A Constructive Proof of Dependent Choice, Compatible with Classical LogicReport as inadecuate




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1 PPS - Preuves, Programmes et Systèmes 2 PI.R2 - Design, study and implementation of languages for proofs and programs PPS - Preuves, Programmes et Systèmes, Inria Paris-Rocquencourt, UPD7 - Université Paris Diderot - Paris 7, CNRS - Centre National de la Recherche Scientifique : UMR7126

Abstract : Martin-Löf-s type theory has strong existential elimination dependent sum type that allows to prove the full axiom of choice. However the theory is intuitionistic. We give a condition on strong existential elimination that makes it computationally compatible with classical logic. With this restriction, we lose the full axiom of choice but, thanks to a lazily-evaluated coinductive representation of quantification, we are still able to constructively prove the axiom of countable choice, the axiom of dependent choice, and a form of bar induction in ways that make each of them computationally compatible with classical logic.

Keywords : Dependent choice classical logic constructive logic strong existential





Author: Hugo Herbelin -

Source: https://hal.archives-ouvertes.fr/



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