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Mackey-complete spaces and power series – a topological model of differential linear logic

Published online by Cambridge University Press:  21 October 2016

MARIE KERJEAN  and
CHRISTINE TASSON
MARIE KERJEAN
Affiliation:
Laboratory PPS, Université Paris Diderot, Paris, France Emails: marie.kerjean@pps.univ-paris-diderot.fr, christine.tasson@pps.univ-paris-diderot.fr
CHRISTINE TASSON
Affiliation:
Laboratory PPS, Université Paris Diderot, Paris, France Emails: marie.kerjean@pps.univ-paris-diderot.fr, christine.tasson@pps.univ-paris-diderot.fr
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Abstract

In this paper, we describe 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 as bounded linear functions. So as to interpret non-linear proofs of Linear Logic, we use a notion of power series between Mackey-complete spaces, generalizing entire functions in $\mathbb{C}$ . Finally, we get a quantitative model of Intuitionist Differential Linear Logic, with usual syntactic differentiation and where interpretations of proofs decompose as a Taylor expansion.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 28 , Issue 4 , April 2018 , pp. 472 - 507
Copyright
Copyright © Cambridge University Press 2016 

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