Correspondence Between Composite Theories and Distributive Laws

Aloïs Rosset; Maaike Zwart; Helle Hvid Hansen; Jörg Endrullis

doi:10.1007/978-3-031-66438-0_10

Correspondence Between Composite Theories and Distributive Laws

Aloïs Rosset, Maaike Zwart, Helle Hvid Hansen, Jörg Endrullis

Research output: Chapter in Book / Report / Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

Composite theories are the algebraic equivalent of distributive laws. In this paper, we delve into the details of this correspondence and concretely show how to construct a composite theory from a distributive law and vice versa. Using term rewriting methods, we also describe when a minimal set of equations axiomatises the composite theory.

Original language	English
Title of host publication	Coalgebraic Methods in Computer Science
Subtitle of host publication	17th IFIP WG 1.3 International Workshop, CMCS 2024 Colocated with ETAPS 2024 Luxembourg City, Luxembourg, April 6–7, 2024, Proceedings
Editors	Barbara König, Henning Urbat
Publisher	Springer Nature Switzerland AG
Pages	194-215
Number of pages	22
ISBN (Electronic)	9783031664380
ISBN (Print)	9783031664373
DOIs	https://doi.org/10.1007/978-3-031-66438-0_10
Publication status	Published - 2024
Event	17th IFIP WG 1.3 International Workshop, CMCS 2024, Colocated with ETAPS 2024 Luxembourg City, Luxembourg, April 6–7, 2024 - Luxembourg City, Luxembourg Duration: 6 Apr 2024 → 7 Apr 2024 Conference number: 17 https://coalg.org/cmcs24/

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	14617 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Workshop

Workshop	17th IFIP WG 1.3 International Workshop, CMCS 2024, Colocated with ETAPS 2024 Luxembourg City, Luxembourg, April 6–7, 2024
Abbreviated title	CMCS 2024
Country/Territory	Luxembourg
City	Luxembourg City
Period	6/04/24 → 7/04/24
Internet address	https://coalg.org/cmcs24/

Funding

We thank all anonymous reviewers for their valuable feedback and suggestions. Alo\u00EFs Rosset and J\u00F6rg Endrullis received funding from the Netherlands Organization for Scientific Research (NWO) under the Innovational Research Incentives Scheme Vidi (project. No. VI.Vidi.192.004).

Funders	Funder number
Netherlands Organization for International Cooperation in Higher Education
Sociale en Geesteswetenschappen, NWO
DSM Research	VI.Vidi.192.004

Keywords

monad
distributive law
algebraic theory
composite theory
Term rewriting

Access to Document

10.1007/978-3-031-66438-0_10

Correspondence Between Composite Theories and Distributive LawsFinal published version, 461 KBLicence: Article 25fa Dutch Copyright Act

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Rosset, A., Zwart, M., Hansen, H. H., & Endrullis, J. (2024). Correspondence Between Composite Theories and Distributive Laws. In B. König, & H. Urbat (Eds.), Coalgebraic Methods in Computer Science: 17th IFIP WG 1.3 International Workshop, CMCS 2024 Colocated with ETAPS 2024 Luxembourg City, Luxembourg, April 6–7, 2024, Proceedings (pp. 194-215). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14617 LNCS). Springer Nature Switzerland AG. https://doi.org/10.1007/978-3-031-66438-0_10

Rosset, Aloïs ; Zwart, Maaike ; Hansen, Helle Hvid et al. / Correspondence Between Composite Theories and Distributive Laws. Coalgebraic Methods in Computer Science: 17th IFIP WG 1.3 International Workshop, CMCS 2024 Colocated with ETAPS 2024 Luxembourg City, Luxembourg, April 6–7, 2024, Proceedings. editor / Barbara König ; Henning Urbat. Springer Nature Switzerland AG, 2024. pp. 194-215 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Rosset, A, Zwart, M, Hansen, HH & Endrullis, J 2024, Correspondence Between Composite Theories and Distributive Laws. in B König & H Urbat (eds), Coalgebraic Methods in Computer Science: 17th IFIP WG 1.3 International Workshop, CMCS 2024 Colocated with ETAPS 2024 Luxembourg City, Luxembourg, April 6–7, 2024, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 14617 LNCS, Springer Nature Switzerland AG, pp. 194-215, 17th IFIP WG 1.3 International Workshop, CMCS 2024, Colocated with ETAPS 2024 Luxembourg City, Luxembourg, April 6–7, 2024, Luxembourg City, Luxembourg, 6/04/24. https://doi.org/10.1007/978-3-031-66438-0_10

Correspondence Between Composite Theories and Distributive Laws. / Rosset, Aloïs; Zwart, Maaike; Hansen, Helle Hvid et al.
Coalgebraic Methods in Computer Science: 17th IFIP WG 1.3 International Workshop, CMCS 2024 Colocated with ETAPS 2024 Luxembourg City, Luxembourg, April 6–7, 2024, Proceedings. ed. / Barbara König; Henning Urbat. Springer Nature Switzerland AG, 2024. p. 194-215 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14617 LNCS).

Research output: Chapter in Book / Report / Conference proceeding › Conference contribution › Academic › peer-review

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Rosset A, Zwart M, Hansen HH, Endrullis J. Correspondence Between Composite Theories and Distributive Laws. In König B, Urbat H, editors, Coalgebraic Methods in Computer Science: 17th IFIP WG 1.3 International Workshop, CMCS 2024 Colocated with ETAPS 2024 Luxembourg City, Luxembourg, April 6–7, 2024, Proceedings. Springer Nature Switzerland AG. 2024. p. 194-215. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). Epub 2024 Jul 26. doi: 10.1007/978-3-031-66438-0_10

Correspondence Between Composite Theories and Distributive Laws

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