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An elementary proof of strong normalization for intersection types

An elementary proof of strong normalization for intersection types We provide a new and elementary proof of strong normalization for the lambda calculus of intersection types. It uses no strong method, like for instance Tait-Girard reducibility predicates, but just simple induction on type complexity and derivation length and thus it is obviously formalizable within first order arithmetic. To obtain this result, we introduce a new system for intersection types whose rules are directly inspired by the reduction relation. Finally, we show that not only the set of strongly normalizing terms of pure lambda calculus can be characterized in this system, but also that a straightforward modification of its rules allows to characterize the set of weakly normalizing terms. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

An elementary proof of strong normalization for intersection types

Valentini, Silvio
Archive for Mathematical Logic , Volume 40 (7) – Oct 1, 2001
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References (10)

Publisher
Springer Journals
Copyright
Copyright © 2001 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/s001530000070
Publisher site
See Article on Publisher Site

Abstract

We provide a new and elementary proof of strong normalization for the lambda calculus of intersection types. It uses no strong method, like for instance Tait-Girard reducibility predicates, but just simple induction on type complexity and derivation length and thus it is obviously formalizable within first order arithmetic. To obtain this result, we introduce a new system for intersection types whose rules are directly inspired by the reduction relation. Finally, we show that not only the set of strongly normalizing terms of pure lambda calculus can be characterized in this system, but also that a straightforward modification of its rules allows to characterize the set of weakly normalizing terms.

Journal

Archive for Mathematical Logic – Springer Journals

Published: Oct 1, 2001

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