Most General Algebraic Specifications for an Abstract Datatype of Rational Numbers

Abstract

The notion of a most general algebraic specification of an arithmetical datatype of characteristic zero is introduced.Three examples of such specifications are given. A preference is formulated for a specification by means of infinitely many equations which can be presented via a finite number of so-called schematic equations phrased in terms of an infinite signature. On the basis of the latter specification three topics are discussed: (i) fracterm decomposition operators and the numerator paradox, (ii) foundational specifications of arithmetical datatypes, and (iii) poly-infix operations.