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The Wheel of Rational Numbers as an Abstract Data Type / Jan A. Bergstra, John Tucker

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

Swansea University Author: John Tucker

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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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 ⊥ 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.
Keywords: Rational numbers; Arithmetic structures; Meadows; Wheels; Division by zero; Infinity; Error; Equational specification; Initial algebra semantics
College: College of Science
Start Page: 13
End Page: 30