Polarity and the Logic of Delimited Continuations

Noam Zeilberger 1, 2
2 PI.R2 - Design, study and implementation of languages for proofs and programs
PPS - Preuves, Programmes et Systèmes, Inria Paris-Rocquencourt, UPD7 - Université Paris Diderot - Paris 7, CNRS - Centre National de la Recherche Scientifique : UMR7126
Abstract : Polarized logic is the logic of values and continuations, and their interaction through continuation-passing style. The main limitations of this logic are the limitations of CPS: that continuations cannot be composed, and that programs are fully sequentialized. Delimited control operators were invented in response to the limitations of classical continuation-passing. That suggests the question: what is the logic of delimited continuations? We offer a simple account of delimited control, through a natural generalization of the classical notion of polarity. This amounts to breaking the perfect symmetry between positive and negative polarity in the following way: answer types are positive. Despite this asymmetry, we retain all of the classical polarized connectives, and can explain ``intuitionistic polarity'' (e.g., in systems like CBPV) as a restriction on the use of connectives, i.e., as a logical fragment. Our analysis complements and generalizes existing accounts of delimited control operators, while giving us a rich logical language through which to understand the interaction of control with monadic effects.
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Submitted on : Sunday, December 19, 2010 - 3:09:52 AM
Last modification on : Friday, January 4, 2019 - 5:33:25 PM

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Noam Zeilberger. Polarity and the Logic of Delimited Continuations. 25th Annual IEEE Symposium on Logic in Computer Science (LICS 2010), Jul 2010, Edinburgh, United Kingdom. pp.219 - 227, 2010, 〈10.1109/LICS.2010.23〉. 〈hal-00548167〉

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