Joseph have you had any progress on this? Seems like very interesting idea and you should probably look into Graph functionality.

Have you seen this example

and did you know that physicist Richard P. Feynman (a big diagramatic person, by the way) in his youth used to use his own symbolics because he felt the official (common-sense) notation awkward and confusing ... later on the wish to be understood and to be able to communicate with others let him switch back to the usual notation (invented on its own by some mindful people, too) ...

Hi Vitaliy;

I have not yet implemented this on any programming language, since my main purpose was to design a notation. However, that would be a good project to implement it in code, and I hope to start a project like that in the future. I know some python and ruby, but I have never used Wolfram Programming Language for projects. I appreciate that suggestion, since I know it is a good language for this purpose.

Also, I would like to find flaws and ambiguity first, before implementing it, because I fear I could loose valuable time implementing something that may not work.

Another question. How do you suggest dealing with self-overlapping branches for large enough expressions? First thing that comes to mind is scaling down the branch size on deeper tree levels.

Good question. I suggest pipes (long lines and L's) to avoid overlapping (you can actually play with the length of the branches), but also variables to replace whole sections of the expression and express them somewhere else (or omit them, if they are not being discussed).

My biggest concerns are redundant variables in the same tree. I know traditional notation would allow them, but I'm not sure they work very well with this notation.

Thanks.