This grammar notation was introduced in 1960 by J. Backus and P. Naur. It is therefore called Backus Naur Form (BNF) (Naur, 1960).
For each EBNF construct there exists a translation rule which yields to a program fragment.
BNF grammars are pretty easy to read (Just replace the ::= sign with is or matches)
Each lexer rule is either matched or not, so every BNF expression is a boolean expression.
Let:
Definition of the structure of these equations in
syntax = production syntax | ∅.
production = identifier "=" expression "." .
expression = term | expression "|" term.
term = factor | term factor.
factor = identifier | string.
identifier = letter | identifier letter | identifier digit.
string = stringhead """.
stringhead = """ | stringhead character.
letter = "A" | ... | "Z".
digit = "0" | ... | "9".
From bnf-syntax
- definition
=
:=
::=
- concatenation
,
<whitespace>
- termination
;
- alternation
|
- option
[ ... ]
?
- repetition
{ ... } => 0..N
expression* => 0..N
expression+ => 1..N
<digits> * expression => <digits>...<digits>
<digits> * [expression] => <0>...<digits>
<digits> * expression? => <0>...<digits>
- grouping
( ... )
- literal
" ... " or ' ... '
- special characters
(? ... ?)
- comments
(* ... *)
Using recursion to express simple repetitions is rather detrimental to readability.
The extension of BNF called EBNF (Wirth, 1977):
syntax = {production}.
production = identifier "=" expression "." .
expression = term {"|" term}.
term = factor {factor}.
factor = identifier | string | "(" expression ")" | "[" expression "]" | "{" expression "}".
identifier = letter {letter | digit}.
string = """ {character} """.
letter = "A" | ... | "Z".
digit = "0" | ... | "9".
where
Hence, the need for the special symbol ∅ for the empty sequence vanishes.
Operators
The differences between standard BNF and ABNF (Augmented BNF) involve naming rules, repetition, alternatives, order-independence, and value ranges.
Augmented BNF for Syntax Specifications: ABNF, D. Crocker, P. Overell. IETF.
Used in HTTP specification
Characters specifications
'%' ( 'b = binary' | 'd = decimal' | 'x = hexadecimal' ) 'value' ( '. = concatenation' 'value' )?
For example in ASCII:
They may have different signification for each different implementation.
| Symbol | Description |
|---|---|
| < > | Angle brackets are used to surround the name of a syntactic element (BNF nonterminal) of the language. |
| ::= | The definition operator is used to provide definitions of the element appearing on the left side of the operator in a production rule. |
| [ ] | Square brackets are used to indicate optional elements in a formula. Optional elements can be specified or omitted. |
| { } | Braces group elements in a formula. Repetitive elements (zero or more elements) can be specified within brace symbols. |
| | | The alternative operator indicates that the portion of the formula following the bar is an alternative to the portion preceding it. |
| … | Ellipsis indicates that the element can be repeated any number of times. If ellipsis appears after grouped elements, the grouped elements enclosed with braces can be repeated any number of times. If ellipsis appears after a single element, only this element can be repeated any number of times. |
| !! | Introduces normal English text. This is used when the definition of a syntactic element is not expressed in BNF. |