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This paper discusses an interpretation of hybrid systems as executable models. A specification of a hybrid system for this purpose can be viewed as a program in a domain-specific programming language. We describe the semantics of HyVisual, which is such a domain-specific programming language. The semantic properties of such a language affect our ability to understand, execute, and analyze a model. We discuss several semantic issues that come in defining such a programming language, such as the interpretation of discontinuities in continuous-time signals, and the interpretation of discrete-event signals in hybrid systems, and the consequences of numerical ODE solver techniques. We describe the solution in HyVisual by giving its operational semantics.