On Formal Semantics and Analysis of Typed Modeling Languages: An Analysis of Ascend

The use of strong typing, exemplified in the Ascend modeling language, is a recent phenomenon in executable modeling languages for mathematical modeling. It is also one that has significant potential for improving the functionality of computer-based modeling environments. Besides being a strongly typed language, Ascend is unique in providing operators that allow dynamic type inference, a feature that has been shown to be useful in assisting model evolution and reuse. We develop formal semantics for the type system in Ascend—focusing on these operators—and analyze its mathematical and computational properties. We show that despite the strong interactions between various statements involving the operators, the language does possess certain desirable mathematical and computational properties. Further, our analysis identifies general issues in the design and implementation of type systems in mathematical modeling languages. The methods used in the paper are applicable beyond Ascend to a class of typed modeling languages that may be developed in the future.