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

摘要

In this paper, we describe a denotational model of Intuitionist Linear Logic which is also arndifferential category. Formulas are interpreted as Mackey-complete topological vector spacernand linear proofs are interpreted as bounded linear functions. So as to interpret non-linearrnproofs of Linear Logic, we use a notion of power series between Mackey-complete spaces,rngeneralizing entire functions in C. Finally, we get a quantitative model of IntuitionistrnDifferential Linear Logic, with usual syntactic differentiation and where interpretations ofrnproofs decompose as a Taylor expansion.