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Analytical Differential Calculus with Integration

Authors Han Xu, Zhenjiang Hu

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Author Details

Han Xu
  • Department of Computer Science and Technology, Peking University, Beijing, China
Zhenjiang Hu
  • Key Laboratory of High Confidence Software Technologies (MoE), Department of Computer Science and Technology, Peking University, Beijing, China

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Han Xu and Zhenjiang Hu. Analytical Differential Calculus with Integration. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 143:1-143:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ICALP.2021.143

Abstract

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.

Subject Classification

ACM Subject Classification
  • Software and its engineering → General programming languages
  • Software and its engineering → Functional languages
Keywords
  • Differential Calculus
  • Integration
  • Lambda Calculus
  • Incremental Computation
  • Adaptive Computing

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