From proof-nets to interaction nets
Proceedings of the workshop on Advances in linear logic
Polarized proof-nets and λµ-calculus
Theoretical Computer Science
Lambda-My-Calculus: An Algorithmic Interpretation of Classical Natural Deduction
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
About Translations of Classical Logic into Polarized Linear Logic
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
The differential Lambda-calculus
Theoretical Computer Science
On Köthe sequence spaces and linear logic
Mathematical Structures in Computer Science
Mathematical Structures in Computer Science
Theoretical Computer Science
Intersection and Union Types in the λμμ~-calculus
Electronic Notes in Theoretical Computer Science (ENTCS)
Electronic Notes in Theoretical Computer Science (ENTCS)
Differential Linear Logic and Polarization
TLCA '09 Proceedings of the 9th International Conference on Typed Lambda Calculi and Applications
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We define an extension of Herbelin's λµ-calculus, introducing a product operation on contexts (in the sense of lists of arguments, or stacks in environment machines), similar to the convolution product of distributions. This is the computational couterpart of some new semantical constructions, extending models of Ehrhard-Regnier's differential interaction nets, along the lines of Laurent's polarization of linear logic. We demonstrate this correspondence by providing this calculus with a denotational semantics inside a lambda-model in the category of sets and relations.