无上下文语法定义中的可选与强制终止符

Question

In a book chapter about compilers, there's the following grammar definition and example code.

...
statement: whileStatement
           | ifStatement
           | ... // Other statement possibilities
           | '{' statementSequence '}'
whileStatement: 'while' '(' expression ')' statement
ifStatement: ... // Definition of "if"
statementSequence: '' // empty sequence (null)
                   | statement ';' statementSequence
expression: ... // Definition of "expression"
...             // More definitions follow

while (expression) {
 statement;
 statement;
 while (expression) {
  while(expression)
     statement;
  statement;
 }
}

How is the code's inner-most while loop valid without { } ? It looks to me that the statement definition requires them. Is this a mistake in the book or am I misunderstanding the syntax?

---

[Edit] My apologies for any ambiguity. Everything typed above is verbatim from the book. The omissions were not my doing.

Answer 1

Your while statement says that after the ) comes a statement. Your grammar doesn't fully specify statement , but it doesn't require braces. Braces are only needed for a statement sequence.

Answer 2

Consider your example code again:

1 while (expression) {
2  statement;
3  statement;
4  while (expression) {
5   while(expression)
6      statement;
7   statement;
8  }
9 }

Why are you concerned that line 6 lacks braces, but don't care that lines 2, 3, and 7 are missing them too? The grammar is saying that a while loop ends with a statement , and a statementSequence , with its required braces, is just one of many alternatives for a statement . Lines 5 and 6 match that rule exactly—except for the ';' , which doesn't have a place in the rule.