Lambda-Calculus, Taylor Expansion and (Tropical) Quantitative Semantics: an overview

The plan of the talk will be, first, to give an overview of the Taylor expansion of the lambda-calculus and, then, to give an overview of some aspects of quantitative categorical semantics.

I will in particular highlight some results obtained for a semantics based on the tropical semiring, which appeared in a recent CSL paper, where programs can be seen as locally Lipschitz functions, and the lambda-calculus Taylor expansion gives local approximants of the Lipschitz constants.

Depending on the interest and the common knowledge of the audience, I will spend more time on one topic or another.