3 Search Results for "Cockett, J. Robin B."

Document
DOI: 10.4230/LIPIcs.CSL.2026.12
String Diagrams for Closed Symmetric Monoidal Categories

Authors: Callum Reader and Alessandro Di Giorgio

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
We introduce a graphical language for closed symmetric monoidal categories based on an extension of string diagrams with special bracket wires representing internal homs. These bracket wires make the structure of the internal hom functor explicit, allowing standard morphism wires to interact with them through a well-defined set of graphical rules. We establish the soundness and completeness of the diagrammatic calculus, and illustrate its expressiveness through examples drawn from category theory, logic and programming language semantics.
Cite as

Callum Reader and Alessandro Di Giorgio. String Diagrams for Closed Symmetric Monoidal Categories. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 12:1-12:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{reader_et_al:LIPIcs.CSL.2026.12,
  author =	{Reader, Callum and Di Giorgio, Alessandro},
  title =	{{String Diagrams for Closed Symmetric Monoidal Categories}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{12:1--12:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.12},
  URN =		{urn:nbn:de:0030-drops-254369},
  doi =		{10.4230/LIPIcs.CSL.2026.12},
  annote =	{Keywords: diagrammatic languages, logic, lambda calculi}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.26
Functorial Models of Differential Linear Logic

Authors: Marie Kerjean, Valentin Maestracci, and Morgan Rogers

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
Differentiation in logic has several sources of inspiration. The most recent is differentiable programming, models of which demand functoriality and good typing properties. More historical is reverse denotational semantics, taking inspiration from models of Linear Logic to differentiate proofs and λ-terms. In this paper, we take advantage of the rich structure of categorical models of Linear Logic to give a new functorial presentation of differentiation. We define differentiation as a functor from a coslice of the category of smooth maps to the category of linear maps. Extending linear-non-linear adjunction models of Linear Logic, this produces models of Differential Linear Logic. We use these functorial presentations to shed new light on integration in differential categories.
Cite as

Marie Kerjean, Valentin Maestracci, and Morgan Rogers. Functorial Models of Differential Linear Logic. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 26:1-26:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kerjean_et_al:LIPIcs.FSCD.2025.26,
  author =	{Kerjean, Marie and Maestracci, Valentin and Rogers, Morgan},
  title =	{{Functorial Models of Differential Linear Logic}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{26:1--26:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.26},
  URN =		{urn:nbn:de:0030-drops-236419},
  doi =		{10.4230/LIPIcs.FSCD.2025.26},
  annote =	{Keywords: Categorical semantics, Differential Programming, Linear Logic}
}
Document
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.
Cite as

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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