Work

Proof-checking Euclid

Year: 2017

Type: preprint

Abstract: We used computer proof-checking methods to verify the correctness of our proofs of the propositions in Euclid Book I. We used axioms as close as possible to those of Euclid, in a language closely related to that used in Tarski's formal geometry. We used proofs as close as possible to those given by Euclid, but filling Euclid's gaps and correcting errors. Euclid Book I has 48 propositions, we proved 235 theorems. The extras were partly "Book Zero", preliminaries of a very fundamental nature, partly propositions that Euclid omitted but were used implicitly, partly advanced theorems that we found necessary to fill Euclid's gaps, and partly just variants of Euclid's propositions. We wrote these proofs in a simple fragment of first-order logic corresponding to Euclid's logic, debugged them using a custom software tool, and then checked them in the well-known and trusted proof checkers HOL Light and Coq.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1710.00787

Authors: Beeson, Michael, Narboux, Julien, Wiedijk, Freek

Institutions: San Jose State University, Centre National de la Recherche Scientifique, Laboratoire des Sciences de l'Ingénieur, de l'Informatique et de l'Imagerie, Université de Strasbourg, Radboud University Nijmegen

Language: English

Topic: Logic, programming, and type systems

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2952398404

Cites:

Cited by: 1

Related to: 20