Formalizing the trading theorem in Coq

Authors:
Christophe Dehlinger;Jean-François Dufourd
Affiliations:
Laboratoire des Sciences de l'Image, de l'Informatique, et de la Télédétection (UMR CNRS 7005), Université Louis-Pasteur de Strasbourg, Pôle API, boulevard S. Brant, 67400 ...;Laboratoire des Sciences de l'Image, de l'Informatique, et de la Télédétection (UMR CNRS 7005), Université Louis-Pasteur de Strasbourg, Pôle API, boulevard S. Brant, 67400 ...
Venue:
Theoretical Computer Science
Year:
2004

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Abstract

This paper is the second half of a two-part series devoted to the formalization of a combinatorial model of geometric varieties, generalized maps. We study here how to express continuous notions like homeomorphisms in the combinatorial world, in order to constructively describe the well-known theorem of surface classification according to genus, number of boundaries and orientability coefficient. We then use the Coq specification elaborated in the previous paper to prove the first half of this theorem, called the trading theorem.