@TECHREPORT{Barras97coqin, author = {Bruno Barras and Benjamin Werner}, title = {Coq in Coq}, institution = {}, year = {1997} }

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Abstract

. We formalize the definition and the metatheory of the Calculus of Constructions (CC) using the proof assistant Coq. In particular, we prove strong normalization and decidability of type inference. From the latter proof, we extract a certified Objective Caml program which performs type inference in CC and use this code to build a small-scale certified proof-checker. Key words: Type Theory, proof-checker, Calculus of Constructions, metatheory, strong normalization proof, program extraction. 1. Introduction 1.1. Motivations This work can be described as the formal certification in Coq of a proof-checker for the Calculus of Constructions (CC). We view it as a first experimental step towards a certified kernel for the whole Coq system, of which CC is a significative fragment. In decidable type theories, a proof-checker is a program which verifies whether a given judgement (input) is valid or not (output). Valid meaning that there exists a derivation for that judgement following the in...