Realizing Continuity Using Stateful Computations

Liron Cohen, Vincent Rahli

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

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.

Original languageEnglish
Title of host publication31st EACSL Annual Conference on Computer Science Logic, CSL 2023
EditorsBartek Klin, Elaine Pimentel
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages15:1-15:18
Number of pages18
ISBN (Electronic)9783959772648
DOIs
StatePublished - 1 Feb 2023
Event31st EACSL Annual Conference on Computer Science Logic, CSL 2023 - Warsaw, Poland
Duration: 13 Feb 202316 Feb 2023

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume252
ISSN (Print)1868-8969

Conference

Conference31st EACSL Annual Conference on Computer Science Logic, CSL 2023
Country/TerritoryPoland
CityWarsaw
Period13/02/2316/02/23

Keywords

  • Agda
  • Constructive Type Theory
  • Continuity
  • Extensional Type Theory
  • Intuitionism
  • Realizability
  • Stateful computations
  • Theorem proving

ASJC Scopus subject areas

  • Software

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