 
Summary: Normalization by Evaluation for System F
Andreas Abel
Department of Computer Science
LudwigMaximiliansUniversity Munich
Department of Mathematics, Savoie University
Chambery, France
12 February 2010
Andreas Abel (LMU Munich) Normalization by Evaluation for System F LAMA '10 1 / 27
Introduction
Normalizers appear in compilers (e.g., typedirected partial
evaluation [Danvy,Filinski])
and HOL theorem provers (Isabelle, Coq, Agda).
Normalization by evaluation is a framework to turn an
evaluator for closed expressions (stop at lambda) into a
normalizer for open expressions (go under lambda).
Has clear semantic foundations.
Is strong for extensional normalization (eta).
My goal: NbE for Calculus of Constructions and Coq.
Andreas Abel (LMU Munich) Normalization by Evaluation for System F LAMA '10 2 / 27
What is Normalization By Evaluation?
