I'll have to defer to you on this one - I've only written a parser combinator type parser once before, and that was before I learned what it was. I did end up using something nearer to filters (i.e. acts on the returned value instead of having a separate 'actions field).
Edit: Perhaps part of the optimization of treeparse could be to eliminate the 'actions field. None of your samples used 'sem, and I might prefer 'filt for such enclosing stuff as ''bold'' and '''italics'''. The [[link]]s might be more difficult (because of the necessity of adding alphadigs after the closing bracket in [[link]]s to the actual link text but not the link target), but I think it's doable.
I've thought several times of removing sem in favor of filt. As features, they are very similar but filt is usually cleaner. If I don't see a compelling use case for actions soon I may indeed remove them. This would simplify the interface considerably.
Just between us, filt is actually an analogue to Haskell's monadic lift operator. They're even anagrams! (this happened by accident.)
Okay, I've since ported the Arki wikiformat parser to use filt instead of sem. Removing 'actions would reduce slightly the memory consumption of treeparse.