Mackey-complete spaces and power series – a topological model of differential linear logic
2016 ◽
Vol 28
(4)
◽
pp. 472-507
◽
Keyword(s):
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.
2002 ◽
Vol 33
(4)
◽
pp. 289-302
◽
2009 ◽
Vol 08
(06)
◽
pp. 863-868
◽
Keyword(s):
1990 ◽
Vol 33
(1)
◽
pp. 53-59
◽
1974 ◽
Vol 26
(4)
◽
pp. 841-853
◽
2015 ◽
Vol 288
(8-9)
◽
pp. 917-924
◽