License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2021.143
URN: urn:nbn:de:0030-drops-142127
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14212/
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Xu, Han ; Hu, Zhenjiang

Analytical Differential Calculus with Integration

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LIPIcs-ICALP-2021-143.pdf (0.6 MB)

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.

BibTeX - Entry

@InProceedings{xu_et_al:LIPIcs.ICALP.2021.143,
  author =	{Xu, Han and Hu, Zhenjiang},
  title =	{{Analytical Differential Calculus with Integration}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{143:1--143:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14212},
  URN =		{urn:nbn:de:0030-drops-142127},
  doi =		{10.4230/LIPIcs.ICALP.2021.143},
  annote =	{Keywords: Differential Calculus, Integration, Lambda Calculus, Incremental Computation, Adaptive Computing}
}

Keywords: Differential Calculus, Integration, Lambda Calculus, Incremental Computation, Adaptive Computing
Collection: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Issue Date: 2021
Date of publication: 02.07.2021

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