 
Summary: Weak Normalization and
Normalization by Evaluation for System F
Andreas Abel
Department of Computer Science
LudwigMaximiliansUniversity Munich
Abstract. A general version of the fundamental theorem for System F
is presented which can be instantiated to obtain proofs of weak  and
normalization and normalization by evaluation.
1 Introduction and Related Work
Dependently typed lambdacalculi have been successfully used as proof languages
in proof assistants like Agda [Nor07], Coq [INR07], LEGO [Pol94], and NuPrl
[Ct86]. Since types may depend on values in these type theories, checking equality
of types, which is crucial for type and, thus, proof checking, is nontrivial for these
languages, and undecidable in the general case. In extensional type theories, such
as the one underlying NuPrl, extensional, hence undecidable, type equality has
been kept with the consequence that type checking is undecidable and requires
user interaction. In intensional type theories, which are the basis of Agda, Coq,
and LEGO, type equality has been restricted to a decidable fragment, called
definitional equality, hence, type checking is decidable. However, the choice of
this fragment strongly influences the comfort in using these systems: the more
