Elementary algebraic specifications of the rational function field

Authors:
J. A. Bergstra
Affiliations:
Programming Research Group, University of Amsterdam, Amsterdam, Netherlands
Venue:
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Year:
2006

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Abstract

The elementary algebraic specifications form a small subset of the range of techniques available for algebraic specifications and are based on equational specifications with hidden functions and sorts and initial algebra semantics. General methods exist to show that all semicomputable and computable algebras can be characterised up to isomorphism by such specifications. Here we consider these specification methods for specific computable rational number arithmetics. In particular, we give an elementary equational specification of the 0-totalised rational function field ℚ0(X) with its degree operator as an auxiliary function.