 
Summary: Normalization by Evaluation for System F
Andreas Abel
Department of Computer Science
LudwigMaximiliansUniversity Munich
Computer Science Theory Seminar
Institute of Cybernetics, Tallinn, Estonia
6 April 2009
Andreas Abel (LMU Munich) Normalization by Evaluation for System F IOC '09 1 / 30
What is this for?
Theorem provers based on CurryHoward: Coq, Agda, ...
Need to compare objects for equality.
E.g. f, g : N N. Need a proof of P(f), have one of P(g).
Extensional equality is undecidable.
Approximation: intensional equality.
Compute normal forms for f, g and compare.
The more the better: , , , . . . normal form.
NB: Coq distinguishes between P(f) and P(x. f x).
Normalizationbyevaluation excellent when is involved.
Andreas Abel (LMU Munich) Normalization by Evaluation for System F IOC '09 2 / 30
Simplytyped lambdacalculus
