31ème Journées Francophones des Langages Applicatifs

International audienc

Differential Linear Logic and Polarization

Abstract. We study an extension of Ehrhard–Regnier’s differential linear logic along the lines of Laurent’s polarization. We show that a particular object of the well-known relational model of linear logic provides a denotational semantics for this new system, which canonically extends the semantics of both differential and polarized linear logics: this justifies our choice of cut elimination rules. Then we show this new system models the recently introduced convolution ¯ λµ-calculus, the same as linear logic decomposes λ-calculus.

Differential linear logic and polarization

International audienceWe 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 lambda-mu-calculus, the same as linear logic decomposes lambda-calculus.