This Small Business Innovation Research Phase I project will explore new programming language concepts aimed at software development of complex hybrid systems: systems containing both discrete (digital) and continuous (analog) components. Many common applications are in fact hybrid systems - for example, interactive graphics and animation, vision and robotics, and manufacturing control systems - and they are often tedious to program. This approach is based on a continuous reactive core language that permits the expression of pure, continuous behaviors, coupled with a notion of discrete reactivity with both internal and external stimuli. The potential pay-off is high in terms of cost savings in software development and maintenance. In addition, this approach will enhance robustness, safety, and security, since it facilitates the application of formal methods to verify critical system properties. Potential commercial applications of this technology include multimedia desktop applications that are expanding. With the recent surge in hardware development to support high-quality 3D graphics and related technologies, the need for high-level programming tools will only increase. A second market that we plan to target is scientific programming, in particular prototyping applications for which commercial systems such as Mathematica play an important role.