# Generating Correctness Proofs with Neural Networks

## TL;DR

Proverbot9001 is a machine learning-based system that automates proof generation in theorem provers, significantly reducing manual effort and improving proof automation success rates in verified software projects.

## Contribution

The paper introduces Proverbot9001, a novel proof search system that enhances automation in theorem proving using machine learning, outperforming previous models in proof completion rates.

## Key findings

- Automates 27.5% of proof obligations in a large verified C compiler.
- Achieves a 4X higher proof completion rate without additional solvers.
- Effectively replaces manual proofs with automated machine learning techniques.

## Abstract

Foundational verification allows programmers to build software which has been empirically shown to have high levels of assurance in a variety of important domains. However, the cost of producing foundationally verified software remains prohibitively high for most projects,as it requires significant manual effort by highly trained experts. In this paper we present Proverbot9001,a proof search system using machine learning techniques to produce proofs of software correctness in interactive theorem provers. We demonstrate Proverbot9001 on the proof obligations from a large practical proof project,the CompCert verified C compiler,and show that it can effectively automate what were previously manual proofs,automatically producing proofs for 27.5% of theorem statements in our test dataset, when combined with solver-based tooling. Without any additional solvers,we exhibit a proof completion rate that is a 4X improvement over prior state-of-the-art machine learning models for generating proofs in Coq.