Additive cellular automata graded-monadically

Capobianco, Silvio; Uustalu, Tarmo

Additive cellular automata graded-monadically

Title:	Additive cellular automata graded-monadically
Author:	Capobianco, Silvio Uustalu, Tarmo orcid.org/0000-0002-1297-0579 2 authors Show fewer authors
Date:	2023-10-22
Language:	English
Scope:	article 13
University/Institute:	Reykjavik University Háskólinn í Reykjavík
School:	School of Technology (RU) Tæknisvið (HR)
Department:	Department of Computer Science (RU) Tölvunarfræðideild (HR)
ISBN:	979-8-4007-0812-1
Series:	ACM International Proceeding Series;
DOI:	10.1145/3610612.3610625
Subject:	models of computation; cellular automata; additive cellular automata; comonads; adjoint comonad-monad pairs; graded comonads; graded monads
URI:	https://hdl.handle.net/20.500.11815/4744
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Citation: S. Capobianco, T. Uustalu. Additive cellular automata graded-monadically. In 25th International Symposium on Principles and Practice of Declarative Programming (PPDP ’23), October 22-23, 2023, Lisbon, Portugal, art. 13, 9 pp. ACM, New York, 2023. doi:10.1145/3610612.3610625
Abstract: Cellular automata are an archetypical comonadic notion of computation in that computation happens in the coKleisli category of a comonad. In this paper, we show that they can also be viewed as graded comonadic—a perspective that turns out to be both more informative and also more basic. We also discuss additive cellular automata to show that they admit both a graded comonadic and a graded monadic view. That these two perspectives are simultaneously available in this special case arises from a graded version of an observation by Kleiner about adjoint comonad-monad pairs.