Proof output and machine learning for inductive theorem provers

Abstract

Automatic theorem provers have lately seen significant performance improvements by utilising knowledge from previously proven theorems using machine learning. HipSpec is an inductive theorem prover that has not yet explored this area, which is the primary motivation for this work. We lay a foundation for supporting machine learning implementations within HipSpec. Firstly, a format for representing inductive proofs of theorems is designed. Secondly, a persistent library is implemented, which allows HipSpec to remember already-proven theorems in between executions. These extensions are vital for allowing machine learning, since they provide the machine learning algorithms with the necessary data. This foundation is used to perform machine learning experiments on theorems from the TIP library, which is a collection of benchmarks for inductive theorem provers. We define several different feature extraction schemes for theorems, and test these using both supervised learning and unsupervised learning algorithms. The results show that although no correlation between induction variables and term structure can be found, it is possible to utilise clustering algorithms in order to identify some theorems about tail-recursive functions.