Verified Representations of Landau's "Grundlagen" in the lambda-delta Family and in the Calculus of Constructions

Ferruccio Guidi

Abstract


Landau's "Grundlagen der Analysis" formalized in the language Aut-QE, represents an early milestone in computer-checked mathematics and is the only non-trivial development finalized in the languages of the Automath family. Here we discuss an implemented procedure producing a faithful representation of the Grundlagen in the Calculus of Constructions, verified by the proof assistant Coq 8.4.3. The point at issue is distinguishing lambda-abstractions from pi-abstractions where the original text uses Automath unified binders, taking care of the cases in which a binder corresponds to both abstractions at one time. It is a fact that some binders can be disambiguated only by verifying the Grundlagen in a calculus accepting Aut-QE and the Calculus of Constructions. To this end, we rely on lambda-delta version 3, a system that the author is proposing here for the first time.

Keywords


Grundlagen der Analysis; Automath; pure type system; unified binders

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DOI: 10.6092/issn.1972-5787/4716

Copyright (c) 2015 Ferruccio Guidi

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