2 Search Results for "Boisseau, Guillaume"

Document
DOI: 10.4230/LIPIcs.FSTTCS.2021.40
Diagrammatic Polyhedral Algebra

Authors: Filippo Bonchi, Alessandro Di Giorgio, and Paweł Sobociński

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract
We extend the theory of Interacting Hopf algebras with an order primitive, and give a sound and complete axiomatisation of the prop of polyhedral cones. Next, we axiomatise an affine extension and prove soundness and completeness for the prop of polyhedra.
Cite as

Filippo Bonchi, Alessandro Di Giorgio, and Paweł Sobociński. Diagrammatic Polyhedral Algebra. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 40:1-40:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bonchi_et_al:LIPIcs.FSTTCS.2021.40,
  author =	{Bonchi, Filippo and Di Giorgio, Alessandro and Soboci\'{n}ski, Pawe{\l}},
  title =	{{Diagrammatic Polyhedral Algebra}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{40:1--40:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.40},
  URN =		{urn:nbn:de:0030-drops-155511},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.40},
  annote =	{Keywords: String diagrams, Polyhedral cones, Polyhedra}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2020.17
String Diagrams for Optics

Authors: Guillaume Boisseau

Published in: LIPIcs, Volume 167, 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)

Abstract
Optics are a data representation for compositional data access, with lenses as a popular special case. Hedges has presented a diagrammatic calculus for lenses, but in a way that does not generalize to other classes of optic. We present a calculus that works for all optics, not just lenses; this is done by embedding optics into their presheaf category, which naturally features string diagrams. We apply our calculus to the common case of lenses, extend it to effectful lenses, and explore how the laws of optics manifest in this setting.
Cite as

Guillaume Boisseau. String Diagrams for Optics. In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 17:1-17:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{boisseau:LIPIcs.FSCD.2020.17,
  author =	{Boisseau, Guillaume},
  title =	{{String Diagrams for Optics}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{17:1--17:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-155-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{167},
  editor =	{Ariola, Zena M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.17},
  URN =		{urn:nbn:de:0030-drops-123399},
  doi =		{10.4230/LIPIcs.FSCD.2020.17},
  annote =	{Keywords: Optic, string diagram, lens, category theory, Yoneda lemma}
}
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