Adapting the Diagonalization Method by Reformulations

Extending the plan-based paradigm for automated theorem proving, we developed in previous work a declarative approach towards representing methods in a proof planning framework to support their mechanical modification. This paper presents a detailed study of a class of particular methods, embodying variations of a mathematical technique called diagonalization. The purpose of this paper is mainly twofold. First we demonstrate that typical mathematical methods can be represented in our framework in a natural way. Second we illustrate our philosophy of proof planning: besides planning with a fixed repertoire of methods, meta-methods create new methods by modifying e..