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DOI: 10.4230/LIPIcs.FSCD.2017.13

There Is Only One Notion of Differentiation

Authors: J. Robin B. Cockett and Jean-Simon Lemay

Published in: LIPIcs, Volume 84, 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)

Abstract

Differential linear logic was introduced as a syntactic proof-theoretic approach to the analysis of differential calculus. Differential categories were subsequently introduce to provide a categorical model theory for differential linear logic. Differential categories used two different approaches for defining differentiation abstractly: a deriving transformation and a coderiliction. While it was thought that these notions could give rise to distinct notions of differentiation, we show here that these notions, in the presence of a monoidal coalgebra modality, are completely equivalent.

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J. Robin B. Cockett and Jean-Simon Lemay. There Is Only One Notion of Differentiation. In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, pp. 13:1-13:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{cockett_et_al:LIPIcs.FSCD.2017.13,
  author =	{Cockett, J. Robin B. and Lemay, Jean-Simon},
  title =	{{There Is Only One Notion of Differentiation}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{13:1--13:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-047-7},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{84},
  editor =	{Miller, Dale},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2017.13},
  URN =		{urn:nbn:de:0030-drops-77166},
  doi =		{10.4230/LIPIcs.FSCD.2017.13},
  annote =	{Keywords: Differential Categories, Linear Logic, Coalgebra Modalities, Bialgebra Modalities}
}

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There Is Only One Notion of Differentiation

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