First-class models : on a noncausal language for higher-order and structurally dynamic modelling and simulation

The field of physical modelling and simulation plays a vital role in advancing numerous scientific and engineering disciplines. To cope with the increasing size and complexity of physical models, a number of modelling and simulation languages have been developed. These languages can be divided into two broad categories: causal and noncausal. Causal languages express a system model in terms of directed equations. In contrast, a noncausal model is formulated in terms of undirected equations. The fact that the causality can be left implicit makes noncausal languages more declarative and noncausal models more reusable. These are considered to be crucial advantages in many physical domains. Current, mainstream noncausal languages do not treat equational models as firstclass values; that is, a model cannot be parametrised on other models or generated at simulation runtime. This results in very limited higher-order and structurally dynamic modelling capabilities, and limits the expressiveness and applicability of noncausal languages. This thesis is about a novel approach to the design and implementation of noncausal languages with first-class models supporting higher-order and structurally dynamic modelling. In particular, the thesis presents a language that enables: (1) higher-order modelling capabilities by embedding noncausal models as first-class entities into a functional programming language and (2) efficient simulation of noncausal models that are generated at simulation runtime by runtime symbolic processing and just-in-time compilation. These language design and implementation approaches can be applied to other noncausal languages. This thesis provides a self-contained reference for such an undertaking by defining the language semantics formally and providing an in-depth description of the implementation. The language provides noncausal modelling and simulation capabilities that go beyond the state of the art, as backed up by a range of examples presented in the thesis, and represents a significant progress in the field of physical modelling and simulation.