Flow Lambda Calculus for Declarative Physical Connection Semantics

One of the most fundamental language constructs of equation-based object-oriented languages is the possibility to state acausal connections, where both potential variables and flow variables exist. Several of the state-of-the art languages in this category are informally specified using natural language. This can make the languages hard to interpret, reason about, and disable the possibility to guarantee the absence of certain errors. In this work, we construct a formal operational small-step semantics based on the lambda-calculus. The calculus is then extended with more convenient modeling capabilities. Examples are given that demonstrate the expressiveness of the language, and some tests are made to verify the correctness of the semantics.