@inproceedings{680781dfd03c4f369c7dcf8bace429b0,
title = "Realizing Continuity Using Stateful Computations",
abstract = "The principle of continuity is a seminal property that holds for a number of intuitionistic theories such as System T. Roughly speaking, it states that functions on real numbers only need approximations of these numbers to compute. Generally, continuity principles have been justified using semantical arguments, but it is known that the modulus of continuity of functions can be computed using effectful computations such as exceptions or reference cells. This paper presents a class of intuitionistic theories that features stateful computations, such as reference cells, and shows that these theories can be extended with continuity axioms. The modulus of continuity of the functionals on the Baire space is directly computed using the stateful computations enabled in the theory.",
keywords = "Agda, Constructive Type Theory, Continuity, Extensional Type Theory, Intuitionism, Realizability, Stateful computations, Theorem proving",
author = "Liron Cohen and Vincent Rahli",
note = "Publisher Copyright: {\textcopyright} Liron Cohen and Vincent Rahli; licensed under Creative Commons License CC-BY 4.0.; 31st EACSL Annual Conference on Computer Science Logic, CSL 2023 ; Conference date: 13-02-2023 Through 16-02-2023",
year = "2023",
month = feb,
day = "1",
doi = "10.4230/LIPIcs.CSL.2023.15",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Bartek Klin and Elaine Pimentel",
booktitle = "31st EACSL Annual Conference on Computer Science Logic, CSL 2023",
address = "Germany",
}