Wirth BNF Grammars

Wirth uses his own meta language to define its own syntax (and serve as an example of its use):

grammar    = { production }.
production = identifier "=" expression ".".
expression = term { "|" term }.
term       = factor { factor }.
factor     = identifier | literal | "(" expression ")" |
             "[" expression "]" | "{" expression "}".
literal    = """" character { character } """".

Repetition is denoted by curly braces, i.e., { a } denotes: empty, a, aa, ... . Optionality is expressed by square brackets, i.e., [ a ] denotes a or empty. Parentheses merely serve for grouping, i.e., ( a | b ) c stands for: a c | b c.

Terminal symbols are either literals, i.e., are enclosed in quote marks or are identifiers which do not appear on the left hand side of the metasymbol =. If a quote mark appears a a literal itself, then it is written twice (as is common in many programming languages).

As a machine readable form, I have added the following additional properties to Wirth BNF grammars:

• Each production must start on a new line and may not have leading spaces.
• Each symbol, whether meta, terminal, or nonterminal, must be separated from all other symbols by spaces, except the terminating period.
• Productions may be freely continued on a new line; for readability these lines are often indented.
• Grammars may contain comments, which are lines which begin with a #, followed by a space. The remainder of the line is ignored.
• Grammars may contain blank lines to improve readability.

References

Niklaus Wirth, What can we do about the unnecessary diversity of notation for syntactic descriptions, CACM, 20 (November 1977), pp. 822-823.