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| HAL : hal-00168402, version 1 |
| arXiv : 0708.3721 |
| Fiche détaillée |  Récupérer au format |
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| Verified Real Number Calculations: A Library for Interval Arithmetic |
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| Marc Daumas 1, 2David Lester 3 |
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| (28/08/2007) |
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| Real number calculations on elementary functions are remarkably difficult to handle in mechanical proofs. In this paper, we show how these calculations can be performed within a theorem prover or proof assistant in a convenient and highly automated as well as interactive way. First, we formally establish upper and lower bounds for elementary functions. Then, based on these bounds, we develop a rational interval arithmetic where real number calculations take place in an algebraic setting. In order to reduce the dependency effect of interval arithmetic, we integrate two techniques: interval splitting and taylor series expansions. This pragmatic approach has been developed, and formally verified, in a theorem prover. The formal development also includes a set of customizable strategies to automate proofs involving explicit calculations over real numbers. Our ultimate goal is to provide guaranteed proofs of numerical properties with minimal human theorem-prover interaction. |
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| 1 : | Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM) |
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CNRS : UMR5506 – Université Montpellier II - Sciences et Techniques du Languedoc |
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| 2 : | Electronique, Informatique, Automatique et Systèmes (ELIAUS) |
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Université de Perpignan |
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| 3 : | University of Manchester (UNIVERSITY OF MANCHESTER) |
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University of Manchester |
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| 4 : | National Institute of Aerospace (NIA) |
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National Institute of Aerospace |
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| Domaine | : | Informatique/Arithmétique des ordinateurs Informatique/Logiciel mathématique Informatique/Logique en informatique Informatique/Performance et fiabilité |
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| hal-00168402, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00168402/fr/ | |
| oai:hal.archives-ouvertes.fr:hal-00168402_v1 | |
| Contributeur : Marc Daumas | |
| Soumis le : Mardi 28 Août 2007, 07:50:49 | |
| Dernière modification le : Mardi 28 Août 2007, 09:14:36 | |
