Well, I think most common transformations work reasonably well. One usually doesn't want to do things completely contrary to the AST, such as convert "while a<b" to "whilea = b".

And it's certainly possible to create any valid AST in the editor I describe. The set of valid trees is extended to those with "holes" in places, which one fills in when entering a program, and it's always possible to do this.

The challenge is one of finding an intuitive user interface, not whether it's possible at all. One issue is that infix notation is unnatural for entering trees (prefix is more natural).

> It can also be quite possible to invent structures which are valid but have no valid path to creating them.

I'm curious if you have an example of such a structure?

Pedantically: if, for every valid tree, there exists a bidirectional path to the empty root node, there's always at least one path between all given pairs of valid trees ... albeit one that no developer would ever take.

One idea would be for it to work like code completion. Once you start writing a structure the rest is auto-suggested so it does not break the tree.