Understanding and using spector's bar recursive interpretation of classical analysis

Authors:
Paulo Oliva
Affiliations:
Department of Computer Science, Queen Mary, University of London, London, UK
Venue:
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Year:
2006

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Abstract

This note reexamines Spector's remarkable computational interpretation of full classical analysis. Spector's interpretation makes use of a rather abstruse recursion schema, so-called bar recursion, used to interpret the double negation shift DNS. In this note bar recursion is presented as a generalisation of a simpler primitive recursive functional needed for the interpretation of a finite (intuitionistic) version of DNS. I will also present two concrete applications of bar recursion in the extraction of programs from proofs of ∀∃-theorems in classical analysis.