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Parametric Linear Arithmetic over Ordered Fields in Isabelle/HOL

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Intelligent Computer Mathematics (CICM 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5144))

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Abstract

We use higher-order logic to verify a quantifier elimination procedure for linear arithmetic over ordered fields, where the coefficients of variables are multivariate polynomials over another set of variables, we call parameters. The procedure generalizes Ferrante and Rackoff’s algorithm for the non-parametric case. The formalization is based on axiomatic type classes and automatically carries over to e.g. the rational, real and non-standard real numbers. It is executable, can be applied to HOL formulae and performs well on practical examples.

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Authors and Affiliations

  1. Institut für Informatik, Technische Universität München,  

    Amine Chaieb

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  1. Amine Chaieb
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Editor information

Serge Autexier John Campbell Julio Rubio Volker Sorge Masakazu Suzuki Freek Wiedijk

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Chaieb, A. (2008). Parametric Linear Arithmetic over Ordered Fields in Isabelle/HOL. In: Autexier, S., Campbell, J., Rubio, J., Sorge, V., Suzuki, M., Wiedijk, F. (eds) Intelligent Computer Mathematics. CICM 2008. Lecture Notes in Computer Science(), vol 5144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85110-3_20

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  • DOI: https://doi.org/10.1007/978-3-540-85110-3_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85109-7

  • Online ISBN: 978-3-540-85110-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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