Abstract
This paper gives an overview of the formalization of the Harthong-Reeb integer number system (HR ω ) in the proof-assistant Isabelle. The work builds on an existing mechanization of nonstandard analysis and describes how the basic notions underlying HR ω can be recovered and shown to have their expected properties, without the need to introduce any axioms. We also look at the formalization of the well-known Euler method over the new integers and formally prove that the algorithmic approximation produced can be made to be infinitely-close to its continuous counterpart. This enables the discretization of continuous functions and of geometric concepts such as the straight line and ellipse and acts as the starting point for the field of discrete analytical geometry.
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Fleuriot, J. (2011). Exploring the Foundations of Discrete Analytical Geometry in Isabelle/HOL. In: Schreck, P., Narboux, J., Richter-Gebert, J. (eds) Automated Deduction in Geometry. ADG 2010. Lecture Notes in Computer Science(), vol 6877. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25070-5_2
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DOI: https://doi.org/10.1007/978-3-642-25070-5_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25069-9
Online ISBN: 978-3-642-25070-5
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