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>Is the built-in Lua parser recursive descent?

Yes, except that expressions are parsed with priorities too.

>My port can parse moderately-sized programs with no trouble; the problem
>seems to be that when an error is detected like this, a lot of nested
>function calls are made, several of which have fairly large stack frames.

You might try to reduce the number of locals and things like that in llimits.h.

>I suppose that for the execution of Lua programs, 4.1's stacklessness will
>help me, but will the parser change?

I think it's likely that the parser structure will not change as a whole,,
but perhaps something can be done about the large stack frames.