Meta-grammar for context-free grammars Formal grammars like regular expressions (REs) or context-free
grammars (CFGs) specify languages, i.e. sets of strings over an
alphabet. 

Grammars themselves can be seen as languages, e.g.
the set of REs over $\{0, 1\}$. In that sense we
can specify a grammars by means of a meta-grammar. For example the language of all REs over a fixed alphabet can be
specified as a context-free grammar (CFG), e.g. like so

$$
   R \quad::=\quad 0 \ |\ a \ |\ RR \ |\  R+R \ |\ (R) \ |\  R^*
$$

where $a$ ranges over the ambient alphabet. One advantage of thinking of grammars in terms of their meta-grammar is that we can parse REs and check them for syntactic correctness.

What kind of meta-grammar (context-free or otherwise) allows us to
specify the language of CFGs over a given alphabet? What about subsets
of CFGs like LL(k) or LR(k)? I'm sure this has been investigated before as there are many tools that take grammars as input, e.g. parser generators.
Backus–Naur Form's syntax can be represented with a BNF itself. Here is an example taken from this Wikipedia article:

&lt;syntax&gt;         ::= &lt;rule&gt; | &lt;rule&gt; &lt;syntax&gt;
&lt;rule&gt;           ::= &lt;opt-whitespace&gt; "&lt;" &lt;rule-name&gt; "&gt;"
                     &lt;opt-whitespace&gt; "::=" &lt;opt-whitespace&gt; 
                     &lt;expression&gt; &lt;line-end&gt;
&lt;opt-whitespace&gt; ::= " " &lt;opt-whitespace&gt; | ""
&lt;expression&gt;     ::= &lt;list&gt; |
                     &lt;list&gt; &lt;opt-whitespace&gt; "|" &lt;opt-whitespace&gt; &lt;expression&gt;
&lt;line-end&gt;       ::= &lt;opt-whitespace&gt; &lt;EOL&gt; | &lt;line-end&gt; &lt;line-end&gt;
&lt;list&gt;           ::= &lt;term&gt; | &lt;term&gt; &lt;opt-whitespace&gt; &lt;list&gt;
&lt;term&gt;           ::= &lt;literal&gt; | "&lt;" &lt;rule-name&gt; "&gt;"
&lt;literal&gt;        ::= '"' &lt;text&gt; '"' | "'" &lt;text&gt; "'"


"" denotes the empty string. The article provides some more details on undefined here rules for &lt;rule-name&gt;, etc.