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Lambda applicative structures and interpretations of lambda abstractions

10 min • 8 oktober 2020

Discussion of definitions in "Pre-logical relations" by Honsell and Sannella, particularly the notion of a lambda applicative structure (similar to a definition in John C. Mitchell's book "Foundations for Programming Languages'). In short, lambda abstractions get interpreted in combinatory algebras by compiling away the lambda abstractions in favor of S and K combinators, which are then interpreted by the combinatory algebra. I complain about the fact that the definition of a lambda applicative structure is required to come with an interpretation function for terms (hence tying the semantics to the syntax).