Formalizing Causal Block Diagrams for Modeling a Class of Hybrid Dynamic Systems

This paper attempts to formalize the semantics of causal block diagrams, a language that is extensively used in the design of technical systems. The formalization is based on lambda calculus, and implemented in the declarative functional language Haskell. Specifically, the combination of discrete-time and continuous-time computations, hybrid dynamic systems, is concentrated on. It shows how in many cases this combination causes multi-rate computations and so transition semantics between the two types of computations are strictly necessary. A loose interpretation is shown to result in an implementation that is amenable to error.