Extensible records in a pure calculus of subtyping

Extensible records were introduced by Mitchell Wand while studying type inference in a polymorphic λ-calculus with record types. This paper describes a calculus with extensible records, F <: ρ, that can be translated into a simpler calculus, F <: , lacking any record primitives. Given independent axiomatizations of F <: ρ and F <: (the former being an extension of the latter) we show that the translation preserves typing, subtyping, and equality. F <: ρ can then be used as an expressive calculus of extensible records, either directly or to give meaning to yet other languages. We show that F <: ρ can express many of the standard benchmark examples that appear in the literature. Like other record calculi that have been proposed, F <: ρ has a rather complex set of rules but, unlike those other calculi, its rules are justified by a translation to a very simple calculus. We argue that thinking in terms of translations may help in simplifying and organizing the various record calculi that have been proposed, as well as in generating new ones.

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