Interactive theorem proving is a challenging and tedious process, which requires non-trivial expertise and detailed low-level instructions (or tactics) from human experts. Tactic prediction is a natural way to automate this process. Existing methods show promising results on tactic prediction by learning a deep neural network (DNN) based model from proofs written by human experts. In this paper, we propose NeuroTactic, a novel extension with a special focus on improving the representation learning for theorem proving. NeuroTactic leverages graph neural networks (GNNs) to represent the theorems and premises, and applies graph contrastive learning for pre-training. We demonstrate that the representation learning of theorems is essential to predict tactics. Compared with other methods, NeuroTactic achieves state-of-the-art performance on the CoqGym dataset.
@article{arxiv.2108.10821,
title = {Graph Contrastive Pre-training for Effective Theorem Reasoning},
author = {Zhaoyu Li and Binghong Chen and Xujie Si},
journal= {arXiv preprint arXiv:2108.10821},
year = {2021}
}