HolStep: A Machine Learning Dataset for Higher-order Logic Theorem Proving

TL;DR

This paper introduces HolStep, a new publicly available dataset based on Higher-Order Logic proofs, designed to facilitate machine learning approaches for theorem proving, with baseline models demonstrating promising results.

Contribution

The paper presents a novel HOL proof dataset and benchmarks simple machine learning models, advancing the integration of ML into higher-order theorem proving.

Findings

Baseline models show potential for HOL theorem proving

Dataset enables new ML tasks for logical step prediction

Initial results suggest ML can assist in proof strategies

Abstract

Large computer-understandable proofs consist of millions of intermediate logical steps. The vast majority of such steps originate from manually selected and manually guided heuristics applied to intermediate goals. So far, machine learning has generally not been used to filter or generate these steps. In this paper, we introduce a new dataset based on Higher-Order Logic (HOL) proofs, for the purpose of developing new machine learning-based theorem-proving strategies. We make this dataset publicly available under the BSD license. We propose various machine learning tasks that can be performed on this dataset, and discuss their significance for theorem proving. We also benchmark a set of simple baseline machine learning models suited for the tasks (including logistic regression, convolutional neural networks and recurrent neural networks). The results of our baseline models show the promise of applying machine learning to HOL theorem proving.