Second-Order Pre-logical Relations and Representation Independence
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 pre-logical 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 pre-logical relation between the representations, thereby varying and generalizing results of J.C. Mitchell to languages with higher-order constants.
KeywordsLogical Relation Logical Predicate Type Constructor Basic Lemma Lambda Calculus
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