Abstract

This paper investigates a novel approach to a type system for modular systems of equations; i.e., equation systems constructed by composition of individual equation system fragments. The purpose of the type system is to ensure, to the extent possible, that the composed system is solvable. The central idea is to attribute a structural type to equation system fragments that reflects which variables occur in which equations. In many instances, this allows over- and underdetermined system fragments to be identified separately, without first having to assemble all fragments into a complete system of equations. The setting of the paper is equation-based, non-causal modelling, specifically Functional Hybrid Modelling (FHM). However, the central ideas are not tied to FHM, but should be applicable to equation-based modelling languages in general, like Modelica, as well as to applications featuring modular systems of equations outside the field of modelling and simulation.