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I've made "proof graphs" with GraphViz, but honestly it was something of a challenge to make them look how I wanted them to. Compared to the time I spent drawing the graph on paper, (ie, collecting the statements and theorems), making the GraphViz version look okay took a long time.

http://www.naftaliharris.com/blog/mc-graph/

http://www.naftaliharris.com/blog/mg-graph/

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Those graphs are good examples of what I want to be able to make. You bring up a critically important point, though: I must be able to write graphs very quickly, easily, and painlessly, like I use vim to write text or Trello for to-do lists. Most tree-editing interfaces are painfully inefficient and slow to use (and are far too reliant on the mouse).

Speaking as someone who has used graphvis before, those examples are one possible mode of output. The input for the graphvis programs are plain text files. See:

https://en.wikipedia.org/wiki/DOT_%28graph_description_langu...

Touch screens might help.

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