HolStep: A Machine Learning Dataset for Higher-order Logic Theorem Proving
This work addresses the challenge of automating theorem proving steps for researchers in automated reasoning and AI, though it is incremental as it focuses on dataset creation and initial benchmarks.
The authors tackled the problem of automating logical steps in theorem proving by introducing HolStep, a publicly available dataset based on Higher-Order Logic proofs, and benchmarked baseline machine learning models that showed promise for this application.
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.