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March 2013 Atomic polymorphism
Fernando Ferreira, Gilda Ferreira
J. Symbolic Logic 78(1): 260-274 (March 2013). DOI: 10.2178/jsl.7801180

Abstract

It has been known for six years that the restriction of Girard's polymorphic system $\mathbf{F}$ to atomic universal instantiations interprets the full fragment of the intuitionistic propositional calculus. We firstly observe that Tait's method of “convertibility” applies quite naturally to the proof of strong normalization of the restricted Girard system. We then show that each $\beta$-reduction step of the full intuitionistic propositional calculus translates into one or more $\beta\eta$-reduction steps in the restricted Girard system. As a consequence, we obtain a novel and perspicuous proof of the strong normalization property for the full intuitionistic propositional calculus. It is noticed that this novel proof bestows a crucial role to $\eta$-conversions.

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Fernando Ferreira. Gilda Ferreira. "Atomic polymorphism." J. Symbolic Logic 78 (1) 260 - 274, March 2013. https://doi.org/10.2178/jsl.7801180

Information

Published: March 2013
First available in Project Euclid: 23 January 2013

zbMATH: 1279.03035
MathSciNet: MR3087075
Digital Object Identifier: 10.2178/jsl.7801180

Rights: Copyright © 2013 Association for Symbolic Logic

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Vol.78 • No. 1 • March 2013
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