Learning Rules Explaining Interactive Theorem Proving Tactic Prediction

Abstract

Formally verifying the correctness of mathematical proofs is more accessible than ever, however, the learning curve remains steep for many of the state-of-the-art interactive theorem provers (ITP). Deriving the most appropriate subsequent proof step, and reasoning about it, given the multitude of possibilities, remains a daunting task for novice users. To improve the situation, several investigations have developed machine learning based guidance for tactic selection. Such approaches struggle to learn non-trivial relationships between the chosen tactic and the structure of the proof state and represent them as symbolic expressions. To address these issues we (i) We represent the problem as an Inductive Logic Programming (ILP) task, (ii) Using the ILP representation we enriched the feature space by encoding additional, computationally expensive properties as background knowledge predicates, (iii) We use this enriched feature space to learn rules explaining when a tactic is applicable to a given proof state, (iv) we use the learned rules to filter the output of an existing tactic selection approach and empirically show improvement over the non-filtering approaches.