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About Translations of Classical Logic into Polarized Linear Logic
 In Proceedings of the eighteenth annual IEEE symposium on Logic In Computer Science
, 2003
"... We show that the decomposition of Intuitionistic Logic into Linear Logic along the equation A ! B = !A ( B may be adapted into a decomposition of classical logic into LLP, the polarized version of Linear Logic. Firstly we build a categorical model of classical logic (a Control Category) from a categ ..."
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We show that the decomposition of Intuitionistic Logic into Linear Logic along the equation A ! B = !A ( B may be adapted into a decomposition of classical logic into LLP, the polarized version of Linear Logic. Firstly we build a categorical model of classical logic (a Control Category) from a categorical model of Linear Logic by a construction similar to the coKleisli category. Secondly we analyse two standard ContinuationPassing Style (CPS) translations, the Plotkin and the Krivine's translations, which are shown to correspond to two embeddings of LLP into LL.
Semantics of linear continuationpassing in callbyname
 In Proc. Functional and Logic Programming, Springer Lecture Notes in Comput. Sci
, 2004
"... Abstract. We propose a semantic framework for modelling the linear usage of continuations in typed callbyname programming languages. On the semantic side, we introduce a construction for categories of linear continuations, which gives rise to cartesian closed categories with “linear classical disj ..."
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Cited by 6 (4 self)
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Abstract. We propose a semantic framework for modelling the linear usage of continuations in typed callbyname programming languages. On the semantic side, we introduce a construction for categories of linear continuations, which gives rise to cartesian closed categories with “linear classical disjunctions ” from models of intuitionistic linear logic with sums. On the syntactic side, we give a simply typed callbyname λµcalculus in which the use of names (continuation variables) is restricted to be linear. Its semantic interpretation into a category of linear continuations then amounts to the callbyname continuationpassing style (CPS) transformation into a linear lambda calculus with sum types. We show that our calculus is sound for this CPS semantics, hence for models given by the categories of linear continuations.
Linear ContinuationPassing
 in the 2001 ACM SIGPLAN Workshop on Continuations (CW'01
, 2002
"... Continuations can be used to explain a wide variety of control behaviours, including calling/returning (procedures), raising/handling (exceptions), labelled jumping (goto statements), process switching (coroutines), and backtracking. However, continuations are often manipulated in a highly stylised ..."
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Cited by 3 (1 self)
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Continuations can be used to explain a wide variety of control behaviours, including calling/returning (procedures), raising/handling (exceptions), labelled jumping (goto statements), process switching (coroutines), and backtracking. However, continuations are often manipulated in a highly stylised way, and we show that all of these, bar backtracking, in fact use their continuations linearly ; this is formalised by taking a target language for cps transforms that has both intuitionistic and linear function types.
Extracting the Range of cps from Affine Typing (Extended Abstract)
"... Increasing degrees of reasoning about programs are being mechanized, and hence more formality is needed. Here we present an instance of this formalization in the form of a precise characterization of the range of the cps transformation using an affine type system. The point is that the range of cps ..."
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Cited by 1 (0 self)
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Increasing degrees of reasoning about programs are being mechanized, and hence more formality is needed. Here we present an instance of this formalization in the form of a precise characterization of the range of the cps transformation using an affine type system. The point is that the range of cps is defined with a type system, that is, in a way quite accessible to tools.
Extracting the Range of cps from Affine Typing
"... Increasing degrees of reasoning about programs are being mechanized, and hence more formality is needed. Here we present an instance of this formalization in the form of a precise characterization of the range of the cps transformation using an ane type system. The point is that the range of cps is ..."
Abstract
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Increasing degrees of reasoning about programs are being mechanized, and hence more formality is needed. Here we present an instance of this formalization in the form of a precise characterization of the range of the cps transformation using an ane type system. The point is that the range of cps is defined with a type system, that is, in a way quite accessible to tools.