Control reduction theories: the benefit of structural substitution

Abstract

AbstractThe historical design of the call-by-value theory of control relies on the reification of evaluation contexts as regular functions and on the use of ordinary term application for jumping to a continuation. To the contrary, thecontrol calculus, developed by the authors, distinguishes betweenjumpsandterms. This alternative calculus, which derives from Parigot's λμ-calculus, works by directstructural substitutionof evaluation contexts. We review and revisit the legacy theories of control and argue thatprovides an observationally equivalent but smoother theory. In an additional note contributed by Matthias Felleisen, we review the story of the birth of control calculi during the mid- to late-eighties at Indiana University.