Interactive theorem provers have been used extensively to reason about various software hardware systems and mathematical theorems. The key challenge when using an interactive prover is finding a suitable sequence of proof steps that will lead to a successful proof requires a significant amount of human intervention. This paper presents an automated technique that takes as input examples of successful proofs and infers an Extended Finite State Machine as output. This can in turn be used to generate proofs of new conjectures. Our preliminary experiments show that the inferred models are generally accurate (contain few false-positive sequences) and that representing existing proofs in such a way can be very useful when guiding new ones.
@cite_7: In this paper we present an approach to automated learning within mathematical reasoning systems. In particular, the approach enables proof planning systems to automatically learn new proof methods from well-chosen examples of proofs which use a similar reasoning pattern to prove related theorems. Our approach consists of an abstract representation for methods and a machine learning technique which can learn methods using this representation formalism. We present an implementation of the approach within the mega proof planning system, which we call Learnma tic. We also present the results of the experiments that we ran on this implementation in order to evaluate if and how it improves the power of proof planning systems.
Such techniques have previously been applied to proof planning. Jamnik @cite_7 used an Inductive Logic Programming technique to infer what are ultimately regular expressions from well chosen sets of proof methods. For example, if we have the following two proofs (where a-d are proof methods): [a, a, c, d] and [a, b, d] they may be generalized as the following: [a*, [b|c], d] .