Inversion, Iteration, and the Art of Dual Wielding

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

Standard

Inversion, Iteration, and the Art of Dual Wielding. / Kaarsgaard, Robin.

Reversible Computation - 11th International Conference, RC 2019, Proceedings. ed. / Mathias Soeken; Michael Kirkedal Thomsen. Springer, 2019. p. 34-50 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 11497 LNCS).

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

Harvard

Kaarsgaard, R 2019, Inversion, Iteration, and the Art of Dual Wielding. in M Soeken & MK Thomsen (eds), Reversible Computation - 11th International Conference, RC 2019, Proceedings. Springer, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11497 LNCS, pp. 34-50, 11th International Conference on Reversible Computation, RC 2019, Lausanne, Switzerland, 24/06/2019. https://doi.org/10.1007/978-3-030-21500-2_3

APA

Kaarsgaard, R. (2019). Inversion, Iteration, and the Art of Dual Wielding. In M. Soeken, & M. K. Thomsen (Eds.), Reversible Computation - 11th International Conference, RC 2019, Proceedings (pp. 34-50). Springer. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) Vol. 11497 LNCS https://doi.org/10.1007/978-3-030-21500-2_3

Vancouver

Kaarsgaard R. Inversion, Iteration, and the Art of Dual Wielding. In Soeken M, Thomsen MK, editors, Reversible Computation - 11th International Conference, RC 2019, Proceedings. Springer. 2019. p. 34-50. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 11497 LNCS). https://doi.org/10.1007/978-3-030-21500-2_3

Author

Kaarsgaard, Robin. / Inversion, Iteration, and the Art of Dual Wielding. Reversible Computation - 11th International Conference, RC 2019, Proceedings. editor / Mathias Soeken ; Michael Kirkedal Thomsen. Springer, 2019. pp. 34-50 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 11497 LNCS).

Bibtex

@inproceedings{2a96dfa66588475dbe5a08f299a96218,
title = "Inversion, Iteration, and the Art of Dual Wielding",
abstract = "The humble (Formula presented) (“dagger”) is used to denote two different operations in category theory: Taking the adjoint of a morphism (in dagger categories) and finding the least fixed point of a functional (in categories enriched in domains). While these two operations are usually considered separately from one another, the emergence of reversible notions of computation shows the need to consider how the two ought to interact. In the present paper, we wield both of these daggers at once and consider dagger categories enriched in domains. We develop a notion of a monotone dagger structure as a dagger structure that is well behaved with respect to the enrichment, and show that such a structure leads to pleasant inversion properties of the fixed points that arise as a result. Notably, such a structure guarantees the existence of fixed point adjoints, which we show are intimately related to the conjugates arising from a canonical involutive monoidal structure in the enrichment. Finally, we relate the results to applications in the design and semantics of reversible programming languages.",
keywords = "Dagger categories, Domain theory, Enriched categories, Iteration categories, Reversible computing",
author = "Robin Kaarsgaard",
year = "2019",
doi = "10.1007/978-3-030-21500-2_3",
language = "English",
isbn = "9783030214999",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer",
pages = "34--50",
editor = "Mathias Soeken and Thomsen, {Michael Kirkedal}",
booktitle = "Reversible Computation - 11th International Conference, RC 2019, Proceedings",
address = "Switzerland",
note = "11th International Conference on Reversible Computation, RC 2019 ; Conference date: 24-06-2019 Through 25-06-2019",

}

RIS

TY - GEN

T1 - Inversion, Iteration, and the Art of Dual Wielding

AU - Kaarsgaard, Robin

PY - 2019

Y1 - 2019

N2 - The humble (Formula presented) (“dagger”) is used to denote two different operations in category theory: Taking the adjoint of a morphism (in dagger categories) and finding the least fixed point of a functional (in categories enriched in domains). While these two operations are usually considered separately from one another, the emergence of reversible notions of computation shows the need to consider how the two ought to interact. In the present paper, we wield both of these daggers at once and consider dagger categories enriched in domains. We develop a notion of a monotone dagger structure as a dagger structure that is well behaved with respect to the enrichment, and show that such a structure leads to pleasant inversion properties of the fixed points that arise as a result. Notably, such a structure guarantees the existence of fixed point adjoints, which we show are intimately related to the conjugates arising from a canonical involutive monoidal structure in the enrichment. Finally, we relate the results to applications in the design and semantics of reversible programming languages.

AB - The humble (Formula presented) (“dagger”) is used to denote two different operations in category theory: Taking the adjoint of a morphism (in dagger categories) and finding the least fixed point of a functional (in categories enriched in domains). While these two operations are usually considered separately from one another, the emergence of reversible notions of computation shows the need to consider how the two ought to interact. In the present paper, we wield both of these daggers at once and consider dagger categories enriched in domains. We develop a notion of a monotone dagger structure as a dagger structure that is well behaved with respect to the enrichment, and show that such a structure leads to pleasant inversion properties of the fixed points that arise as a result. Notably, such a structure guarantees the existence of fixed point adjoints, which we show are intimately related to the conjugates arising from a canonical involutive monoidal structure in the enrichment. Finally, we relate the results to applications in the design and semantics of reversible programming languages.

KW - Dagger categories

KW - Domain theory

KW - Enriched categories

KW - Iteration categories

KW - Reversible computing

U2 - 10.1007/978-3-030-21500-2_3

DO - 10.1007/978-3-030-21500-2_3

M3 - Article in proceedings

AN - SCOPUS:85068232293

SN - 9783030214999

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 34

EP - 50

BT - Reversible Computation - 11th International Conference, RC 2019, Proceedings

A2 - Soeken, Mathias

A2 - Thomsen, Michael Kirkedal

PB - Springer

T2 - 11th International Conference on Reversible Computation, RC 2019

Y2 - 24 June 2019 through 25 June 2019

ER -

ID: 227331432