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

Authors:
Venanzio Capretta;Silvio Valentini
Affiliations:
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;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
Venue:
Mathematical Structures in Computer Science
Year:
1999

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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.