Second-order pre-logical relations and representation independence

Authors:
Hans Leib
Affiliations:
Centrum für Informations-und Sprachverarbeitung, Universität München, München
Venue:
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
Year:
2001

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Abstract

We extend the notion of pre-logical relation between models of simply typed lambda-calculus, recently introduced by F. Honsell and D. Sannella, to models of second-order lambda calculus. With prelogical relations, we obtain characterizations of the lambda-definable elements of and the observational equivalence between second-order models. These are are simpler than those using logical relations on extended models. We also characterize representation independence for abstract data types and abstract data type constructors by the existence of a prelogical relation between the representations, thereby varying and generalizing results of J.C. Mitchell to languages with higher-order constants.