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Conference Paper/Proceeding/Abstract 934 views 155 downloads

The Wheel of Rational Numbers as an Abstract Data Type

Jan A. Bergstra, John Tucker Orcid Logo

Recent Trends in Algebraic Development Techniques, Volume: Springer LNCS 12669, Pages: 13 - 30

Swansea University Author: John Tucker Orcid Logo

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DOI (Published version): 10.1007/978-3-030-73785-6_2

Abstract

In an arithmetical structure one can make division a total function by defining 1/0 to be an element of the structure, or by adding a new element such as infinity ∞ or error element ⊥. A wheel is an algebra in which division is totalised by setting 1/0 = ∞ but which also contains an error element ⊥...

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Published in: Recent Trends in Algebraic Development Techniques
ISBN: 9783030737849 9783030737856
ISSN: 0302-9743 1611-3349
Published: Cham Springer International Publishing 2021
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa56722
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first_indexed 2021-04-22T22:00:59Z
last_indexed 2021-09-17T03:19:27Z
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spelling 2021-09-16T10:56:51.3692355 v2 56722 2021-04-22 The Wheel of Rational Numbers as an Abstract Data Type 431b3060563ed44cc68c7056ece2f85e 0000-0003-4689-8760 John Tucker John Tucker true false 2021-04-22 SCS In an arithmetical structure one can make division a total function by defining 1/0 to be an element of the structure, or by adding a new element such as infinity ∞ or error element ⊥. A wheel is an algebra in which division is totalised by setting 1/0 = ∞ but which also contains an error element ⊥ to help control its use. We construct the wheel of rational numbers as an abstract data type Qw and give it an equational specification without auxiliary operators under initial algebra semantics. Conference Paper/Proceeding/Abstract Recent Trends in Algebraic Development Techniques Springer LNCS 12669 13 30 Springer International Publishing Cham 9783030737849 9783030737856 0302-9743 1611-3349 Rational numbers; Arithmetic structures; Meadows; Wheels; Division by zero; Infinity; Error; Equational specification; Initial algebra semantics 11 4 2021 2021-04-11 10.1007/978-3-030-73785-6_2 COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University 2021-09-16T10:56:51.3692355 2021-04-22T22:15:36.7481060 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Jan A. Bergstra 1 John Tucker 0000-0003-4689-8760 2 56722__19740__7a3959b236894769b4b934750c20b417.pdf Bergstra-Tucker The Wheel of Rational Numbers as an ADT.pdf 2021-04-22T22:58:56.1496807 Output 284559 application/pdf Version of Record true false
title The Wheel of Rational Numbers as an Abstract Data Type
spellingShingle The Wheel of Rational Numbers as an Abstract Data Type
John Tucker
title_short The Wheel of Rational Numbers as an Abstract Data Type
title_full The Wheel of Rational Numbers as an Abstract Data Type
title_fullStr The Wheel of Rational Numbers as an Abstract Data Type
title_full_unstemmed The Wheel of Rational Numbers as an Abstract Data Type
title_sort The Wheel of Rational Numbers as an Abstract Data Type
author_id_str_mv 431b3060563ed44cc68c7056ece2f85e
author_id_fullname_str_mv 431b3060563ed44cc68c7056ece2f85e_***_John Tucker
author John Tucker
author2 Jan A. Bergstra
John Tucker
format Conference Paper/Proceeding/Abstract
container_title Recent Trends in Algebraic Development Techniques
container_volume Springer LNCS 12669
container_start_page 13
publishDate 2021
institution Swansea University
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issn 0302-9743
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doi_str_mv 10.1007/978-3-030-73785-6_2
publisher Springer International Publishing
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description In an arithmetical structure one can make division a total function by defining 1/0 to be an element of the structure, or by adding a new element such as infinity ∞ or error element ⊥. A wheel is an algebra in which division is totalised by setting 1/0 = ∞ but which also contains an error element ⊥ to help control its use. We construct the wheel of rational numbers as an abstract data type Qw and give it an equational specification without auxiliary operators under initial algebra semantics.
published_date 2021-04-11T04:11:53Z
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