Simple Equational Specifications of Rational Arithmetic

Simple Equational Specifications of Rational Arithmetic

We exhibit an initial specification of the rational numbers equipped with addition, subtraction, multiplication, greatest integer function, and absolute value. Our specification uses only the sort of rational numbers. It uses one hidden function; that function is unary. But it does not use an e...

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Main Author: Lawrence S. Moss
Format: Article
Language:English
Published: Discrete Mathematics & Theoretical Computer Science 2001-12-01
Series:Discrete Mathematics & Theoretical Computer Science
Online Access:http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/147
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spelling doaj-1eec6150683a49a7a913b0e1c8e8f9aa2020-11-24T20:53:52ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1462-72641365-80502001-12-0142Simple Equational Specifications of Rational ArithmeticLawrence S. MossWe exhibit an initial specification of the rational numbers equipped with addition, subtraction, multiplication, greatest integer function, and absolute value. Our specification uses only the sort of rational numbers. It uses one hidden function; that function is unary. But it does not use an error constant, or extra (hidden) sorts, or conditional equations. All of our work is elementary and self-contained. http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/147
collection DOAJ
language English
format Article
sources DOAJ
author Lawrence S. Moss
spellingShingle Lawrence S. Moss
Simple Equational Specifications of Rational Arithmetic
Discrete Mathematics & Theoretical Computer Science
author_facet Lawrence S. Moss
author_sort Lawrence S. Moss
title Simple Equational Specifications of Rational Arithmetic
title_short Simple Equational Specifications of Rational Arithmetic
title_full Simple Equational Specifications of Rational Arithmetic
title_fullStr Simple Equational Specifications of Rational Arithmetic
title_full_unstemmed Simple Equational Specifications of Rational Arithmetic
title_sort simple equational specifications of rational arithmetic
publisher Discrete Mathematics & Theoretical Computer Science
series Discrete Mathematics & Theoretical Computer Science
issn 1462-7264
1365-8050
publishDate 2001-12-01
description We exhibit an initial specification of the rational numbers equipped with addition, subtraction, multiplication, greatest integer function, and absolute value. Our specification uses only the sort of rational numbers. It uses one hidden function; that function is unary. But it does not use an error constant, or extra (hidden) sorts, or conditional equations. All of our work is elementary and self-contained.
url http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/147
work_keys_str_mv AT lawrencesmoss simpleequationalspecificationsofrationalarithmetic
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