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Modular proof of strong normalization for the calculus of constructions

Published online by Cambridge University Press:  10 August 2016

Herman Geuvers  and
Mark-Jan Nederhof
Herman Geuvers
Affiliation:
Faculty of Mathematics and Computer Science, University of Nijmegen, The Netherlands
Mark-Jan Nederhof
Affiliation:
Faculty of Mathematics and Computer Science, University of Nijmegen, The Netherlands
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Abstract

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We present a modular proof of strong normalization for the Calculus of Constructions of Coquand and Huet (1985, 1988). This result was first proved by Coquand (1986), but our proof is more perspicious. The method consists of a little juggling with some systems in the cube of Barendregt (1989), which provides a fine structure of the calculus of constructions. It is proved that the strong normalization of the calculus of constructions is equivalent with the strong normalization of Fω.

In order to give the proof, we first establish some properties of various type systems. Therefore, we present a general framework of typed lambda calculi, including many well-known ones.

Type
Research Article
Information
Journal of Functional Programming , Volume 1 , Issue 2 , April 1991 , pp. 155 - 189
Copyright
Copyright © Cambridge University Press 1991

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