Engineering safe and secure cyber-physical systems requires system engineers to develop and maintain a number of model views, both dynamic and static, which can be seen as algebras. We posit that verifying the composition of requirement, behavioral, and architectural models using category theory gives rise to a strictly compositional interpretation of cyber-physical systems theory, which can assist in the modeling and analysis of safety-critical cyber-physical systems.
APPLIED COMPOSITIONAL THINKINGLee [2], among others, recognized early in the development of the field of cyber-physical systems that there is a need for developing competing methods to hybrid systems and process algebras. While this is true, an important observation is that both these formalisms form algebras. In fact, the design of cyber-physical systems involves the study of different algebras (Figure 1).There is significant research in developing these individual algebras and implementing composition within a particular algebra. However, there is still an open problem about how to relate those paradigms that in practice represent individual models and to examine the behavior of the system as a whole must be composed too. Compositional cyber-physical systems theory [3], [4] uses category theory to transform data from one algebra to another and to ultimately relate them formally, such that we can compose across domains. This provides one solution to the open problem of composition between formal methods and their corresponding model views in cyberphysical system design [5], [6].Recently all these three areas of control [10], contracts [4], and co-design [11, chapter 4] have been described, generalized, and unified with fun-