Elementary algebraic specifications of the rational complex numbers

Jan A. Bergstra

John V. Tucker

pp. 459-475

in: Kokichi Futatsugi, Jean-Pierre Jouannaud, José Meseguer (eds), Algebra, meaning, and computation, Berlin, Springer, 2006

Abstract

From the range of techniques available for algebraic specifications we select a core set of features which we define to be the elementary algebraic specifications. These include equational specifications with hidden functions and sorts and initial algebra semantics. We give an elementary equational specification of the field operations and conjugation operator on the rational complex numbers ℚ(i) and discuss some open problems.