Abstract
A definition of a typed language is said to be “intrinsic” if it assigns meanings to typings rather than arbitrary phrases, so that ill-typed phrases are meaningless. In contrast, a definition is said to be “extrinsic” if all phrases have meanings that are independent of their typings, while typings represent properties of these meanings.
For a simply typed lambda calculus, extended with integers, recursion, and conditional expressions, we give an intrinsic denotational semantics and a denotational semantics of the underlying untyped language. We then estab?lish a logical relations theorem between these two semantics, and show that the logical relations can be “bracketed” by retractions between the domains of the two semantics. From these results, we derive an extrinsic semantics that uses partial equivalence relations.
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Reynolds, J.C. (2003). What do types mean? — From intrinsic to extrinsic semantics. In: McIver, A., Morgan, C. (eds) Programming Methodology. Monographs in Computer Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21798-7_15
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DOI: https://doi.org/10.1007/978-0-387-21798-7_15
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