Mechanical theorem proving in computational geometry

Authors:
Laura I. Meikle;Jacques D. Fleuriot
Affiliations:
School of Informatics, University of Edinburgh, Edinburgh, UK;School of Informatics, University of Edinburgh, Edinburgh, UK
Venue:
ADG'04 Proceedings of the 5th international conference on Automated Deduction in Geometry
Year:
2004

Citing 8
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Abstract

Algorithms for solving geometric problems are widely used in many scientific disciplines. Applications range from computer vision and robotics to molecular biology and astrophysics. Proving the correctness of these algorithms is vital in order to boost confidence in them. By specifying the algorithms formally in a theorem prover such as Isabelle, it is hoped that rigorous proofs showing their correctness will be obtained. This paper outlines our current framework for reasoning about geometric algorithms in Isabelle. It focuses on our case study of the convex hull problem and shows how Hoare logic can be used to prove the correctness of such algorithms.