Container combinatorics: Monads and lax monoidal functors

Tarmo Uustalu

doi:10.1007/978-3-319-68953-1_8

Container combinatorics: Monads and lax monoidal functors

Tarmo Uustalu^*

^*Corresponding author for this work

Department of Computer Science

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

6 Citations (Scopus)

Abstract

Abbott et al.’s containers are a “syntax” for a wide class of set functors in terms of shapes and positions. Containers whose “denotation” carries a comonad structure can be characterized as directed containers, or containers where a shape and a position in it determine another shape, intuitively a subshape of this shape rooted by this position. In this paper, we develop similar explicit characterizations for container functors with a monad structure and container functors with a lax monoidal functor structure as well as some variations. We argue that this type of characterizations make a tool, e.g., for enumerating the monad structures or lax monoidal functors that some set functor admits. Such explorations are of interest, e.g., in the semantics of effectful functional programming languages.

Original language	English
Title of host publication	Topics in Theoretical Computer Science
Subtitle of host publication	2nd IFIP WG 1.8 International Conference, TTCS 2017, Tehran, Iran, September 12-14, 2017, Proceedings
Editors	Mohammad Reza Mousavi, Jirí Sgall
Publisher	Springer, Cham
Pages	91-105
ISBN (Electronic)	978-3-319-68953-1
ISBN (Print)	978-3-319-68952-4
DOIs	https://doi.org/10.1007/978-3-319-68953-1_8
Publication status	Published - 9 Dec 2017
Event	2nd IFIP WG 1.8 International Conference on Topics in Theoretical Computer Science - Tehran, Iran, Islamic Republic of Duration: 12 Sept 2017 → 14 Sept 2017

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	10608
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	2nd IFIP WG 1.8 International Conference on Topics in Theoretical Computer Science
Abbreviated title	TTCS 2017
Country/Territory	Iran, Islamic Republic of
City	Tehran
Period	12/09/17 → 14/09/17

Bibliographical note

Funding Information:
This work was supported by the Estonian Ministry of Education and Research institutional research grant IUT33-13.

Publisher Copyright:
© 2017 IFIP International Federation for Information Processing.

Access to Document

10.1007/978-3-319-68953-1_8

Cite this

Uustalu, T. (2017). Container combinatorics: Monads and lax monoidal functors. In M. R. Mousavi, & J. Sgall (Eds.), Topics in Theoretical Computer Science: 2nd IFIP WG 1.8 International Conference, TTCS 2017, Tehran, Iran, September 12-14, 2017, Proceedings (pp. 91-105). (Lecture Notes in Computer Science; Vol. 10608). Springer, Cham. https://doi.org/10.1007/978-3-319-68953-1_8

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Uustalu, T 2017, Container combinatorics: Monads and lax monoidal functors. in MR Mousavi & J Sgall (eds), Topics in Theoretical Computer Science: 2nd IFIP WG 1.8 International Conference, TTCS 2017, Tehran, Iran, September 12-14, 2017, Proceedings. Lecture Notes in Computer Science, vol. 10608, Springer, Cham, pp. 91-105, 2nd IFIP WG 1.8 International Conference on Topics in Theoretical Computer Science, Tehran, Iran, Islamic Republic of, 12/09/17. https://doi.org/10.1007/978-3-319-68953-1_8

Container combinatorics: Monads and lax monoidal functors. / Uustalu, Tarmo.
Topics in Theoretical Computer Science: 2nd IFIP WG 1.8 International Conference, TTCS 2017, Tehran, Iran, September 12-14, 2017, Proceedings. ed. / Mohammad Reza Mousavi; Jirí Sgall. Springer, Cham, 2017. p. 91-105 (Lecture Notes in Computer Science; Vol. 10608).

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

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Container combinatorics: Monads and lax monoidal functors

Abstract

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Bibliographical note

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