2026-07-23T22:21:27Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:14212 2024-03-06T10:53:46Z ddc:004 open_access

Analytical Differential Calculus with Integration Xu, Han Hu, Zhenjiang Differential Calculus Integration Lambda Calculus Incremental Computation Adaptive Computing 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 shall propose a differential calculus with integration from a programming point of view. We show its good correspondence with mathematics, which is manifested by how we construct these reduction rules and how we preserve important mathematical theorems in our calculus. Moreover, we highlight applications of the calculus in incremental computation, automatic differentiation, and computation approximation. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Han Xu and Zhenjiang Hu 2021 Is Part Of LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2021.143 urn:nbn:de:0030-drops-142127 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.143 eng https://creativecommons.org/licenses/by/4.0/legalcode