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Normalization by Evaluation
for Martin­L˜of Type Theory
with One Universe
Andreas Abel 1 ,2
Institut f˜ur Informatik, Ludwig­Maximilians­Universit˜at
Oettingenstr. 67, D­80538 M˜unchen
Klaus Aehlig 3 ,4
Department of Computer Science, University of Wales Swansea
Singleton Park, Swansea SA2 8PP
Peter Dybjer 5 ,6
Department of Computer Science, Chalmers University of Technology
R˜annv˜agen 6, S­41296 G˜oteborg
Abstract
We present an algorithm for computing normal terms and types in Martin­L˜of type theory with one universe
and eta­conversion. We prove that two terms or types are equal in the theory i# the normal forms are
identical (as de Bruijn terms). It thus follows that our algorithm can be used for deciding equality in
Martin­L˜of type theory. The algorithm uses the technique of normalization by evaluation; normal forms

Source: Abel, Andreas - Theoretische Informatik, Ludwig-Maximilians-Universität München

Collections: Computer Technologies and Information Sciences