A Complete Finite Axiomatisation of the Equational Theory of Common Meadows
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909210619412480 |
|---|---|
| author | Bergstra, Jan A Tucker, John V |
| author_facet | Bergstra, Jan A Tucker, John V |
| contents | 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 $\bot$ whose main purpose is to always return a value for division. To rings and fields, we add a division operator $x/y$ and study a class of algebras called common meadows wherein $x/0 = \bot$. The set of equations true in all common meadows is named the equational theory of common meadows. We give a finite equational axiomatisation of the equational theory of common meadows and prove that it is complete and that the equational theory is decidable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_04270 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Complete Finite Axiomatisation of the Equational Theory of Common Meadows Bergstra, Jan A Tucker, John V Logic in Computer Science 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 $\bot$ whose main purpose is to always return a value for division. To rings and fields, we add a division operator $x/y$ and study a class of algebras called common meadows wherein $x/0 = \bot$. The set of equations true in all common meadows is named the equational theory of common meadows. We give a finite equational axiomatisation of the equational theory of common meadows and prove that it is complete and that the equational theory is decidable. |
| title | A Complete Finite Axiomatisation of the Equational Theory of Common Meadows |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2307.04270 |