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Formalizing Constructive Quantifier Elimination in Agda

Journal article
Authors Jeremy Pope
Published in Electronic Proceedings in Theoretical Computer Science
Issue 275
Pages 2-17
ISSN 2075-2180
Publication year 2018
Published at Department of Computer Science and Engineering (GU)
Pages 2-17
Language en
Links dx.doi.org/10.4204/eptcs.275.2
Keywords Computer Science
Subject categories Computer Science

Abstract

In this paper a constructive formalization of quantifier elimination is presented, based on a classical formalization by Tobias Nipkow. The formalization is implemented and verified in the programming language/proof assistant Agda. It is shown that, as in the classical case, the ability to eliminate a single existential quantifier may be generalized to full quantifier elimination and consequently a decision procedure. The latter is shown to have strong properties under a constructive metatheory, such as the generation of witnesses and counterexamples. Finally, this is demonstrated on a minimal theory on the natural numbers.

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