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Theory of Computing Systems

, Volume 43, Issue 3–4, pp 410–424 | Cite as

Division Safe Calculation in Totalised Fields

  • J. A. Bergstra
  • J. V. Tucker
Open Access
Article
First Online:

Abstract

A 0-totalised field is a field in which division is a total operation with 0−1=0. Equational reasoning in such fields is greatly simplified but in deriving a term one still wishes to know whether or not the calculation has invoked 0−1. If it has not then we call the derivation division safe. We propose three methods of guaranteeing division safe calculations in 0-totalised fields.

Keywords

Rational number Meadow Zero totalised field Elementary algebraic specification 
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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Informatics InstituteUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.Department of Computer ScienceSwansea UniversitySwanseaUK

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