A Complete Finite Axiomatisation of the Equational Theory of Common Meadows-Reference-Cited by-同舟云学术

A Complete Finite Axiomatisation of the Equational Theory of Common Meadows

Published:2024-08-17 Issue: Volume: Page:
ISSN:1529-3785
Container-title:ACM Transactions on Computational Logic
language:en
Short-container-title:ACM Trans. Comput. Logic

Author:

Bergstra Jan A¹^ORCID,Tucker John V²^ORCID

Affiliation:

1. Informatics Institute, University of Amsterdam, Netherlands

2. Department of Computer Science, Swansea University, United Kingdom

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

\(\bot\)

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.

Publisher

Association for Computing Machinery (ACM)

Link

https://dl.acm.org/doi/pdf/10.1145/3689211

Reference63 articles.

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3. Term Rewriting and All That

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