把以上文法消除左递归

消除左递归后的C语言文法如下：

<program> ::= <declaration-list>

<declaration-list> ::= <declaration> <declaration-list-tail>

<declaration-list-tail> ::= ε
                           | <declaration> <declaration-list-tail>

<declaration> ::= <type-specifier> <declaration-tail>;

<declaration-tail> ::= <var-declaration-tail>
                      | <fun-declaration-tail>

<var-declaration-tail> ::= <id-list>
                          | <id-list> = <expression>

<fun-declaration-tail> ::= <identifier> (<params>) <compound-stmt>

<params> ::= <param-list>
            | void

<param-list> ::= <param> <param-list-tail>

<param-list-tail> ::= ε
                     | , <param> <param-list-tail>

<param> ::= <type-specifier> <identifier>

<compound-stmt> ::= { <local-declarations> <statement-list> }

<local-declarations> ::= ε
                        | <var-declaration> <local-declarations>

<statement-list> ::= ε
                     | <statement> <statement-list>

<statement> ::= <expression-stmt>
                | <compound-stmt>
                | <selection-stmt>
                | <iteration-stmt>
                | <return-stmt>

<expression-stmt> ::= <expression> ;
                     | ;

<selection-stmt> ::= if ( <expression> ) <statement> <else>

<else> ::= ε
         | else <statement>

<iteration-stmt> ::= while ( <expression> ) <statement>

<return-stmt> ::= return <return-stmt-tail>

<return-stmt-tail> ::= ε
                      | <expression> ;

<expression> ::= <var> = <expression-tail>
                 | <simple-expression>

<expression-tail> ::= <expression>
                     | <simple-expression>

<var> ::= <identifier> <var-tail>

<var-tail> ::= ε
             | [ <expression> ]

<simple-expression> ::= <additive-expression> <simple-expression-tail>

<simple-expression-tail> ::= <relop> <additive-expression>
                            | ε

<additive-expression> ::= <term> <additive-expression-tail>

<additive-expression-tail> ::= <additive-operator> <term> <additive-expression-tail>
                              | ε

<additive-operator> ::= +
                       | -

<term> ::= <factor> <term-tail>

<term-tail> ::= <mulop> <factor> <term-tail>
               | ε

<mulop> ::= *
            | /

<factor> ::= ( <expression> )
             | <var>
             | <call>
             | <number>

<call> ::= <identifier> (<args>)

<args> ::= ε
          | <arg-list>

<arg-list> ::= <expression> <arg-list-tail>

<arg-list-tail> ::= ε
                   | , <expression> <arg-list-tail>

<relop> ::= <=
            | <
            | >=
            | >
            | ==
            | !=

其中，`<declaration-list-tail>`、`<var-declaration-tail>`和`<fun-declaration-tail>`是为了消除左递归而引入的辅助符号；`<else>`表示if语句的else部分，可以为空；`<expression-tail>`用于消除赋值语句的左递归；`<var-tail>`用于表示数组下标；`<simple-expression-tail>`用于判断是否有关系运算符；`<additive-expression-tail>`和`<term-tail>`用于表示加减和乘除运算符。