Measuring the Readability of Geometric Proofs: The Area Method Case

Abstract

Using an approach, inspired by our modernisation of Lemoine’s Geometrography, this paper proposes a new readability criterion for formal proofs produced by automated theorem provers for geometry. We analyse two criteria to measure the readability of a proof: the criterion given by Chou et al. and the one given by Wiedijk. After discussing the limitations of these two criteria, we introduce a novel approach, which provides a new criterion. We conclude discussing some future work.

A Machine Proof System of Point Geometry Based on Coq

“…For instance, Julien Narboux et al used Coq to implement the process of the area method and proposed GeoCoq, a formalized geometry theory based on the Tarski axiom system [29][30][31][32]. Furthermore, Pedro Quaresma et al proposed a new readability criterion for formal proofs produced by automated theorem provers for geometry, inspired by their modernization of Lemoine's Geometrography, to enhance the readability of automated proofs in geometry [33]. These works have not only promoted the development of geometry but also demonstrated the importance of interactive proofs in automated theorem proving for geometry.…”