Abstract
We extend Ehrhard–Regnier’s differential linear logic along the lines of Laurent’s polarization. We provide a denotational semantics of this new system in the well-known relational model of linear logic, extending canonically the semantics of both differential and polarized linear logics: this justifies our choice of cut elimination rules. Then we show this polarized differential linear logic refines the recently introduced convolution \({\bar\lambda}\mu\)-calculus, the same as linear logic decomposes λ-calculus.
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Vaux, L. (2009). Differential Linear Logic and Polarization. In: Curien, PL. (eds) Typed Lambda Calculi and Applications. TLCA 2009. Lecture Notes in Computer Science, vol 5608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02273-9_27
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DOI: https://doi.org/10.1007/978-3-642-02273-9_27
Publisher Name: Springer, Berlin, Heidelberg
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