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A Complete Finite Axiomatisation of the Equational Theory of Common Meadows
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John Tucker
ACM Transactions on Computational Logic
Swansea University Author:
John Tucker
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DOI (Published version): 10.1145/3689211
Abstract
We analyse abstract data types that model numerical structures with a concept of error. Specifically, we focus on arithmetic data types that contain an error value whose main purpose is to alwaysreturn a value for division. To rings and fields, we add a division operatorx/y and study a class of alge...
| Published in: | ACM Transactions on Computational Logic |
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| ISSN: | 1529-3785 1557-945X |
| Published: |
Association for Computing Machinery (ACM)
2024
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa67357 |
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| Abstract: |
We analyse abstract data types that model numerical structures with a concept of error. Specifically, we focus on arithmetic data types that contain an error value whose main purpose is to alwaysreturn a value for division. To rings and fields, we add a division operatorx/y and study a class of algebras called common meadows whereinx/0 is the error value. The set of equations true in all common meadows is namedthe equational theory of common meadows. We give a finite equationalaxiomatisation of the equational theory of common meadows and provethat it is complete and that the equational theory is decidable. |
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| Keywords: |
arithmetical data type, division by zero, error value, common meadow, fracterm, fracterm calculus, equational theory |
| College: |
Faculty of Science and Engineering |