Proving bounds on real-valued functions with computations

Abstract : Interval-based methods are commonly used for computing numerical bounds on expressions and proving inequalities on real numbers. Yet they are hardly used in proof assistants, as the large amount of numerical computations they require keeps them out of reach from deductive proof processes. However, evaluating programs inside proofs is an efficient way for reducing the size of proof terms while performing numerous computations. This work shows how programs combining automatic differentiation with floating-point and interval arithmetic can provide some efficient yet guaranteed solvers within the Coq proof system.
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Alessandro Armando, Peter Baumgartner, Gilles Dowek. International Joint Conference on Automated Reasoning, IJCAR 2008, Aug 2008, Sydney, Australia. Springer-Verlag, 5195, pp.2--17, 2008, Lecture Notes in Artificial Intelligence. <10.1007/978-3-540-71070-7_2>
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Guillaume Melquiond. Proving bounds on real-valued functions with computations. Alessandro Armando, Peter Baumgartner, Gilles Dowek. International Joint Conference on Automated Reasoning, IJCAR 2008, Aug 2008, Sydney, Australia. Springer-Verlag, 5195, pp.2--17, 2008, Lecture Notes in Artificial Intelligence. <10.1007/978-3-540-71070-7_2>. <hal-00180138>

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