Modeling with monads: extensible modeling semantics as syntactic sugar

We present an extensible implementation of Modelica-style modeling semantics. Modeling features are implemented using an intuitive encoding as an extensible state monad. Monadic computation naturally yields model composition and interpretation. This in turn allows for a clear separation between the modular aspects of a modeling language (e.g. classes and inheritance) and the symbolical and numerical treatment of models: While the former can be implemented by a compiler or interpreter, the latter can be moved into a core-library to be maintained by domain-experts. In a second step, we show how the elaboration aspects of the language can be removed by a correct and complete desugaring procedure. The residual language is a simple extension of a call-by-value λ-calculus. Thus it becomes possible to implement a compiler for a modeling language using existing standard techniques.