The 48th International Colloquium on Automata, Languages, and Programming (ICALP) will take place in Glasgow, Scotland, on 12-16 July 2021. Researchers from the Programming Languages Lab presented their paper "Analytical Differential Calculus with Integration" at the conference.

Differential lambda-calculus was first introduced by Thomas Ehrhard and Laurent Regnier in 2003. Despite more than 15 years of history, little work has been done on a differential calculus with integration. In this paper, we propose a differential calculus with integration from a programming point of view. It shows good correspondence with mathematics, which is manifested by its reduction rules and preservation of important mathematical theorems. Moreover, it has many profound applications of the calculus in incremental computation, automatic differentiation, and computation approximation.