Linear Quantifier Elimination

Tobias Nipkow

This paper presents verified quantifier elimination procedures for dense linear orders (two of them novel), for real and for integer linear arithmetic. All procedures are defined and verified in the theorem prover Isabelle/HOL, are executable and can be applied to HOL formulae themselves (by reflection). The formalization of the different theories is highly modular.

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BibTeX:

@article{Nipkow-JAR10,author={Tobias Nipkow},
title={Linear Quantifier Elimination},journal={J. Automated Reasoning},
volume=45,pages={189-212},year=2010}

Isabelle theories in the Archive of Formal Proofs

This is an extended version of a conference paper.