Parametric Linear Arithmetic over Ordered Fields in Isabelle/HOL

Authors:
Amine Chaieb
Affiliations:
Institut für Informatik, Technische Universität München,
Venue:
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Year:
2008

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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 anotherset 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.