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Summary: Normalization by Evaluation (NbE) Techniques
and Abstract Values
Andreas Abel1, Thierry Coquand2, Ulf Norell2
1Ludwig-Maximilians-University Munich
2Chalmers University of Technology
Curry-Howard Implementation Techniques 2006
December 19, 2006
Abel Coquand Norell (LMU Chalmers) NbE and Abstract Values CHIT'06 1 / 13
Introduction
Normalization by Evaluation
Evaluate term t, obtain value v = [[t]] Val.
Val contains the variables and neutral terms.
Reify v to a normal form.
Semantical type-checking is NbE, without reification.
Abel Coquand Norell (LMU Chalmers) NbE and Abstract Values CHIT'06 2 / 13
Introduction
The Language
Set Tm of raw terms:
r, s, t, A, B, C ::= x | xt | r s | x :A.B | Type
Judgements
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