自顶向下的语法分析器—采用递归下降方法

在之前已经通过手写的方式实现了一个词法分析器，现在，我将利用之前手写的词法分析器，使用递归下降的方式，实现一个简单的语法分析器。

首先看看实验要求：

用递归下降法编写一个语法分析程序，使之与词法分析器结合，能够根据语言的上下文无关文法，识别输入的单词序列是否文法的句子。

为减轻实验编程负担，这里只要求实现部分产生式，文法的开始符号为 program 。

第一步，消除左递归。观察上面各个产生式，出现左递归的地方有expr和term。

针对以上式子，首先提取左因子：

消除左递归：

观察到 在if语句处也存在左公因子，一并提取，最终文法定义为：

定义好文法后，考虑词法分析与语法分析的接口，由于采用递归下降的分析过程中，存在对token的回溯操作，因此，每次逐个获取词法单元并不容易实现，考虑将token对应的标志和内容使用pair的数组保存下来。

pair<int, string> tokens[10000];
int cursor_;
int tokens_size_;

并使用cursor_记录当前准备分析的位置，通过移动cursor_实现对token串的回溯过程。然后根据每一条语句，写出对应的梯度下降递归函数，就可以完成本实验，使用yylex自动生成的方法也类似，只需要维护tokens数组即可。

// 工具函数：获得一个向前看，但并不移动指针
pair<int, string> get_ahead(){
    return tokens[cursor_];
}


// 工具函数：尝试匹配一个类型，匹配返回真
bool match(int type){
    if(cursor_ >= tokens_size_) return false;
    if(tokens[cursor_].first == type)
    {
        cursor_ ++;
        return true;
    }
    return false;
}


// 工具函数：尝试匹配一个类型和字符串，都匹配返回真
bool match(int type, string target){
    if(tokens[cursor_].first == type && tokens[cursor_].second == target)
    {
        cursor_ ++;
        return true;
    }
    return false;
}


bool factor(){
    cout << "Try to match factor" << endl;
    if(match(IDENTITY)) return true;
    if(match(DIGIT)) return true;
    return match(SYMBOL, "(") && expr() && match(SYMBOL, ")");
}


bool B3(){
    cout << "Try to match B3" << endl;
    return match(SYMBOL, "%") && factor();
}


bool B2(){
    cout << "Try to match B2" << endl;
    return match(SYMBOL, "/") && factor();
}


bool B1(){
    cout << "Try to match B1" << endl;
    return match(SYMBOL, "*") && factor();
}


bool B(){
    cout << "Try to match B" << endl;
    int backup_cursor = cursor_;
    if(B1()) return true;
    cursor_ = backup_cursor;
    if(B2()) return true;
    cursor_ = backup_cursor;
    if(B3()) return true;
    cursor_ = backup_cursor;
    return false;
}


bool D(){
    cout << "Try to match D" << endl;
    pair<int, string> ahead = get_ahead();
    if(ahead.first == SYMBOL && (ahead.second == "*" || ahead.second == "/" || ahead.second == "%")) return B() && D();
    return true;
}


bool term(){
    cout << "Try to match term" << endl;
    return factor() && D();
}


bool A2(){
    cout << "Try to match A2" << endl;
    return match(SYMBOL, "-") && term();
}


bool A1(){
    cout << "Try to match A1" << endl;
    return match(SYMBOL, "+") && term();
}


bool A(){
    cout << "Try to match A" << endl;
    int backup_cursor = cursor_;
    if(A1()) return true;
    cursor_ = backup_cursor;
    if(A2()) return true;
    cursor_ = backup_cursor;
    return false;
}


bool C(){
    cout << "Try to match C" << endl;
    pair<int, string> ahead = get_ahead();
    if(ahead.first == SYMBOL && (ahead.second == "+" || ahead.second == "-")) return A() && C();
    return true;
}


bool expr(){
    cout << "Try to match expr" << endl;
    return term() && C();
}


bool F(){
    cout << "Try to match F" << endl;
    pair<int, string> ahead = get_ahead();
    if(ahead.first == RELOP) return match(RELOP) && expr();
    return true;
}


bool bool_(){
    cout << "Try to match bool" << endl;
    return expr() && F();
}


bool E(){
    cout << "Try to match E" << endl;
    pair<int, string> ahead = get_ahead();
    if(ahead.first == KEYWORD && ahead.second == "else") return match(KEYWORD, "else") && stmt();
    return true;
}


bool stmt6(){
    cout << "Try to match stmt choice 6" << endl;
    return block();
}


bool stmt5(){
    cout << "Try to match stmt choice 5" << endl;
    return match(KEYWORD, "break") && match(SYMBOL, ";");
}


bool stmt4(){
    cout << "Try to match stmt choice 4" << endl;
    return match(KEYWORD, "do") && stmt() && match(KEYWORD, "while") && match(SYMBOL, "(") && bool_() && match(SYMBOL, ")") && match(SYMBOL, ";");
}


bool stmt3(){
    cout << "Try to match stmt choice 3" << endl;
    return match(KEYWORD, "while") && match(SYMBOL, "(") && bool_() && match(SYMBOL, ")") && stmt();
}


bool stmt2(){
    cout << "Try to match stmt choice 2" << endl;
    return match(KEYWORD, "if") && match(SYMBOL, "(") && bool_() && match(SYMBOL, ")") && stmt() && E();
}


bool stmt1(){
    cout << "Try to match stmt choice 1" << endl;
    return match(IDENTITY) && match(SYMBOL, "=") && expr() && match(SYMBOL, ";");
}


bool stmt(){
    cout << "Try to match stmt" << endl;
    int backup_cursor = cursor_; // 指针的回溯
    if(stmt1()) return true;
    cursor_ = backup_cursor;
    if(stmt2()) return true;
    cursor_ = backup_cursor;
    if(stmt3()) return true;
    cursor_ = backup_cursor;
    if(stmt4()) return true;
    cursor_ = backup_cursor;
    if(stmt5()) return true;
    cursor_ = backup_cursor;
    if(stmt6()) return true;
    cursor_ = backup_cursor;
    return false;
}


bool stmts(){
    cout << "Try to match stmts" << endl;
    pair<int, string> ahead = get_ahead();
    if(ahead.first == SYMBOL && ahead.second == "}") return true;
    else return stmt() && stmts();
}


bool block(){
    cout << "Try to match block" << endl;
    return match(SYMBOL, "{") && stmts() && match(SYMBOL, "}");
}


bool program(){
    cout << "Try to match program" << endl;
    return block();
}

由于已经高度模块化，main函数很简单：

int main()
{
    if(!DFA()) return 0; // 词法分析
    tokens_size_ = cursor_; 
    cursor_ = 0; // 初始化指针
    if(program()) cout << "ACCEPT !" << endl;
    else cout << "ERROR !" << endl;
}

测试：

使用实验指导代码测试：

input:
{
i = 2;
   sum = 0;
     while (i <=100)   {
          sum = sum + i;
       i = i + 2;
          if(i%5==0) break;
     }
}


output:
SYMBOL : {
i = 2;
IDENTITY : i
SYMBOL : =
DIGIT : 2
SYMBOL : ;
   sum = 0;
IDENTITY : sum
SYMBOL : =
DIGIT : 0
SYMBOL : ;
KEYWORD : while
SYMBOL : (
IDENTITY : i
RELOP : <=
DIGIT : 100
SYMBOL : )
SYMBOL : {
IDENTITY : sum
SYMBOL : =
IDENTITY : sum
SYMBOL : +
IDENTITY : i
SYMBOL : ;
IDENTITY : i
SYMBOL : =
IDENTITY : i
SYMBOL : +
DIGIT : 2
SYMBOL : ;
KEYWORD : if
SYMBOL : (
IDENTITY : i
SYMBOL : %
DIGIT : 5
RELOP : ==
DIGIT : 0
SYMBOL : )
KEYWORD : break
SYMBOL : ;
SYMBOL : }
SYMBOL : }
Try to match program
Try to match block
Try to match stmts
Try to match stmt
Try to match stmt choice 1
Try to match expr
Try to match term
Try to match factor
Try to match D
Try to match C
Try to match stmts
Try to match stmt
Try to match stmt choice 1
Try to match expr
Try to match term
Try to match factor
Try to match D
Try to match C
Try to match stmts
Try to match stmt
Try to match stmt choice 1
Try to match stmt choice 2
Try to match stmt choice 3
Try to match bool
Try to match expr
Try to match term
Try to match factor
Try to match D
Try to match C
Try to match F
Try to match expr
Try to match term
Try to match factor
Try to match D
Try to match C
Try to match stmt
Try to match stmt choice 1
Try to match stmt choice 2
Try to match stmt choice 3
Try to match stmt choice 4
Try to match stmt choice 5
Try to match stmt choice 6
Try to match block
Try to match stmts
Try to match stmt
Try to match stmt choice 1
Try to match expr
Try to match term
Try to match factor
Try to match D
Try to match C
Try to match A
Try to match A1
Try to match term
Try to match factor
Try to match D
Try to match C
Try to match stmts
Try to match stmt
Try to match stmt choice 1
Try to match expr
Try to match term
Try to match factor
Try to match D
Try to match C
Try to match A
Try to match A1
Try to match term
Try to match factor
Try to match D
Try to match E
Try to match stmts
Try to match stmts
ACCEPT !

最后发现梯度递归函数已经成功地接受了我们的输入。