Mackey-complete spaces and power series -- A topological model of Differential Linear Logic

Marie Kerjean; Christine Tasson

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arXiv · 1507.03262

Mackey-complete spaces and power series -- A topological model of Differential Linear Logic

Marie Kerjean·Christine Tasson

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Abstract

In this paper, we have described a denotational model of Intuitionist Linear Logic which is also a differential category. Formulas are interpreted as Mackey-complete topological vector space and linear proofs are interpreted by bounded linear functions. So as to interpret non-linear proofs of Linear Logic, we have used a notion of power series between Mackey-complete spaces, generalizing the notion of entire functions in C. Finally, we have obtained a quantitative model of Intuitionist Differential Linear Logic, where the syntactic differentiation correspond to the usual one and where the interpretations of proofs satisfy a Taylor expansion decomposition.

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Marie Kerjean, Christine Tasson. 2015-07-12. Mackey-complete spaces and power series -- A topological model of Differential Linear Logic. https://arxiv.org/abs/1507.03262

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