何时在EBNF中使用括号？

Question

如果你的语法是这样的：

<assign> → <id> = <expr> 
<id> → A | B | C 
<expr> → <expr> + <term> 
     | <term> 
<term> → <term> * <factor> 
     | <factor> 
<factor> → (<expr>) 
      | <id> 

然后是句子A = B + C * A，你得到这个最左推导：

<assign> => <id> = <expr> 
     => A = <expr> 
     => A = <expr> + <term> 
     => A = <term> + <term> 
     => A = <factor> + <term> 
     => A = <id> + <term> 
     => A = B + <term> 
     => A = B + <term> * <factor> 
     => A = B + <factor> * <factor> 
     => A = B + <id> * <factor> 
     => A = B + C * <factor> 
     => A = B + C * <id> 
     => A = B + C * A 

但对于A = B +（C * 一个 ）？

Answer 1

(C * A)不需要paren，因为*具有更高的优先级。你会看到它的一个案例是A = B * (C + B)。

您不会在最后两行看到它，因为<factor>将要评估为<term> + <term>或<id>。在这种情况下，没有+因此它必须是<id>。

Answer 2

A = B +（C * A）？

首先五个步骤，和上面一样，然后...

 => A = B + <term> 
    => A = B + <factor>  
    => A = B + (<expr>) 
    => A = B + (<term>) 
    => A = B + (<term> * <factor>) 
    => A = B + (<factor> * <factor>) 
    => A = B + (<id> * <id>) 
    => A = B + ( C * A )