Uploaded September 2026 | Updated September 2026, 2 weeks ago

---

Topos Institute Colloquium, 10th of September 2026.
———
Reverse denotational semantics is a well-established methodology which examines mathematical models of proofs (or programs) and extracts from them new logical paradigms. A typical example is linear logic, which was derived by Girard from a lambda calculus model in which certain interpretations of programs can be characterized as linear functions. Another successful example is the one by Ehrhard and Regnier: by studying specific models of linear logic in which the interpretation of proofs can be made linear – and thus differentiated – they constructed differential linear logic.

During this talk, we will review these examples and present new ones. I will show how the categorical models of differential linear logic are elegantly interpreted within the theory of topological vector spaces and
distributions. I will also expose a link between linear logic and more recent higher-order constructions in topological vector spaces. Finally, following the methodology of reverse denotational semantics, I will explain how these models enable the construction of refined versions of differential linear logic.