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An example grammar that generates strings representing arithmetic expressions with the four operators
+, -, *, /,
and numbers as operands is:
1. <expression>: number 2. <expression>: ( <expression> ) 3. <expression>: <expression> + <expression> 4. <expression>: <expression> - <expression> 5. <expression>: <expression> * <expression> 6. <expression>: <expression> / <expression>
The only nonterminal symbol in this grammar is <expression>, which is also the start symbol. The terminal symbols are
{ +, -, *, /, (, ), number } .
(We will interpret "number" to represent any valid number.)
The first rule (or production) states that an <expression> can be rewritten as (or replaced by) a number. In other words, a number is a valid expression.
The second rule says that an <expression> enclosed in parentheses is also an <expression>. Note that this rule defines an expression in terms of expressions, an example of the use of recursion in the definition of context-free grammars.
The remaining rules say that the sum, difference, product, or division of two <expression>s is also an expression.
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Last modified 22/May/97