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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2017.13
URN: urn:nbn:de:0030-drops-77166
URL: http://drops.dagstuhl.de/opus/volltexte/2017/7716/
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Cockett, J. Robin B. ; Lemay, Jean-Simon

There Is Only One Notion of Differentiation

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LIPIcs-FSCD-2017-13.pdf (0.6 MB)


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.

BibTeX - Entry

@InProceedings{cockett_et_al:LIPIcs:2017:7716,
  author =	{J. Robin B. Cockett and Jean-Simon Lemay},
  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 =	{Dale Miller},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7716},
  URN =		{urn:nbn:de:0030-drops-77166},
  doi =		{10.4230/LIPIcs.FSCD.2017.13},
  annote =	{Keywords: Differential Categories, Linear Logic, Coalgebra Modalities, Bialgebra Modalities}
}

Keywords: Differential Categories, Linear Logic, Coalgebra Modalities, Bialgebra Modalities
Seminar: 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)
Issue Date: 2017
Date of publication: 21.08.2017


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