Cezary Kaliszyk, François Chollet, Christian Szegedy
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.
| Task | Dataset | Metric | Value | Model |
|---|---|---|---|---|
| Automated Theorem Proving | HolStep (Unconditional) | Classification Accuracy | 0.83 | 1D CNN |
| Automated Theorem Proving | HolStep (Unconditional) | Classification Accuracy | 0.83 | 1D CNN-LSTM |
| Automated Theorem Proving | HolStep (Conditional) | Classification Accuracy | 0.83 | Siamese 1D CNN-LSTM |
| Automated Theorem Proving | HolStep (Conditional) | Classification Accuracy | 0.82 | Siamese 1D CNN |
| Mathematical Proofs | HolStep (Unconditional) | Classification Accuracy | 0.83 | 1D CNN |
| Mathematical Proofs | HolStep (Unconditional) | Classification Accuracy | 0.83 | 1D CNN-LSTM |
| Mathematical Proofs | HolStep (Conditional) | Classification Accuracy | 0.83 | Siamese 1D CNN-LSTM |
| Mathematical Proofs | HolStep (Conditional) | Classification Accuracy | 0.82 | Siamese 1D CNN |