首先，給出文法定義：
經典表達式文法：
Expr -> Expr + Term
|Expr - Term
|Term
Term -> Term * Factor
|Term / Factor
|Factor
Factor -> (Expr)
|num
遞歸下降法，無法處理左遞歸文法
消除左遞歸後，用BNF表示
<Expr> -> <Term> { (+|-) <Term> }
<Term> -> <Factor> { (*|/) <Factor> }
<Factor> -> (<Expr>) | num | indent
程序：
1 /*
2 遞歸下降法構造經典表達式的語法分析
3 編寫遞歸下降子程序有一個協定:
4 每一個子程序都在全局量nextToken中放入下一個輸入的token。
5 因而，當開始一個語法分析函數時，假定nextToken具有還沒有被語法分析過程使用的輸入標記中最左面的那個標記。
6 */
7 #include <stdio.h>
8 #include <ctype.h>
9 #include <stdlib.h>
10
11 enum token_type{
12 NUMBER, OPERATOR, SEPARATOR, UNKOWN
13 };
14
15 struct Token{
16 int type;
17 int val;
18 };
19
20 struct Token next_token; // 下一個未處理的token
21 // put next token into next_token
22 void lex();
23
24 // 三個非終結符
25 double expr();
26 double term();
27 double factor();
28
29 int main()
30 {
31 // input:
32 // 每個表達式, 以';'結尾
33 freopen("test.in", "r", stdin);
34
35 while (1){
36 lex(); // 取得第一個token
37 if (next_token.type == UNKOWN && next_token.val == EOF)
38 break;
39
40 printf("%lf\n", expr());
41
42 if (next_token.type != SEPARATOR || next_token.val != ';' ){
43 fprintf(stderr, "未以\';\'結尾\n");
44 break;
45 }
46 }
47 return 0;
48 }
49
50 // <expr> -> <term> { (+ | -) <term> }
51 double expr()
52 {
53 double val;
54
55 // parse first term
56 val = term();
57
58 // As long as the next token is + or - ,
59 // call lex() get next token，
60 // and parse the next term.
61 while(next_token.type == OPERATOR &&
62 (next_token.val == '+' || next_token.val == '-')){
63 int op = next_token.val;
64 lex();
65
66 if(op == '+')
67 val += term();
68 else if(op == '-')
69 val -= term();
70 }
71 return val;
72 }
73
74 // <term> -> <factor> { (* | /) <factor> }
75 double term()
76 {
77 double val;
78
79 // parse first factor
80 val = factor();
81
82 // As long as the next token is * or / ,
83 // call lex() get next token，
84 // and parse the next factor.
85 while(next_token.type == OPERATOR &&
86 (next_token.val == '*' || next_token.val == '/')){
87 int op = next_token.val;
88 lex();
89
90 if(op == '*')
91 val *= factor();
92 else if(op == '-')
93 val /= factor();
94 }
95 return val;
96 }
97
98 // <factor> -> (<expr>) | num
99 double factor(){
100 double val;
101 if(next_token.type == SEPARATOR && next_token.val == '('){
102 lex();
103 val = expr();
104 if(next_token.type == SEPARATOR && next_token.val == ')'){
105 lex(); // 讀取下一個token
106 }else{
107 fprintf(stderr, "括號不匹配\n");
108 exit(1);
109 }
110 }else if(next_token.type == NUMBER){
111 val = next_token.val;
112 lex();
113 }else{ // 既不是數字也不是'('
114 fprintf(stderr, "unkown factor: %c\n", next_token.val);
115 exit(1);
116 }
117 return val;
118 }
119
120 void lex(){
121 int c;
122 while((c = getchar()) != EOF && isspace(c))
123 ;
124 if(isdigit(c)){
125 int val;
126 val = c - '0';
127 while(isdigit(c = getchar()))
128 val = val * 10 + c - '0';
129 ungetc(c, stdin);
130 next_token.type = NUMBER;
131 next_token.val = val;
132 return;
133 }
134 next_token.val = c;
135 switch(c){
136 case '+':
137 case '-':
138 case '*':
139 case '/':
140 next_token.type = OPERATOR;
141 break;
142 case '(':
143 case ')':
144 case ';':
145 next_token.type = SEPARATOR;
146 break;
147 default:
148 next_token.type = UNKOWN;
149 }
150 }
測試數據， 以分號結尾的表達式，main()中將stdin重定向到文件test.in
12 + 2*30; (1+2)* 5; 4+5; 8+8*7;
