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Flexibly graded monads and graded algebras

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dc.contributor Reykjavik University
dc.contributor Háskólinn í Reykjavík
dc.contributor.author McDermott, Dylan
dc.contributor.author Uustalu, Tarmo
dc.date.accessioned 2023-02-21T11:20:41Z
dc.date.available 2023-02-21T11:20:41Z
dc.date.issued 2022-09-22
dc.identifier.citation D. McDermott, T. Uustalu. Flexibly graded monads and graded algebras. In E. Komendantskaya, ed., Mathematics of Program Construction: 14th International Conference, MPC 2022, Tbilisi, Georgia, September 26-28, 2022, Proceedings, Lecture Notes in Computer Science, v. 13544, pp. 102-128. Springer, 2022. doi:10.1007/978-3-031-16912-0_4
dc.identifier.isbn 9783031169113
dc.identifier.isbn 9783031169120
dc.identifier.issn 0302-9743
dc.identifier.issn 1611-3349
dc.identifier.uri https://hdl.handle.net/20.500.11815/4016
dc.description Post-print (lokagerð höfundar)
dc.description.abstract When modelling side-effects using a monad, we need to equip the monad with effectful operations. This can be done by noting that each algebra of the monad carries interpretations of the desired operations. We consider the analogous situation for graded monads, which are a generalization of monads that enable us to track quantitative information about side-effects. Grading makes a significant difference: while many graded monads of interest can be equipped with similar operations, the algebras often cannot. We explain where these operations come from for graded monads. To do this, we introduce the notion of flexibly graded monad, for which the situation is similar to the situation for ordinary monads. We then show that each flexibly graded monad induces a canonical graded monad in such a way that operations for the flexibly graded monad carry over to the graded monad. In doing this, we reformulate grading in terms of locally graded categories, showing in particular that graded monads are a particular kind of relative monad. We propose that locally graded categories are a useful setting for work on grading in general.
dc.description.sponsorship Both authors were supported by the Icelandic Research Fund grants no. 196323-053 and 228684-051.
dc.format.extent 102-128
dc.language.iso en
dc.publisher Springer
dc.relation.ispartofseries Lecture Notes in Computer Science;13544
dc.rights info:eu-repo/semantics/embargoedAccess
dc.subject Graded monad
dc.subject Graded algebra
dc.subject Flexible grading
dc.subject Relative monad
dc.subject Computational effect
dc.subject Locally graded category
dc.subject Stærðfræði
dc.subject Algebra
dc.subject Tölvunarfræði
dc.title Flexibly graded monads and graded algebras
dc.type info:eu-repo/semantics/bookPart
dcterms.license From License to Publish, Article 3(c): The Licensee grants to the Author (i) the right to make the Accepted Manuscript available on their own personal, self-maintained website immediately on acceptance, (ii) the right to make the Accepted Manuscript available for public release on any of the following twelve (12) months after first publication (the “Embargo Period”): their employer’s internal website; their institutional and/or funder repositories. Accepted Manuscripts may be deposited in such repositories immediately upon acceptance, provided they are not made publicly available until after the Embargo Period. The rights granted to the Author with respect to the Accepted Manuscript are subject to the conditions that (i) the Accepted Manuscript is not enhanced or substantially reformatted by the Author or any third party, and (ii) the Author includes on the Accepted Manuscript an acknowledgement in the following form, together with a link to the published version on the publisher’s website: “This version of the contribution has been accepted for publication, after peer review (when applicable) but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/[insert DOI]. Use of this Accepted Version is subject to the publisher’s Accepted Manuscript terms of use https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms”. Under no circumstances may an Accepted Manuscript be shared or distributed under a Creative Commons or other form of open access licence. Any use of the Accepted Manuscript not expressly permitted under this subclause (c) is subject to the Licensee’s prior consent.
dc.description.version Peer reviewed (ritrýnd grein)
dc.identifier.journal Mathematics of Program Construction: 14th International Conference, MPC 2022, Tbilisi, Georgia, September 26-28, 2022, Proceedings
dc.identifier.doi 10.1007/978-3-031-16912-0_4
dc.relation.url https://link.springer.com/content/pdf/10.1007/978-3-031-16912-0_4
dc.contributor.department Department of Computer Science (RU)
dc.contributor.department Tölvunarfræðideild (HR)
dc.contributor.school School of Technology (RU)
dc.contributor.school Tæknisvið (HR)

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