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 error...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2001-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/280/pdf |
| _version_ | 1827323883858952192 |
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| author | Lawrence S. Moss |
| author_facet | Lawrence S. Moss |
| author_sort | Lawrence S. Moss |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-04-25T02:00:51Z |
| format | Article |
| id | doaj.art-a0e28dae458e4d51a95ef546dce2dfcc |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:00:51Z |
| publishDate | 2001-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-a0e28dae458e4d51a95ef546dce2dfcc2024-03-07T15:04:11ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502001-01-01Vol. 4 no. 210.46298/dmtcs.280280Simple Equational Specifications of Rational ArithmeticLawrence S. Moss0Department of mathematics [Bloomington]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.https://dmtcs.episciences.org/280/pdfequational specificationhidden function symbolsrational numbers[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Lawrence S. Moss Simple Equational Specifications of Rational Arithmetic Discrete Mathematics & Theoretical Computer Science equational specification hidden function symbols rational numbers [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | 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_short | Simple Equational Specifications of Rational Arithmetic |
| title_sort | simple equational specifications of rational arithmetic |
| topic | equational specification hidden function symbols rational numbers [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/280/pdf |
| work_keys_str_mv | AT lawrencesmoss simpleequationalspecificationsofrationalarithmetic |