License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITP.2019.8
URN: urn:nbn:de:0030-drops-110638
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11063/
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Bréhard, Florent ; Mahboubi, Assia ; Pous, Damien

A Certificate-Based Approach to Formally Verified Approximations

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Abstract

We present a library to verify rigorous approximations of univariate functions on real numbers, with the Coq proof assistant. Based on interval arithmetic, this library also implements a technique of validation a posteriori based on the Banach fixed-point theorem. We illustrate this technique on the case of operations of division and square root. This library features a collection of abstract structures that organise the specfication of rigorous approximations, and modularise the related proofs. Finally, we provide an implementation of verified Chebyshev approximations, and we discuss a few examples of computations.

BibTeX - Entry

@InProceedings{brhard_et_al:LIPIcs:2019:11063,
  author =	{Florent Br{\'e}hard and Assia Mahboubi and Damien Pous},
  title =	{{A Certificate-Based Approach to Formally Verified Approximations}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{8:1--8:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{John Harrison and John O'Leary and Andrew Tolmach},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11063},
  URN =		{urn:nbn:de:0030-drops-110638},
  doi =		{10.4230/LIPIcs.ITP.2019.8},
  annote =	{Keywords: approximation theory, Chebyshev polynomials, Banach fixed-point theorem, interval arithmetic, Coq}
}

Keywords: approximation theory, Chebyshev polynomials, Banach fixed-point theorem, interval arithmetic, Coq
Collection: 10th International Conference on Interactive Theorem Proving (ITP 2019)
Issue Date: 2019
Date of publication: 05.09.2019
Supplementary Material: https://gitlab.inria.fr/amahboub/approx-models

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