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Polarity and the Logic of Delimited Continuations
"... Abstract—Polarized logic is the logic of values and continuations, and their interaction through continuationpassing 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 w ..."
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Abstract—Polarized logic is the logic of values and continuations, and their interaction through continuationpassing 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 continuationpassing. 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. I.
unknown title
, 2009
"... A short proof that adding some permutation rules to β preserves SN ..."
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unknown title
, 2009
"... A short proof that adding some permutation rules to β preserves SN ..."
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, 2007
"... The purpose of this paper is to prove the claim in [DL06, DL07] that typed terms of λLJQ are terminating. ..."
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The purpose of this paper is to prove the claim in [DL06, DL07] that typed terms of λLJQ are terminating.