Duoidally enriched Freyd categories

Chris Heunen; Jesse Sigal

doi:10.1007/978-3-031-28083-2_15

Duoidally enriched Freyd categories

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract / Description of output

Freyd categories provide a semantics for first-order effectful programming languages by capturing the two different orders of evaluation for products. We enrich Freyd categories in a duoidal category, which provides a new, third choice of parallel composition. Duoidal categories have two monoidal structures which account for the sequential and parallel compositions. The traditional setting is recovered as a full coreflective subcategory for a judicious choice of duoidal category. We give several worked examples of this uniform framework, including the parameterised state monad, basic separation semantics for resources, and interesting cases of change of enrichment

Original language	English
Title of host publication	Proceedings of the 20th International Conference on Relational and Algebraic Methods in Computer Science (RAMiCS 2023)
Editors	Roland Glück, Luigi Santocanale, Michael Winter
Publisher	Springer
Pages	241-257
Number of pages	16
ISBN (Electronic)	9783031280832
ISBN (Print)	9783031280825
DOIs	https://doi.org/10.1007/978-3-031-28083-2_15
Publication status	Published - 8 Mar 2023
Event	The 20th International Conference on Relational and Algebraic Methods in Computer Science, 2023 - Augsburg, Germany Duration: 3 Apr 2023 → 6 Apr 2023 Conference number: 20 https://ramics20.lis-lab.fr/

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Number	1
Volume	13896
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	The 20th International Conference on Relational and Algebraic Methods in Computer Science, 2023
Abbreviated title	RAMiCS 2023
Country/Territory	Germany
City	Augsburg
Period	3/04/23 → 6/04/23
Internet address	https://ramics20.lis-lab.fr/

Keywords / Materials (for Non-textual outputs)

Freyd category
duoidal category
Kleisli category
Lawvere theory
monad

Access to Document

10.1007/978-3-031-28083-2_15Licence: All Rights Reserved

2301.05162v1Accepted author manuscript, 305 KBLicence: Creative Commons: Attribution (CC-BY)

https://link.springer.com/chapter/10.1007/978-3-031-28083-2_15#chapter-infoLicence: All Rights Reserved

Cite this

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title = "Duoidally enriched Freyd categories",

abstract = " Freyd categories provide a semantics for first-order effectful programming languages by capturing the two different orders of evaluation for products. We enrich Freyd categories in a duoidal category, which provides a new, third choice of parallel composition. Duoidal categories have two monoidal structures which account for the sequential and parallel compositions. The traditional setting is recovered as a full coreflective subcategory for a judicious choice of duoidal category. We give several worked examples of this uniform framework, including the parameterised state monad, basic separation semantics for resources, and interesting cases of change of enrichment ",

keywords = "Freyd category, duoidal category, Kleisli category, Lawvere theory, monad",

author = "Chris Heunen and Jesse Sigal",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.; The 20th International Conference on Relational and Algebraic Methods in Computer Science, 2023<br/>, RAMiCS 2023 ; Conference date: 03-04-2023 Through 06-04-2023",

year = "2023",

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doi = "10.1007/978-3-031-28083-2_15",

language = "English",

isbn = "9783031280825",

series = "Lecture Notes in Computer Science",

publisher = "Springer",

number = "1",

pages = "241--257",

editor = "Roland Gl{\"u}ck and Luigi Santocanale and Michael Winter",

booktitle = "Proceedings of the 20th International Conference on Relational and Algebraic Methods in Computer Science (RAMiCS 2023)",

url = "https://ramics20.lis-lab.fr/",

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Heunen, C & Sigal, J 2023, Duoidally enriched Freyd categories. in R Glück, L Santocanale & M Winter (eds), Proceedings of the 20th International Conference on Relational and Algebraic Methods in Computer Science (RAMiCS 2023). Lecture Notes in Computer Science, no. 1, vol. 13896, Springer, pp. 241-257, The 20th International Conference on Relational and Algebraic Methods in Computer Science, 2023
, Augsburg, Bavaria, Germany, 3/04/23. https://doi.org/10.1007/978-3-031-28083-2_15

Duoidally enriched Freyd categories. / Heunen, Chris ; Sigal, Jesse.
Proceedings of the 20th International Conference on Relational and Algebraic Methods in Computer Science (RAMiCS 2023). ed. / Roland Glück; Luigi Santocanale; Michael Winter. Springer, 2023. p. 241-257 (Lecture Notes in Computer Science; Vol. 13896, No. 1).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Duoidally enriched Freyd categories

AU - Heunen, Chris

AU - Sigal, Jesse

N1 - Conference code: 20

PY - 2023/3/8

Y1 - 2023/3/8

N2 - Freyd categories provide a semantics for first-order effectful programming languages by capturing the two different orders of evaluation for products. We enrich Freyd categories in a duoidal category, which provides a new, third choice of parallel composition. Duoidal categories have two monoidal structures which account for the sequential and parallel compositions. The traditional setting is recovered as a full coreflective subcategory for a judicious choice of duoidal category. We give several worked examples of this uniform framework, including the parameterised state monad, basic separation semantics for resources, and interesting cases of change of enrichment

AB - Freyd categories provide a semantics for first-order effectful programming languages by capturing the two different orders of evaluation for products. We enrich Freyd categories in a duoidal category, which provides a new, third choice of parallel composition. Duoidal categories have two monoidal structures which account for the sequential and parallel compositions. The traditional setting is recovered as a full coreflective subcategory for a judicious choice of duoidal category. We give several worked examples of this uniform framework, including the parameterised state monad, basic separation semantics for resources, and interesting cases of change of enrichment

KW - Freyd category

KW - duoidal category

KW - Kleisli category

KW - Lawvere theory

KW - monad

U2 - 10.1007/978-3-031-28083-2_15

DO - 10.1007/978-3-031-28083-2_15

M3 - Conference contribution

SN - 9783031280825

T3 - Lecture Notes in Computer Science

SP - 241

EP - 257

BT - Proceedings of the 20th International Conference on Relational and Algebraic Methods in Computer Science (RAMiCS 2023)

A2 - Glück, Roland

A2 - Santocanale, Luigi

A2 - Winter, Michael

PB - Springer

T2 - The 20th International Conference on Relational and Algebraic Methods in Computer Science, 2023<br/>

Y2 - 3 April 2023 through 6 April 2023

ER -

Duoidally enriched Freyd categories

Abstract / Description of output

Publication series

Conference

Keywords / Materials (for Non-textual outputs)

Access to Document

Fingerprint

Cite this