Remember the nice outline calculus I presented recently? I did a fatal mistake there: The outline normal form is not confluent, here is a counterexample:
Thus, order of rule application matters.
Which kind of destroys all usefulness… cause then, fully-parenthesized form is not a valid transformation.
I discovered this issue when I wanted to find a nicer way to write the x.0y items, e.g. the preface to a chapter:
(Chapter 1 ((Preface) Section 1 (...)) (Section 2 (...)) )
It is misleading that the Preface is in the same parenthesis as Section 1, therefore I applied a variant of FPF and wrote:
Chapter 1 ((Preface)) (Section 1) ((...)) (Section 2) ((...))
And then it’s easy to see.
It’s always sad to see a nice thing disappear (especially if you found it). I wonder how I could fix this? (Removing the (())-rule would be an option, but make everything much harder to deal with.)