Implementing level 4 liveness in declarative visual programming languages

An increasingly common characteristic in visual programming languages (VPLs) is level 4 liveness-the constant monitoring of the system state with continuous redisplay as events arrive and computations progress. However, level 4 liveness can be expensive. We present an implementation method that supports level 4 liveness in declarative VPLs, ensuring without "unreasonable" cost that all values on the screen are correctly updated as computations progress. The method is especially well suited for the growing class of declarative VPLs that display continuously time varying calculations and graphics, such as GUI specification VPLs, event based or reactive VPLs, scientific visualization VPLs, or graphical simulation VPLs.