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

Marie Kerjean (1, 2, 3) , Christine Tasson (1)

1 PPS - Preuves, Programmes et Systèmes
2 INS2I-CNRS - Institut des sciences informatiques et de leurs interactions - CNRS Sciences informatiques
3 LIPN - Laboratoire d'Informatique de Paris-Nord

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.

Domaines: Logique en informatique [cs.LO]

Marie Kerjean, Christine Tasson. Mackey-complete spaces and power series – A topological model of Differential Linear Logic. Mathematical Structures in Computer Science, 2018, 28 (4), pp.472-507. ⟨10.1017/S0960129516000281⟩. ⟨hal-01175662⟩