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A general method for proving the normalization theorem for first and second order typed λ-calculi

Published online by Cambridge University Press:  01 December 1999

VENANZIO CAPRETTA  and
SILVIO VALENTINI
VENANZIO CAPRETTA
Affiliation:
Dipartimento di Matematica Pura ed Applicata, Università di Padova, via G. Belzoni n.7, I–35131 Padova, Italy. Email: cprvnn12@leonardo.math.unipd.it and silvio@math.unipd.it
SILVIO VALENTINI
Affiliation:
Dipartimento di Matematica Pura ed Applicata, Università di Padova, via G. Belzoni n.7, I–35131 Padova, Italy. Email: cprvnn12@leonardo.math.unipd.it and silvio@math.unipd.it
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Abstract

In this paper we describe a method for proving the normalization property for a large variety of typed lambda calculi of first and second order, which is based on a proof of equivalence of two deduction systems. We first illustrate the method on the elementary example of simply typed lambda calculus, and then we show how to extend it to a more expressive dependent type system. Finally we use it to prove the normalization theorem for Girard's system F.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 9 , Issue 6 , December 1999 , pp. 719 - 739
Copyright
1999 Cambridge University Press

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