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Synthetic Fracterm Calculus
,
John Tucker
JUCS - Journal of Universal Computer Science, Volume: 30, Issue: 3, Pages: 289 - 307
Swansea University Author:
John Tucker
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DOI (Published version): 10.3897/jucs.107082
Abstract
Previously, in [Bergstra and Tucker 2023], we provided a systematic description of elementaryarithmetic concerning addition, multiplication, subtraction and division as it is practiced.Called the naive fracterm calculus, it captured a consensus on what ideas and options were widelyaccepted, rejected...
| Published in: | JUCS - Journal of Universal Computer Science |
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| ISSN: | 0948-695X 0948-6968 |
| Published: |
Pensoft Publishers
2024
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa65233 |
| Abstract: |
Previously, in [Bergstra and Tucker 2023], we provided a systematic description of elementaryarithmetic concerning addition, multiplication, subtraction and division as it is practiced.Called the naive fracterm calculus, it captured a consensus on what ideas and options were widelyaccepted, rejected or varied according to taste. We contrasted this state of the practical art witha plurality of its formal algebraic and logical axiomatisations, some of which were motivated bycomputer arithmetic. We identified a significant gap between the wide embrace of the naive fractermcalculus and the narrow precisely defined formalisations. In this paper, we introduce a newintermediate and informal axiomatisation of elementary arithmetic to bridge that gap; it is calledthe synthetic fracterm calculus. Compared with naive fracterm calculus, the synthetic fractermcalculus is more systematic, resolves several ambiguities and prepares for reasoning underpinnedby logic; indeed, it admits direct formalisations, which the naive fracterm calculus does not. Themethods of these papers may have wider application, wherever formalisations are needed to analyseand standardise practices. |
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| Keywords: |
fracterm calculus, partial meadow, common meadow, abstract data type |
| College: |
Faculty of Science and Engineering |
| Issue: |
3 |
| Start Page: |
289 |
| End Page: |
307 |