Conference Paper/Proceeding/Abstract 1306 views 217 downloads
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
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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 ⊥...
| Published in: | Recent Trends in Algebraic Development Techniques |
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| ISBN: | 9783030737849 9783030737856 |
| ISSN: | 0302-9743 1611-3349 |
| Published: |
Cham
Springer International Publishing
2021
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| Online Access: |
Check full text
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| 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. |
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| Keywords: |
Rational numbers; Arithmetic structures; Meadows; Wheels; Division by zero; Infinity; Error; Equational specification; Initial algebra semantics |
| College: |
Faculty of Science and Engineering |
| Start Page: |
13 |
| End Page: |
30 |