Enriching an effect calculus with linear types

  • Authors:

  • Jeff Egger;Rasmus Ejlers Møgelberg;Alex Simpson

  • Affiliations:

  • LFCS, School of Informatics, University of Edinburgh, Scotland, UK;IT University of Copenhagen, Copenhagen, Denmark;LFCS, School of Informatics, University of Edinburgh, Scotland, UK

  • Venue:
  • CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
  • Year:
  • 2009

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Abstract

We define an enriched effect calculus by extending a type theory for computational effects with primitives from linear logic. The new calculus provides a formalism for expressing linear aspects of computational effects; for example, the linear usage of imperative features such as state and/or continuations. Our main syntactic result is the conservativity of the enriched effect calculus over a basic effect calculus without linear primitives (closely related to Moggi's computational metalanguage, Filinski's effect PCF and Levy's call-by-push-value). The proof of this syntactic theorem makes essential use of a category-theoretic semantics, whose study forms the second half of the paper. Our semantic results include soundness, completeness, the initiality of a syntactic model, and an embedding theorem: every model of the basic effect calculus fully embeds in a model of the enriched calculus. The latter means that our enriched effect calculus is applicable to arbitrary computational effects, answering in the positive a question of Benton and Wadler (LICS 1996).