A Graphical Multi-stage Calculus

While visual programming languages continue to gain popularity in domains ranging from scientific computing to real-time systems, the wealth of abstraction mechanisms, reasoning principles, and type systems developed over the last thirty years is currently avail- able mainly for textual languages. With the goal of understanding how results in the textual languages can be mapped to the graphical setting, we develop the visual calculus PreVIEW. While this calcu- lus visualizes computations in dataflow-style similar to languages like LabVIEW and Simulink, its formal model is based on Ariola and Blom's work on cyclic lambda calculi. We extend this model with staging constructs, establish a precise connection between tex- tual and graphical program representations, and show how a reduc- tion semantics for a multi-stage language can be lifted from the textual to the graphical setting.