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

By Marie Kerjean and Christine Tasson

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

Topics: [ INFO.INFO-LO ] Computer Science [cs]/Logic in Computer Science [cs.LO]
Publisher: HAL CCSD
Year: 2015
OAI identifier: oai:HAL:hal-01175662v1
Provided by: Hal-Diderot

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