Appears in collection : Differential $\lambda$-Calculus and Differential Linear Logic, 20 Years Later / $ \lambda $-calcul différentiel et logique linéaire différentielle, 20 ans après

In this talk, we introduce the syntax and semantics of Differential Linear Logic. We explain how its rules relate to Linear Logic's rules, and give informal intuitions in terms of functions and distributions. We show how its cut-elimination rules are a reflection of basic calculus rules. We also review Differential Lambda-calculus, with matching intuitions. At the end of the talk, we briefly review two recent development about Differential Linear Logic, in terms of Laplace transformation and co-promotion.