A simple proof of the undecidability of strong normalisation

Authors:
Paweł Urzyczyn
Affiliations:
Institute of Informatics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland Email: urzy@mimuw.edu.pl
Venue:
Mathematical Structures in Computer Science
Year:
2003

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Abstract

The purpose of this note is to give a methodologically simple proof of the undecidability of strong normalisation in the pure lambda calculus. For this we show how to represent an arbitrary partial recursive function by a term whose application to any Church numeral is either strongly normalizable or has no normal form. Intersection types are used for the strong normalization argument.