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Conference Papers Year : 2012

A Constructive Proof of Dependent Choice, Compatible with Classical Logic

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.
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Dates and versions

hal-00697240 , version 1 (15-05-2012)

Identifiers

  • HAL Id : hal-00697240 , version 1

Cite

Hugo Herbelin. A Constructive Proof of Dependent Choice, Compatible with Classical Logic. LICS 2012 - 27th Annual ACM/IEEE Symposium on Logic in Computer Science, Jun 2012, Dubrovnik, Croatia. pp.365-374. ⟨hal-00697240⟩
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