Syntax Definition

A contex free grammar, CFG, (synonyms: Backus-Naur Firm of BNF) is a common notation for specifying the syntax of a languages

For example, an "IF-ELSE" statement in c-language has the form
        IF         (Expr)         stmt         ELSE         stmt

In other words, it is the concatenation of:

• the keyword IF ;
• an opening parenthesis ( ;
• an expression Expr ;
• a closing parenthesis ) ;
• a statement stmt ;
• a keyword ELSE ;
• Finally, another statement stmt.

The syntax of an 'IF-ELSE' statement can be specified by the following 'production rule' in the CFG.
        stmt     →     IF     (Expr)     stmt     ELSE     stmt

The arrow ( → ) is read as "can have the form".

A context-free grammar (CFG) has four components:

1. A set of tokens called terminals.
2. A set of variable called nonterminals.
3. A set of production rules.
4. A designation of one of the nonterminals as the start symbol.

Multiple production with the same nonterminal on the left like:

list  → + digit
list  →  - digit
list  → 

may be grouped together separated by vertical bars, like:

list   →  list + digit | list - digit | digit