BNF

• BNF (Backus-Naur Form)
• A formal mathematical way to describe the syntax of a language

Syntax

Production rules

• syntactic_category ::= definition   (production rule)
• syntactic_category := definition   (alternate syntax for production rules)

Terminals

• "word"  : Literal words (terminals) (i.e. "if")

Symbols

• word  : Syntactic categories (nonterminals / symbols) (i.e. if_statement) (not in double quotes)

Number of occurrences

• [expr]  : Optional
• {expr}  : Zero or more times

• expr?  : Optional
• expr*  : Zero or more times
• expr+  : One or more times

Logical operators

• expr | expr  : Alternatives
• (expr)  : One or more items logically treated as a single item

Misc

• @  : Nothing (a placeholder that can be removed outright)
• double_quote   : Used to represent a double-quote character

Examples

if_statement ::=
    "if" condition "then"
         sequence_of_statements
    {"elsif" condition "then"
         sequence_of_statements}
    ["else" 
         sequence_of_statements]
    "end if;"

sequence_of_statements ::= statement { statement }

statement ::= { label } ( simple_statement | compound_statement )

compound_statement ::=
    if_statement
    | case_statement
    | loop_statement


S  := '-' FN | FN
FN := DL FP
FP := @ | '.' DL
DL := D DR
DR := D DR | @
D  := '0' | '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9'

Sources

• http://www.dwheeler.com/lovelace/bnf.htm
• http://www.garshol.priv.no/download/text/bnf.html