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So it's basically as useless for general processing as Markdown, because you won't have a grammar from which you can generate parser, hence all the parsers will be handcoded with various quirks differing from one to another and none of which will produce a parse tree.

I'm baffled. Without a formal grammar CommonMark is useless. Who implements a parser without a formal grammar?

If the syntax has so many issues that you can't specify a formal grammar, there's a problem with the spec.

If it's hard to write a BNF, it's also hard to write a parser.