Preserving model structure and constraints in scientific computing

In this paper, we look at how model structure and constraints can be incorporated into scientific computing using functional programming and, implicitly, category theory, in a way that constraints are automatically satisfied. Category theory is the study of different types of objects (e.g., sets, groups, vector spaces) and mappings between them (e.g., functions, homomorphisms, matrices) and is used in mathematics to model the underlying structure associated with systems we wish to describe and how this underlying structure is preserved under transformations. In this paper, we look at the structure associated with the representation of, and calculations using, quantitative data. In particular, we describe how measurement data can be represented in terms of the product C × D of two groups: the first, C, the counting algebra, and the second, D, the dimension algebra. Different but equivalent unit systems are related through group isomorphisms. The structure associated with this representation can be embedded in software using functional programming.