A Complete Finite Equational Axiomatisation of the Fracterm Calculus for Common Meadows

07/09/2023

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by   Jan A. Bergstra, et al.

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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 flag 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 =. The set of equations true in all common meadows is named the fracterm calculus of common meadows. We give a finite equational axiomatisation of the fracterm calculus of common meadows and prove that it is complete and that the fracterm calculus is decidable.