Functional Hybrid Modelling

Modelling and simulation plays an increasingly important role in the design,analysis, and implementation of real-world systems. Examples includeelectronic circuits, VLSI layout, chemical processes, manufacturing plants,weather prediction, biological processes, mechanical devices, traffic control,network congestion, and so on. Modelling and simulation efforts are sopervasive that specialised software tools have been designed to support them.Although such tools greatly facilitate software development, there isconsiderable room for improvement. In particular, to cope with the everincreasing size and complexity of models, it is of key importance is that theypromote modularity and facilitate reuse.The so called non-causal modelling languages are one recent development withthat aim. These languages are declarative in that they allow the modeller tofocus more on what to model and less on how to express the model forsimulation purposes. The result is models that are much more modular andreusable than those developed using the earlier causal techniques.Modularity and reuse is, of course, central to all programming paradigms.Modern declarative languages, in particular functional ones, have been verysuccessful in that respect thanks to powerful abstraction facilities andsophisticated type systems. However, these developments have largely gone byunnoticed in the modelling community. Earlier work on Functional ReactiveProgramming (FRP) has demonstrated the benefits a modern functional languagecan offer in the context of causal modelling by promoting higher-orderprogramming techniques and giving key simulation abstractions first classstatus. In particular, it was shown how this enabled hybrid modelling ofsystems with highly dynamic structure.As these benefits are complementary to those offered by non-causal modellinglanguages, it is highly desirable to merge the two approaches. That is thegoal of this project. The resulting approach to non-causal modelling is calledFunctional Hybrid Modelling (FHM). FHM will yield a non-causal modellinglanguage that not only makes the benefits of modern declarative languages withsophisticated type systems available to the non-causal modelling community,but also advances the state-of-the-art of non-causal hybrid modelling bysupporting modelling of highly dynamic systems.The key objectives are:* Integrating non-causal modelling capabilities into a modern functional language by giving first class status to model fragments and providing suitable language mechanisms for their composition.* Adding hybrid modelling capabilities to this language through a mechanism to switch between structural configurations that are computed at the time of switching, as opposed to being statically enumerated as is required by current mainstream non-causal languages.* Designing a type system for this language that helps ensure the correctness of models by enforcing important domain-specific invariants, such as the number of variables and model equations being equal, and physical dimensions being used consistently.