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An Approach to Call-by-Name Delimited Continuations

Hugo Herbelin 1 Silvia Ghilezan 2
1 TYPICAL - Types, Logic and computing
Inria Saclay - Ile de France, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
Abstract : We show that a variant of Parigot's λμ-calculus, originally due to de Groote and proved to satisfy Böhm's theorem by Saurin, is canonically interpretable as a call-by-name calculus of delim- ited control. This observation is expressed using Ariola et al's call-by-value calculus of delimited control, an extension of λμ-calculus with delimited control known to be equationally equivalent to Danvy and Filinski's calculus with shift and reset. Our main result then is that de Groote and Saurin's variant of λμ-calculus is equivalent to a canonical call-by-name variant of Ariola et al's calculus. The rest of the paper is devoted to a comparative study of the call-by-name and call-by-value variants of Ariola et al's calculus, covering in particular the questions of simple typing, operational semantics, and continuation-passing-style semantics. Finally, we discuss the relevance of Ariola et al's calculus as a uniform framework for representing different calculi of delimited continuations, including "lazy" variants such as Sabry's shift and lazy reset calculus.
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Submitted on : Friday, October 29, 2010 - 10:59:35 AM
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Hugo Herbelin, Silvia Ghilezan. An Approach to Call-by-Name Delimited Continuations. Symposium on Principles of Programming Languages, Jan 2008, San Francisco, United States. pp.383-394, ⟨10.1145/1328438.1328484⟩. ⟨inria-00524949⟩

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