Typed Applicative Structures and Normalization by Evaluation for System Fomega

We present a normalization-by-evaluation (NbE) algorithm for System F with βη-equality, the simplest impredicative type theory with computation on the type level. Values are kept abstract and requirements on values are kept to a minimum, allowing many different implementations of the algorithm. The algorithm is verified through a general model construction using typed applicative structures, called type and object structures. Both soundness and completeness of NbE are conceived as an instance of a single fundamental theorem.