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Implementing the cylindrical algebraic decomposition within the Coq system

Published online by Cambridge University Press:  01 February 2007

ASSIA MAHBOUBI*
Affiliation:
INRIA Sophia Antipolis, 2004, routes des Lucioles – B.P. 93, 06902 Sophia Antipolis Cedex, France Email: assia.mahboubi@sophia.inria.fr

Abstract

The Coq system is a Curry–Howard based proof assistant. Therefore, it contains a full functional, strongly typed programming language, which can be used to enhance the system with powerful automation tools through the implementation of reflexive tactics. We present the implementation of a cylindrical algebraic decomposition algorithm within the Coq system, whose certification leads to a proof producing decision procedure for the first-order theory of real numbers.

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Paper
Copyright
Copyright © Cambridge University Press 2007

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