  Following the introduction of BNF notation by Backus for the Algol 60 report
and subsequent notational variants, a metalanguage involving formal "grammars"
has developed for discussing structured objects in Computer Science and
Mathematical Logic. We refer to this offspring of BNF as Math-BNF or MBNF, to
the original BNF and its notational variants just as BNF, and to aspects common
to both as BNF-style. What all BNF-style notations share is the use of
production rules roughly of this form: $$\bullet \mathrel{::=} \circ_1 \mid
\cdots \mid \circ_n $$ Normally, such a rule says "every instance of $\circ_i$
for $i \in \{1, \ldots, n\}$ is also an in stance of $\bullet$". MBNF is
distinct from BNF in the entities and operations it allows. Instead of strings,
MBNF builds arrangements of symbols that we call math-text. Sometimes "syntax"
is defined by interleaving MBNF production rules and other mathematical
definitions that can contain chunks of math-text. There is no clear definition
of MBNF. Readers do not have a document which tells them how MBNF is to be read
and must learn MBNF through a process of cultural initiation. To the extent
that MBNF is defined, it is largely through examples scattered throughout the
literature and which require readers to guess the mathematical structures
underpinning them. This paper gives MBNF examples illustrating some of the
differences between MBNF and BNF. We propose a definition of syntactic math
text (SMT) which handles many (but far from all) uses of math-text and MBNF in
the wild. We aim to balance the goal of being accessible and not requiring too
much prerequisite knowledge with the conflicting goal of providing a rich
mathematical structure that already supports many uses and has possibilities to
be extended to support more challenging cases.
