The Interval Domain in Homotopy Type Theory

Niels van der Weide*, Dan Frumin

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

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Abstract

Even though the real numbers are the cornerstone of many fields in mathematics, it is challenging to formalize them in a constructive setting, and in particular, homotopy type theory. Several approaches have been established to define the real numbers, and the most prominent of them are based on Dedekind cuts and on Cauchy sequences. In this paper, we study a different approach towards defining the real numbers. Our approach is based on domain theory, and in particular, the interval domain, and we build forth on recent work on domain theory in univalent foundations. All the results in this paper have been formalized in Coq as part of the UniMath library.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsVenanzio Capretta, Robbert Krebbers, Freek Wiedijk
PublisherSpringer Science and Business Media Deutschland GmbH
Pages241-256
Number of pages16
ISBN (Electronic)978-3-031-61716-4
ISBN (Print)978-3-031-61715-7
DOIs
Publication statusPublished - 22-May-2024

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume14560 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

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