5 Search Results for "Zwart, Maaike"

Document
DOI: 10.4230/LIPIcs.CALCO.2025.4
Distributive Laws of Monadic Containers

Authors: Chris Purdy and Stefania Damato

Published in: LIPIcs, Volume 342, 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)

Abstract
Containers are used to carve out a class of strictly positive data types in terms of shapes and positions. They can be interpreted via a fully-faithful functor into endofunctors on Set. Monadic containers are those containers whose interpretation as a Set functor carries a monad structure. The category of containers is closed under container composition and is a monoidal category, whereas monadic containers do not in general compose. In this paper, we develop a characterisation of distributive laws of monadic containers. Distributive laws were introduced as a sufficient condition for the composition of the underlying functors of two monads to also carry a monad structure. Our development parallels Ahman and Uustalu’s characterisation of distributive laws of directed containers, i.e. containers whose Set functor interpretation carries a comonad structure. Furthermore, by combining our work with theirs, we construct characterisations of mixed distributive laws (i.e. of directed containers over monadic containers and vice versa), thereby completing the "zoo" of container characterisations of (co)monads and their distributive laws. We have found these characterisations amenable to development of existence and uniqueness proofs of distributive laws, particularly in the mechanised setting of Cubical Agda, in which most of the theory of this paper has been formalised.
Cite as

Chris Purdy and Stefania Damato. Distributive Laws of Monadic Containers. In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 4:1-4:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{purdy_et_al:LIPIcs.CALCO.2025.4,
  author =	{Purdy, Chris and Damato, Stefania},
  title =	{{Distributive Laws of Monadic Containers}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{4:1--4:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-383-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{342},
  editor =	{C\^{i}rstea, Corina and Knapp, Alexander},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2025.4},
  URN =		{urn:nbn:de:0030-drops-235633},
  doi =		{10.4230/LIPIcs.CALCO.2025.4},
  annote =	{Keywords: distributive laws, monadic containers, monads, dependent types, cubical agda}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.10
Monotone Weak Distributive Laws over the Lifted Powerset Monad in Categories of Algebras

Authors: Quentin Aristote

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
In both the category of sets and the category of compact Hausdorff spaces, there is a monotone weak distributive law that combines two layers of non-determinism. Noticing the similarity between these two laws, we study whether the latter can be obtained automatically as a weak lifting of the former. This holds partially, but does not generalize to other categories of algebras. We then characterize when exactly monotone weak distributive laws over powerset monads in categories of algebras exist, on the one hand exhibiting a law combining probabilities and non-determinism in compact Hausdorff spaces and showing on the other hand that such laws do not exist in a lot of other cases.
Cite as

Quentin Aristote. Monotone Weak Distributive Laws over the Lifted Powerset Monad in Categories of Algebras. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{aristote:LIPIcs.STACS.2025.10,
  author =	{Aristote, Quentin},
  title =	{{Monotone Weak Distributive Laws over the Lifted Powerset Monad in Categories of Algebras}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{10:1--10:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.10},
  URN =		{urn:nbn:de:0030-drops-228356},
  doi =		{10.4230/LIPIcs.STACS.2025.10},
  annote =	{Keywords: weak distributive law, weak extension, weak lifting, iterated distributive law, Yang-Baxter equation, powerset monad, Vietoris monad, Radon monad, Eilenberg-Moore category, regular category, relational extension}
}
Document
DOI: 10.4230/LIPIcs.CSL.2024.39
What Monads Can and Cannot Do with a Bit of Extra Time

Authors: Rasmus Ejlers Møgelberg and Maaike Annebet Zwart

Published in: LIPIcs, Volume 288, 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)

Abstract
The delay monad provides a way to introduce general recursion in type theory. To write programs that use a wide range of computational effects directly in type theory, we need to combine the delay monad with the monads of these effects. Here we present a first systematic study of such combinations. We study both the coinductive delay monad and its guarded recursive cousin, giving concrete examples of combining these with well-known computational effects. We also provide general theorems stating which algebraic effects distribute over the delay monad, and which do not. Lastly, we salvage some of the impossible cases by considering distributive laws up to weak bisimilarity.
Cite as

Rasmus Ejlers Møgelberg and Maaike Annebet Zwart. What Monads Can and Cannot Do with a Bit of Extra Time. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 39:1-39:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{mgelberg_et_al:LIPIcs.CSL.2024.39,
  author =	{M{\o}gelberg, Rasmus Ejlers and Zwart, Maaike Annebet},
  title =	{{What Monads Can and Cannot Do with a Bit of Extra Time}},
  booktitle =	{32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)},
  pages =	{39:1--39:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-310-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{288},
  editor =	{Murano, Aniello and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2024.39},
  URN =		{urn:nbn:de:0030-drops-196823},
  doi =		{10.4230/LIPIcs.CSL.2024.39},
  annote =	{Keywords: Delay Monad, Monad Compositions, Distributive Laws, Guarded Recursion, Type Theory}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.77
Preservation of Equations by Monoidal Monads

Authors: Louis Parlant, Jurriaan Rot, Alexandra Silva, and Bas Westerbaan

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
If a monad T is monoidal, then operations on a set X can be lifted canonically to operations on TX. In this paper we study structural properties under which T preserves equations between those operations. It has already been shown that any monoidal monad preserves linear equations; affine monads preserve drop equations (where some variable appears only on one side, such as x⋅ y = y) and relevant monads preserve dup equations (where some variable is duplicated, such as x ⋅ x = x). We start the paper by showing a converse: if the monad at hand preserves a drop equation, then it must be affine. From this, we show that the problem whether a given (drop) equation is preserved is undecidable. A converse for relevance turns out to be more subtle: preservation of certain dup equations implies a weaker notion which we call n-relevance. Finally, we identify a subclass of equations such that their preservation is equivalent to relevance.
Cite as

Louis Parlant, Jurriaan Rot, Alexandra Silva, and Bas Westerbaan. Preservation of Equations by Monoidal Monads. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 77:1-77:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{parlant_et_al:LIPIcs.MFCS.2020.77,
  author =	{Parlant, Louis and Rot, Jurriaan and Silva, Alexandra and Westerbaan, Bas},
  title =	{{Preservation of Equations by Monoidal Monads}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{77:1--77:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.77},
  URN =		{urn:nbn:de:0030-drops-127460},
  doi =		{10.4230/LIPIcs.MFCS.2020.77},
  annote =	{Keywords: monoidal monads, algebraic theories, preservation of equations}
}
Document
DOI: 10.4230/LIPIcs.CSL.2018.32
Quantitative Foundations for Resource Theories

Authors: Dan Marsden and Maaike Zwart

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
Considering resource usage is a powerful insight in the analysis of many phenomena in the sciences. Much of the current research on these resource theories focuses on the analysis of specific resources such quantum entanglement, purity, randomness or asymmetry. However, the mathematical foundations of resource theories are at a much earlier stage, and there has been no satisfactory account of quantitative aspects such as costs, rates or probabilities. We present a categorical foundation for quantitative resource theories, derived from enriched category theory. Our approach is compositional, with rich algebraic structure facilitating calculations. The resulting theory is parameterized, both in the quantities under consideration, for example costs or probabilities, and in the structural features of the resources such as whether they can be freely copied or deleted. We also achieve a clear separation of concerns between the resource conversions that are freely available, and the costly resources that are typically the object of study. By using an abstract categorical approach, our framework is naturally open to extension. We provide many examples throughout, emphasising the resource theoretic intuitions for each of the mathematical objects under consideration.
Cite as

Dan Marsden and Maaike Zwart. Quantitative Foundations for Resource Theories. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 32:1-32:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{marsden_et_al:LIPIcs.CSL.2018.32,
  author =	{Marsden, Dan and Zwart, Maaike},
  title =	{{Quantitative Foundations for Resource Theories}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{32:1--32:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.32},
  URN =		{urn:nbn:de:0030-drops-96996},
  doi =		{10.4230/LIPIcs.CSL.2018.32},
  annote =	{Keywords: Resource Theory, Enriched Category, Profunctor, Monad, Combinatorial Species, Multicategory, Operad, Bimodule}
}
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