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Normalization by Evaluation
for MartinL¨of Type Theory
with One Universe
Andreas Abel1,2
Institut f¨ur Informatik, LudwigMaximiliansUniversit¨at
Oettingenstr. 67, D80538 M¨unchen
Klaus Aehlig3,4
Department of Computer Science, University of Wales Swansea
Singleton Park, Swansea SA2 8PP
Peter Dybjer5,6
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 iff 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
