Formal Verification of a Geometry Algorithm: A Quest for Abstract Views and Symmetry in Coq Proofs

TL;DR

This paper presents a formal verification of a geometry triangulation algorithm in Coq, focusing on handling symmetries and abstract views to improve proof robustness and clarity.

Contribution

It introduces a formal approach to model and verify a triangulation algorithm with symmetry considerations using Coq and mathematical components.

Findings

Successful formalization of the triangulation algorithm in Coq

Effective handling of symmetry in geometric proofs

Enhanced understanding of abstract views in geometric algorithms

Abstract

This extended abstract is about an effort to build a formal description of a triangulation algorithm starting with a naive description of the algorithm where triangles, edges, and triangulations are simply given as sets and the most complex notions are those of boundary and separating edges. When performing proofs about this algorithm, questions of symmetry appear and this exposition attempts to give an account of how these symmetries can be handled. All this work relies on formal developments made with Coq and the mathematical components library.