Document Open Access Logo

There Is Only One Notion of Differentiation

Authors J. Robin B. Cockett, Jean-Simon Lemay

PDF

File

Thumbnail PDF
PDF
LIPIcs.FSCD.2017.13.pdf
  • Filesize: 0.55 MB
  • 21 pages

Document Identifiers

Subject Classification

Keywords
  • Differential Categories
  • Linear Logic
  • Coalgebra Modalities
  • Bialgebra Modalities

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

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.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.FSCD.2017.13

Author Details

J. Robin B. Cockett
Jean-Simon Lemay

References

  1. Gavin Bierman. What is a categorical model of intuitionistic linear logic? Typed Lambda Calculi and Applications, pages 78-93, 1995. Google Scholar
  2. Richard F. Blute, J. Robin B. Cockett, and Robert A. G. Seely. Differential categories. Mathematical structures in computer science, 16(06):1049-1083, 2006. Google Scholar
  3. Richard F. Blute, J. Robin B. Cockett, and Robert A. G. Seely. Cartesian differential categories. Theory and Applications of Categories, 22(23):622-672, 2009. Google Scholar
  4. Richard F. Blute, J. Robin B. Cockett, and Robert A. G. Seely. Cartesian differential storage categories. Theory and Applications of Categories, 30(18):620-686, 2015. Google Scholar
  5. Thomas Ehrhard and Laurent Regnier. The differential lambda-calculus. Theoretical Computer Science, 309(1):1-41, 2003. Google Scholar
  6. Thomas Ehrhard and Laurent Regnier. Differential interaction nets. Theoretical Computer Science, 364(2):166-195, 2006. Google Scholar
  7. Marcelo P. Fiore. Differential structure in models of multiplicative biadditive intuitionistic linear logic. In International Conference on Typed Lambda Calculi and Applications, pages 163-177. Springer, 2007. Google Scholar
  8. André Joyal and Ross Street. The geometry of tensor calculus, I. Advances in Mathematics, 88(1):55-112, 1991. Google Scholar
  9. Saunders Mac Lane. Categories for the working mathematician, volume 5. Springer Science &Business Media, 2013. Google Scholar
  10. Paul-André Mellies. Categorical models of linear logic revisited, 2003. Google Scholar
  11. Robert A. G. Seely. Linear logic,*-autonomous categories and cofree coalgebras. Ste. Anne de Bellevue, Quebec: CEGEP John Abbott College, 1987. Google Scholar
  12. Peter Selinger. A survey of graphical languages for monoidal categories. In New structures for physics, pages 289-355. Springer, 2010. Google Scholar
  13. Shilong Zhang, Li Guo, and William Keigher. Monads and distributive laws for rota-baxter and differential algebras. Advances in Applied Mathematics, 72:139-165, 2016. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact