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Summary: Normalization by Evaluation for
Martin-L¨of Type Theory
Andreas Abel1 Klaus Aehlig2
Thierry Coquand3 Peter Dybjer3
1Ludwig-Maximilians-University Munich
2University of Wales Swansea
3Chalmers University of Technology
LORIA, Nancy, France
February 27, 2007
Andreas Abel, Klaus Aehlig Thierry Coquand, Peter Dybjer (LMU Munich)NbE for Type Theory LORIA'07 1 / 24
Introduction
Normalization by Evaluation
Slogan: implement computation in the object language (syntax) by
mapping it to computation in the meta language (semantics)
For the -calculus: interpret object-level abstraction and
application by meta-level abstraction and application
Berger Schwichtenberg (LICS91): objects of the meta-language
can be brought "down" to the object-language
Andreas Abel, Klaus Aehlig Thierry Coquand, Peter Dybjer (LMU Munich)NbE for Type Theory LORIA'07 2 / 24
Untyped -calculus
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