aux files to cache compilation info

[Ramana Kumar]

In this message on users
http://lists.gnu.org/archive/html/lilypond-user/2012-08/msg00094.html
Mike mentioned the possibility of generating cache files to speed up
recompilation. He also said working out the details might take months
of discussion. I'd like to start that discussion in a relaxed way (we
have no deadlines after all), at least to generate an archive of
issues relevant to such a project. (Let me know if this has been
discussed before.)

People seem to agree that line breaking is the major bottleneck in
compilation. What would it take to cache just line breaking?

I suggest there are at least (and probably exactly) two things the
cache needs to contain:
1. enough information about the last score compiled to know where the
new (current) score differs
2. line breaking information for the cached score

Given that information, a possible use of the cache is: reuse line
breaking for any stretch of unchanged score where the line breaks
happen to be in sync (this always at least includes the stretch from
the beginning up to the first difference).

Thoughts on how to represent 1 and 2 above, and how to use them (to
find the stretches in sync)?