Progress in Proof Planning : Planning Limit Theorems Automatically

Abstract

Proof planning is an alternative methodology to classical automated theorem proving based on exhaustive search that was first introduced by Bundy [8]. The goal of this paper is to extend the current realm of proof planning to cope with genuinely mathematical problems such as the well-known limit theorems first investigated for automated theorem proving by Bledsoe. The report presents a general methodology and contains ideas that are new for proof planning and theorem proving, most importantly ideas for search control and for the integration of domain knowledge into a general proof planning framework. We extend proof planning by employing explicit control-rules and supermethods. We combine proof planning with constraint solving. Experiments show the influence of these mechanisms on the performance of a proof planner. For instance, the proofs of LIM+ and LIM* have been automatically proof planned in the extended proof planner OMEGA. In a general proof planning framework we rationally reconstruct the proofs of limit theorems for real numbers (R) that were first computed by the special-purpose program reported in [6]. Compared with this program, the rational reconstruction has several advantages: It relies on a general-purpose problem solver; it provides high-level, hierarchical representations of proofs that can be expanded to checkable ND-proofs; it employs declarative contol knowledge that is modularly organized.