Summary: Normalization by Evaluation (NbE) Techniques
and Abstract Values
Andreas Abel 1 , Thierry Coquand 2 , Ulf Norell 2
1 Ludwig­Maximilians­University Munich
2 Chalmers University of Technology
Curry­Howard 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 type­checking 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:

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

Collections: Computer Technologies and Information Sciences