Incomplete grammars

I’ve been thinking more about modularity in Invisible XML. Michael Sperberg-McQueen first drew my attention to the similarities between Invisible XML and RELAX NG: they are both expressions of a grammar that parses a sequence of input tokens, perhaps ambiguously.

The RELAX NG tutorial includes a nested grammar example that relates to tables. It didn’t take me long to construct a roughly analogous example in iXML:

table = row+ .
row   = (-'|', cell)+, -'|', nl .
cell  = -cell-content .
-nl   = -#a .

In the RELAX NG case, you could define cell-content as notAllowed, but iXML doesn’t have anything like “not allowed”, so I’ve left the rule out. That’s an incomplete grammar that won’t parse.

But suppose that you had a modularity framework that let you say: “use that tables grammar with this definition of cell-content​”:

cell-content = -" "*, ["0"-"9"]+, (".", ["0"-"9"]*)?, -" "* .

Now you’d have a grammar that would parse a table of numbers. Similarly, if you defined cell-content this way, you’d have a grammar that would parse a table of words:

cell-content = -" "*, [L]+, -" "* .

That seems like it could be interesting.