Most General Algebraic Specifications for an Abstract Datatype of Rational Numbers

Jan Bergstra, Informatics Institute, Faculty of Science, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, the Netherlands
2020 Scientific Annals of Computer Science  
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
more » ... d the numerator paradox, (ii) foundational specifications of arithmetical datatypes, and (iii) poly-infix operations.
doi:10.7561/sacs.2020.1.1 fatcat:g5zrpmavqncnposlhgbepwxqqm