art for fully automated proof synthesis. We reify our method in a prototype, Baldur, and evaluate it on a benchmark of 6,336 Isabelle/HOL theorems and their proofs, empirically showing the effectiveness of whole-proof generation, repair, and added context. We also show that Baldur complements the state-of-the-art tool, Thor, by automatically generating proofs for an additional 8.7% of the theorems. Together, Baldur and Thor can prove 65.7% of the theorems fully automatically. This paper paves the way for new research into using large language models for automating formal verification.
MoreTranslated text
Key words
Proof assistants,proof synthesis,proof repair,machine learning,large language models,automated formal verification
AI Read Science
Must-Reading Tree
Example
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined