A type-inference approach to reduction properties and semantics of polymorphic expressions (summary)

Some insight into both the operational and denotational semantics of polymorphic lambda calculus may be gained by considering types as equivalence relations on subsets of an untyped domain. A general theorem stating that the meaning of any typed term belongs to the appropriate collection of values may be used to prove strong normalization of typed terms. The interpretation of types as equivalence relations also gives rise to the "HEO-like" models of polymorphic lambda calculus. We characterize the equational theories of HEO-like models and prove a completeness theorem for a non-standard set of axioms.

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