The use of explicit plans to guide inductive proofs

Abstract

We propose the use of explicit proof plans to guide the search for a proof in automatic theorem proving. By representing proof plans as the specifications of LCF-like tactics, [Gordon et al 79], and by recording these specifications in a sorted meta-logic, we are able to reason about the conjectures to be proved and the methods available to prove them. In this way we can build proof plans of wide generality, formally account for and predict their successes and failures, apply them flexibly, recover from their failures, and learn them from example proofs.

We illustrate this technique by building a proof plan based on a simple subset of the implicit proof plan embedded in the Boyer-Moore theorem prover, [Boyer & Moore 79].

Space restrictions have forced us to omit many of the details of our work. These are included in a longer version of this paper which is available from: The Documentation Secretary, Department of Artificial Intelligence, University of Edinburgh, Forrest Hill, Edinburgh EH1 2QL, Scotland.

I am grateful for many long conversations with other members of the mathematical reasoning group, from which many of the ideas in this paper emerged. In particular, I would like to thank Frank van Harmelen, Jane Hesketh and Andrew Stevens for feedback on this paper. The research reported in this paper was supported by SERC grant GR/D/44874 and Alvey/SERC grant GR/D/44270.