License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7716/
Cockett, J. Robin B. ;
Lemay, Jean-Simon
There Is Only One Notion of Differentiation
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}
}
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Keywords: |
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Differential Categories, Linear Logic, Coalgebra Modalities, Bialgebra Modalities |
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Collection: |
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2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017) |
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Issue Date: |
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2017 |
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Date of publication: |
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30.08.2017 |
