Journal of Automated Reasoning

, Volume 7, Issue 3, pp 303–324

Experiments with proof plans for induction

  • Alan Bundy
  • Frank van Harmelen
  • Jane Hesketh
  • Alan Smaill
Article

DOI: 10.1007/BF00249016

Cite this article as:
Bundy, A., van Harmelen, F., Hesketh, J. et al. J Autom Reasoning (1991) 7: 303. doi:10.1007/BF00249016

Abstract

The technique of proof plans is explained. This technique is used to guide automatic inference in order to avoid a combinatorial explosion. Empirical research is described to test this technique in the domain of theorem proving by mathematical induction. Heuristics, adapted from the work of Boyer and Moore, have been implemented as Prolog programs, called tactics, and used to guide an inductive proof checker, Oyster. These tactics have been partially specified in a meta-logic, and the plan formation program, CLAM, has been used to reason with these specifications and form plans. These plans are then executed by running their associated tactics and, hence, performing an Oyster proof. Results are presented of the use of this technique on a number of standard theorems from the literature. Searching in the planning space is shown to be considerably cheaper than searching directly in Oyster's search space. The success rate on the standard theorems is high.

Key words

Theorem provingmathematical inductionsearchcombinatorial explosionproof planstacticsplanningprogram synthesis

Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • Alan Bundy
    • 1
  • Frank van Harmelen
    • 1
  • Jane Hesketh
    • 1
  • Alan Smaill
    • 1
  1. 1.Department of Artificial IntelligenceUniversity of EdinburghEdinburghScotland