Technical Report Number
Traditional computation models such as Turing machines, lambda-calculus, Markov's normal algorithms, are not suitable models for visual programming languages because they are all based on one-dimensional text strings and visual programming uses two-dimensional graphic diagrams. We propose a two-dimensional computation model, called Boxgraph, that requires no text. The syntax of the model consists of nested boxes connected by arrows, and the semantics consists of dataflow and the concept of consistency. The expressive power of the model is demonstrated by constructing representations of a binary full adder, the Fibonacci function, and the GCD function. The model, with a small extension to make it a practical visual programming language, has been implemented using the Overon operating system running on a SPARCstation equipped with a pen-tablet and udner the PenPoint operating system running on an EO-440 pen computer.
Kimura, Takayuki Dan and Brown, Timothy B., "BoxGraph: A Two-Dimensional Visual Computation Model" Report Number: WUCS-94-5 (1994). All Computer Science and Engineering Research.