Toward Automating the Discovery of Decreasing Measures

Abstract

An often neglected part of proof automation is simply admitting recursive function definitions into a constructive logic. Since function termination in general is undecidable, current generation theorem provers are quick to involve the human. There is, however, a substantial subset of the class of recursive functions for which termination arguments can be provided automatically. In particular, when the ordinal measure used to justify termination is less than $\omega^{\omega}$, we provide algorithms and proofs that guarantee optimum results, given the capability of existing proof libraries on the theorem-proving system.