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Summary: Normalization by Evaluation for
Martin-L¨of Type Theory
with Typed Equality Judgements
Andreas Abel1
Thierry Coquand2 Peter Dybjer2
1Ludwig-Maximilians-University Munich
2Chalmers University of Technology
Logic in Computer Science
Wroclaw, Poland
10 July 2007
Abel Coquand Dybjer (LMU, CTH) NbE for Type Theory LICS'07 1 / 21
Introduction
My Talk
Dependent type theory basis for theorem provers (functional
programming languages) Agda, Coq, Epigram, . . .
Intensional theory with predicative universes.
Judgemental -equality.
Deciding type equality with Normalization-By-Evaluation.
Semantic proof of decidability of typing.
Abel Coquand Dybjer (LMU, CTH) NbE for Type Theory LICS'07 2 / 21
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