Typed applicative structures and normalization by evaluation for system Fω

Authors:
Andreas Abel
Affiliations:
Department of Computer Science, Ludwig-Maximilians-University, Munich
Venue:
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Year:
2009

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Abstract

We present a normalization-by-evaluation (NbE) algorithm for System Fω; 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.