A hypermap framework for computer-aided proofs in surface subdivisions: genus theorem and Euler's formula

Authors:
Jean-François Dufourd
Affiliations:
Louis-Pasteur University of Strasbourg, Illkirch, France
Venue:
Proceedings of the 2007 ACM symposium on Applied computing
Year:
2007

Citing 10
Cited 3

Algebraic specification of a 3D-modeler based on hypermaps

CVGIP: Graphical Models and Image Processing
Formalizing mathematics in higher-order logic: a case study in geometric modelling

Theoretical Computer Science
Functional specification and prototyping with oriented combinatorial maps

Computational Geometry: Theory and Applications
Representations for Rigid Solids: Theory, Methods, and Systems

ACM Computing Surveys (CSUR)
The design and implementation of panar maps in CGAL

Journal of Experimental Algorithmics (JEA)
The 5 Colour Theorem in Isabelle/Isar

TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
Topological model for two-dimensional image representation: definition and optimal extraction algorithm

Computer Vision and Image Understanding
Interactive Theorem Proving and Program Development

Interactive Theorem Proving and Program Development
Formalizing the trading theorem in Coq

Theoretical Computer Science
Mechanical theorem proving in computational geometry

ADG'04 Proceedings of the 5th international conference on Automated Deduction in Geometry

Design and formal proof of a new optimal image segmentation program with hypermaps

Pattern Recognition
Constructive mathematics and functional programming

ESOP'08/ETAPS'08 Proceedings of the Theory and practice of software, 17th European conference on Programming languages and systems
Designing and proving correct a convex hull algorithm with hypermaps in Coq

Computational Geometry: Theory and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper presents a new framework to conduct formal proofs concerning the topology of surface subdivisions. The subdivisions are modeled by hypermaps specified through the Calculus of Inductive Constructions. Proofs are computer-aided using the Coq system. A significant example is emphasized: the proof of the genus theorem and of the Euler formula for hypermaps.