A First Look into a Formal and ConstructiveApproach for Discrete Geometry Using Nonstandard Analysis

摘要

In this paper, we recall the origins of discrete analytical geometry developed by J-P. Reveilles [1] in the nonstandard model of the continuum based on integers proposed by Harthong and Reeb [2,3]. We present some basis on constructive mathematics [4] and its link with programming [5,6]. We show that a suitable version of this new model of the continuum partly fits with the constructive axiomatic of R proposed by Bridges [7]. The aim of this paper is to take a first look at a possible formal and constructive approach to discrete geometry. This would open the way to better algorithmic definition of discrete differential concepts.