Exploring the Foundations of Discrete Analytical Geometry in Isabelle/HOL

Fleuriot, Jacques

doi:10.1007/978-3-642-25070-5_2

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Cited by 2 publications

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“…It led to an alternative formalization in Isabelle/HOL [13]. The two formalizations are independent and do not rely on the same foundations.…”

Section: Related Workmentioning

confidence: 99%

Formalizing a discrete model of the continuum in Coq from a discrete geometry perspective

Magaud

Chollet

Fuchs

2014

Ann Math Artif Intell

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Abstract. This work presents a formalization of the discrete model of the continuum introduced by Harthong and Reeb [16], the HarthongReeb line. This model was at the origin of important developments in the Discrete Geometry field [31]. The formalization is based on the work presented in [8,7] where it was shown that the Harthong-Reeb line satisfies the axioms for constructive real numbers introduced by Bridges [4]. Laugwitz-Schmieden numbers [20] are then introduced and their limitations with respect to being a model of the Harthong-Reeb line is investigated [7]. In this paper, we transpose all these definitions and properties into a formal description using the Coq proof assistant. We also show that Laugwitz-Schmieden numbers can be used to actually compute continuous functions. We hope that this work could improve techniques for both implementing numeric computations and reasoning about them in geometric systems.

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“…It led to an alternative formalization in Isabelle/HOL [13]. The two formalizations are independent and do not rely on the same foundations.…”

Section: Related Workmentioning

confidence: 99%