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arXiv · 2307.04270

A Complete Finite Axiomatisation of the Equational Theory of Common Meadows

Jan A Bergstra·John V Tucker
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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 $\bot$ 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.

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Jan A Bergstra, John V Tucker. 2024-05-26. A Complete Finite Axiomatisation of the Equational Theory of Common Meadows. https://arxiv.org/abs/2307.04270

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