This is the first paper in this new research area and we focus here on algebraic properties. Our specification of these properties in terms of concepts provides a fine-grained distinction between different basic properties and establishes a clear border between mathematical and implementation requirements.
The application of these concepts is illustrated on the generic computation of the power function. Other important applications of algebraic concepts shown in this paper are the constraints on generic reductions in order to verify? the applicability of high-performance source code transformations and the type-dependent and operation-aware handling of rounding errors. In addition, theory on the inclusion of model sets with respect to arity-changing refinements is introduced.