Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH scholarly article en Obua, Steven License
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URN: urn:nbn:de:0030-drops-4351

Proving Bounds for Real Linear Programs in Isabelle/HOL



Linear programming is a basic mathematical technique for optimizing a linear function on a domain that is constrained by linear inequalities. We restrict ourselves to linear programs on bounded domains that involve only real variables. In the context of theorem proving, this restriction makes it possible for any given linear program to obtain certificates from external linear programming tools that help to prove arbitrarily precise bounds for the given linear program. To this end, an explicit formalization of matrices in Isabelle/HOL is presented, and how the concept of lattice-ordered rings allows for a smooth integration of matrices with the axiomatic type classes of Isabelle. As our work is a contribution to the Flyspeck project, we demonstrate that via reflection and with the above techniques it is now possible to prove bounds for the linear programs arising in the proof of the Kepler conjecture sufficiently fast.

BibTeX - Entry

  author =	{Steven Obua},
  title =	{Proving Bounds for Real Linear Programs in Isabelle/HOL},
  booktitle =	{Mathematics, Algorithms, Proofs},
  year =	{2006},
  editor =	{Thierry Coquand and Henri Lombardi and Marie-Fran{\c{c}}oise Roy},
  number =	{05021},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{},
  annote =	{Keywords: Certified proofs, Kepler conjecture}

Keywords: Certified proofs, Kepler conjecture
Seminar: 05021 - Mathematics, Algorithms, Proofs
Issue date: 2006
Date of publication: 2006

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