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Cancellation Meadows: A Generic Basis Theorem and Some Applications (2012)

Bergstra, J. A., Bethke, I., Ponse, A.

Oxford University Press

In: Computer Journal

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Publication Date: 2012-12-25

Description: Let Q 0 denote the rational numbers expanded to a ‘meadow’, that is, after taking its zero-totalized form (0 –1 =0) as the preferred interpretation. In this paper, we consider ‘cancellation meadows’, i.e. meadows without proper zero divisors, such as Q 0 and prove a generic completeness result. We apply this result to cancellation meadows expanded with differentiation operators, the sign function, and with floor, ceiling and a signed variant of the square root, respectively. We give an equational axiomatization of these operators and thus obtain a finite basis for various expanded cancellation meadows.

Print ISSN: 0010-4620

Electronic ISSN: 1460-2067

Topics: Computer Science

Published by Oxford University Press

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