+> Trying to make a formal definition of this: (Note, I'm using the term sets rather than lists, but they're roughly equivalent)
+>
+> * Let the *matching set* for a pagespec be the set of existing pages that the pagespec matches.
+> * Let the *missing document matching set* be the set of pages that would match the spec if they didn't exist. These pages may or may not currently exist. Note that membership of this set depends upon how the `match_()` functions react to non-existant pages.
+> * Let the *indirect influence set* for a pagespec be the set of all pages, *p*, whose alteration might:
+> * cause the pagespec to include or exclude a page other than *p*, or
+> * cause the pagespec to exclude *p*, unless the alteration is the removal of *p* and *p* is in the missing document matching set.
+>
+> Justification: The 'base dependency mechanism' is to compare changed pages against each pagespec. If the page matches, then rebuild the spec. For this comparison, creation and removal
+> of pages are both considered changes. This base mechanism will catch:
+>
+> * The addition of any page to the matching set through its own modification/creation
+> * The removal of any page *that would still match while non-existant* from the matching set through its own removal. (Note: The base mechanism cannot remove a page from the matching set because of that page's own modification (not deletion). If the page should be removed matching set, then it obviously cannot match the spec after the change.)
+> * The modification (not deletion) of any page that still matches after the modification.
+>
+> The base mechanism may therefore not catch:
+>
+> * The addition or removal of any page from the matching set through the modification/addition/removal of any other page.
+> * The removal of any page from the matching set through its own modification/removal if it does not still match after the change.
+>
+> The indirect influence set then should handle anything that the base mechanism will not catch.
+>
+> --[[Will]]
+
+>> I appreciate the formalism!
+>>
+>> Only existing pages need to be in these sets, because if a page is added
+>> in the future, the existing dependency code will always test to see
+>> if it matches. So it will be in the maching set (or not) at that point.
+>>
+>>> Hrm, I agree with you in general, but I think I can come up with nasty counter-examples. What about a pagespec
+>>> of "!backlink(bogus)" where the page bogus doesn't exist? In this case, the page 'bogus' needs to be in the influence
+>>> set even though it doesn't exist.
+>>>
+>>>> I think you're right, this is a case that the current code is not
+>>>> handling. Actually, I made all the pagespecs return influences
+>>>> even if the influence was not present or did not match. But, it
+>>>> currently only records influences as dependencies when a pagespec
+>>>> successfully matches. Now I'm sure that is wrong, and I've removed
+>>>> that false optimisation. I've updated some of the below. --[[Joey]]
+>>>
+>>> Also, I would really like the formalism to include the whole dependency system, not just any additions to it. That will make
+>>> the whole thing much easier to reason about.
+>>
+>> The problem with your definition of direct influence set seems to be
+>> that it doesn't allow `link()` and `title()` to have as an indirect
+>> influence, the page that matches. But I'm quite sure we need those.
+>> --[[Joey]]
+
+>>> I see what you mean. Does the revised definition capture this effectively?
+>>> The problem with this revised definition is that it still doesn't match your examples below.
+>>> My revised definition will include pretty much all currently matching pages to be in the influence list
+>>> because deletion of any of them would cause a change in which pages are matched - the removal problem.
+>>> -- [[Will]]
+