A Type-Theoretic Foundation of Delimited Continuations - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Higher-Order and Symbolic Computation Year : 2007

A Type-Theoretic Foundation of Delimited Continuations

Zena Ariola
  • Function : Author
  • PersonId : 843206
Amr Sabry
  • Function : Author
  • PersonId : 843207


There is a correspondence between classical logic and programming language calculi with first-class continuations. With the addition of control delimiters, the continuations become composable and the calculi become more expressive. We present a fine-grained analysis of control delimiters and formalise that their addition corresponds to the addition of a single dynamically-scoped variable modelling the special top-level continuation. From a type perspective, the dynamically-scoped variable requires effect annotations. In the presence of control, the dynamically-scoped variable can be interpreted in a purely functional way by applying a store-passing style. At the type level, the effect annotations are mapped within standard classical logic extended with the dual of implication, namely subtraction. A continuation-passing-style transformation of lambda-calculus with control and subtraction is defined. Combining the translations provides a decomposition of standard CPS transformations for delimited continuations. Incidentally, we also give a direct normalisation proof of the simply-typed lambda-calculus with control and subtraction.
Fichier principal
Vignette du fichier
hosc-AriHerSab07-delim-cont.pdf (391.95 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

inria-00177326 , version 1 (07-10-2007)


  • HAL Id : inria-00177326 , version 1


Zena Ariola, Hugo Herbelin, Amr Sabry. A Type-Theoretic Foundation of Delimited Continuations. Higher-Order and Symbolic Computation, 2007. ⟨inria-00177326⟩
236 View
350 Download


Gmail Facebook Twitter LinkedIn More