プログラミング言語のコンパイラで用いられる構文解析の手法を図解で解説。 演算子順位法・LR法・再帰下降構文解析・Backtrack parsing・Packrat parsing・左再帰を許すPackrat parsingを扱っています。 非常に長いですがパラパラ漫画的な感覚で読んでみてください。

1. 1

2. 2

3. 3

4. 4

5. 5

6. 6

7. 7

8. 8

9. 9

10. 10

11. 11

12. 12

13. 13
•
•

14. 14
num
+
num
*
num
2 + 3 * 4

15. 15
expr
num
+
num
*
num
2 + 3 * 4

16. 16
expr
expr
num
+
num
*
num
2 + 3 * 4

17. 17
•
• LR
• SLR
• LALR
• GLR
• etc...

18. 18
num
+
*
num
x
>
>
+
<
>
<
*
<
>
>
num
+
num
*
num

19. 19
num
+
*
num
x
>
>
+
<
>
<
*
<
>
>
num
+
num
*
num

20. 20
num > +
num
+
*
num
x
>
>
+
<
>
<
*
<
>
>
num
+
num
*
num

21. 21
num > +
num
+
*
num
x
>
>
+
<
>
<
*
<
>
>
num
+
num
*
num

22. 22
num
+
*
num
x
>
>
+
<
>
<
*
<
>
>
num
+
num
*
num

23. 23
+ < num
num
+
*
num
x
>
>
+
<
>
<
*
<
>
>
num
+
num
*
num

24. 24
+ < num
num
+
*
num
x
>
>
+
<
>
<
*
<
>
>
num
num
+
*
num

25. 25
num
+
*
num
x
>
>
+
<
>
<
*
<
>
>
num
num
+
*
num

26. 26
num > *
num
+
*
num
x
>
>
+
<
>
<
*
<
>
>
num
num
+
*
num

27. 27
num > *
num
+
*
num
x
>
>
+
<
>
<
*
<
>
>
num
num
+
*
num

28. 28
num
+
*
num
x
>
>
+
<
>
<
*
<
>
>
+ < *
num
num
+
*
num

29. 29
num
+
*
num
x
>
>
+
<
>
<
*
<
>
>
+ < *
num
num
*
+
num

30. 30
num
+
*
num
x
>
>
+
<
>
<
*
<
>
>
num
num
*
+
num

31. 31
num
+
*
num
x
>
>
+
<
>
<
*
<
>
>
* < num
num
num
*
+
num

32. 32
num
+
*
num
x
>
>
+
<
>
<
*
<
>
>
* < num
num
num
num
*
+

33. 33
num
+
*
num
x
>
>
+
<
>
<
*
<
>
>
num
num
num
*
+

34. 34
num
+
*
num
x
>
>
+
<
>
<
*
<
>
>
num
num
num
*
+

35. 35
num
+
*
num
x
>
>
+
<
>
<
*
<
>
>
num
num
num
*
+

36. 36
num
+
*
num
x
>
>
+
<
>
<
*
<
>
>
num
num
num
*
+

37. 37
LR
1. E → E + T
2. E → T
3. T → T * num
4. T → num

38. 38
LR
1. E → E + T
2. E → T
3. T → T * num
4. T → num

39. 39
LR
GOTO
*
+
num
$
E
T
0
s3
1
2
1
s4
acc
1. E → E + T
2
s5
r2
r2
2. E → T 3
r4
r4
r4
4
s3
6
3. T → T * num
5
s7
4. T → num
6
s5
r1
r1
7
r3
r3
r3

40. 40
LR
*
+
num
$
E
T
0
s3
1
2
0
num
+
num
*
num

41. 41
LR
*
+
num
$
E
T
0
s3
1
2
shift 3
0
num
+
num
*
num

42. 42
LR
*
+
num
$
E
T
0
s3
1
2
shift 3
0
+
num
*
num

43. 43
LR
*
+
num
$
E
T
0
s3
1
2
shift 3
3
3
0
+
num
*
num

44. 44
LR
*
+
num
$
E
T
3
r4
r4
r4
3
0
+
num
*
num

45. 45
LR
*
+
num
$
E
T
3
r4
r4
r4
reduce 4
3
0
+
num
*
num

46. 46
LR
*
+
num
$
E
T
3
r4
r4
r4
reduce 4
4
4
3
0
+
num
*
num

47. 47
LR
*
+
num
$
E
T
3
r4
r4
r4
T → num
reduce 4
4
3
0
+
num
*
num

48. 48
LR
*
+
num
$
E
T
3
r4
r4
r4
T → num
reduce 4
4
0
+
num
*
num

49. 49
LR
*
+
num
$
E
T
3
r4
r4
r4
0
s3
1
2
T → num
reduce 4
4
0
+
num
*
num

50. 50
LR
*
+
num
$
E
T
3
r4
r4
r4
0
s3
1
2
T → num
reduce 4
go to 2
4
0
+
num
*
num

51. 51
LR
*
+
num
$
E
T
3
r4
r4
r4
0
s3
1
2
T → num
reduce 4
2
go to 2
4
2
0
+
num
*
num

52. 52
LR
*
+
num
$
E
T
2
s5
r2
r2
4
2
0
+
num
*
num

53. 53
LR
*
+
num
$
E
T
2
s5
r2
r2
reduce 2
4
2
0
+
num
*
num

54. 54
LR
*
+
num
$
E
T
2
s5
r2
r2
reduce 2
4
2
2
0
+
num
*
num

55. 55
LR
*
+
num
$
E
T
2
s5
r2
r2
E → T
reduce 2
4
2
2
0
+
num
*
num

56. 56
LR
*
+
num
$
E
T
2
s5
r2
r2
E → T
reduce 2
4
2
0
+
num
*
num

57. 57
LR
*
+
num
$
E
T
2
s5
r2
r2
0
s3
1
2
E → T
reduce 2
4
2
0
+
num
*
num

58. 58
LR
*
+
num
$
E
T
2
s5
r2
r2
0
s3
1
2
E → T
reduce 2
go to 1
4
2
0
+
num
*
num

59. 59
LR
*
+
num
$
E
T
2
s5
r2
r2
0
s3
1
2
E → T
reduce 2
go to 1
4
2
1
0
+
num
*
num

60. 60
LR
*
+
num
$
E
T
1
s4
acc
4
2
1
0
+
num
*
num

61. 61
LR
*
+
num
$
E
T
1
s4
acc
shift 4
4
2
1
0
+
num
*
num

62. 62
LR
*
+
num
$
E
T
1
s4
acc
shift 4
4
2
1
0
num
*
num

63. 63
LR
*
+
num
$
E
T
1
s4
acc
shift 4
4
4
2
1
0
num
*
num

64. 64
LR
*
+
num
$
E
T
4
s3
6
4
4
2
1
0
num
*
num

65. 65
LR
*
+
num
$
E
T
4
s3
6
shift 3
4
4
2
1
0
num
*
num

66. 66
LR
*
+
num
$
E
T
4
s3
6
shift 3
4
4
2
1
0
*
num

67. 67
LR
*
+
num
$
E
T
4
s3
6
shift 3
3
4
4
2
1
0
*
num

68. 68
LR
*
+
num
$
E
T
3
r4
r4
r4
3
4
4
2
1
0
*
num

69. 69
LR
*
+
num
$
E
T
3
r4
r4
r4
reduce 4
3
4
4
2
1
0
*
num

70. 70
LR
*
+
num
$
E
T
3
r4
r4
r4
reduce 4
T → N
3
4
4
2
4
1
0
*
num

71. 71
LR
*
+
num
$
E
T
3
r4
r4
r4
reduce 4
T → N
4
4
2
4
1
0
*
num

72. 72
LR
*
+
num
$
E
T
3
r4
r4
r4
4
s3
6
reduce 4
T → N
4
4
2
4
1
0
*
num

73. 73
LR
*
+
num
$
E
T
3
r4
r4
r4
4
s3
6
reduce 4
T → N
go to 6
4
4
2
4
1
0
*
num

74. 74
LR
*
+
num
$
E
T
3
r4
r4
r4
4
s3
6
reduce 4
T → N
6
go to 6
4
4
2
4
1
0
*
num

75. 75
LR
*
+
num
$
E
T
6
s5
r1
r1
6
4
4
2
4
1
0
*
num

76. 76
LR
*
+
num
$
E
T
6
s5
r1
r1
shift 5
6
4
4
2
4
1
0
*
num

77. 77
LR
*
+
num
$
E
T
6
s5
r1
r1
shift 5
6
4
4
2
4
1
0
num

78. 78
LR
*
+
num
$
E
T
6
s5
r1
r1
5
shift 5
6
4
4
2
4
1
0
num

79. 79
LR
*
+
num
$
E
T
5
s7
5
6
4
4
2
4
1
0
num

80. 80
LR
*
+
num
$
E
T
5
s7
5
shift 7
6
4
4
2
4
1
0
num

81. 81
LR
*
+
num
$
E
T
5
s7
5
shift 7
6
4
4
2
4
1
0

82. 82
LR 7
*
+
num
$
E
T
5
s7
5
shift 7
6
4
4
2
4
1
0

83. 83
LR 7
*
+
num
$
E
T
7
r3
r3
r3
5
6
4
4
2
4
1
0

84. 84
LR 7
*
+
num
$
E
T
7
r3
r3
r3
5
reduce 3
6
4
4
2
4
1
0

85. 85
LR 7
*
+
num
$
E
T
7
r3
r3
r3
5
reduce 3
6
4
4
2
4
3
1
0

86. 86
LR 7
*
+
num
$
E
T
7
r3
r3
r3
5
reduce 3
6
4
4
2
4
3
1
0
T → T * N

87. 87
LR
*
+
num
$
E
T
7
r3
r3
r3
reduce 3
4
4
2
4
3
1
0
T → T * N

88. 88
LR
*
+
num
$
E
T
7
r3
r3
r3
4
s3
6
reduce 3
4
4
2
4
3
1
0
T → T * N

89. 89
LR
*
+
num
$
E
T
7
r3
r3
r3
4
s3
6
reduce 3
go to 6
4
4
2
4
3
1
0
T → T * N

90. 90
LR
*
+
num
$
E
T
7
r3
r3
r3
4
s3
6
reduce 3
6
go to 6
4
4
2
4
3
1
0
T → T * N

91. 91
LR
*
+
num
$
E
T
6
s5
r1
r1
6
4
4
2
4
3
1
0

92. 92
LR
*
+
num
$
E
T
6
s5
r1
r1
reduce 1
6
4
4
2
4
3
1
0

93. 93
LR
*
+
num
$
E
T
6
s5
r1
r1
reduce 1
6
4
4
2
4
3
1
1
0

94. 94
LR
*
+
num
$
E
T
6
s5
r1
r1
reduce 1
6
4
4
2
4
3
1
1
0
E → E + T

95. 95
LR
*
+
num
$
E
T
6
s5
r1
r1
reduce 1
4
2
4
3
1
0
E → E + T

96. 96
LR
*
+
num
$
E
T
6
s5
r1
r1
0
s3
1
2
reduce 1
4
2
4
3
1
0
E → E + T

97. 97
LR
*
+
num
$
E
T
6
s5
r1
r1
0
s3
1
2
reduce 1
go to 1
4
2
4
3
1
0
E → E + T

98. 98
LR
*
+
num
$
E
T
6
s5
r1
r1
0
s3
1
2
reduce 1
go to 1
4
2
4
3
1
1
0
E → E + T

99. 99
LR
*
+
num
$
E
T
1
s4
acc
4
2
4
3
1
1
0

100. 100
LR
*
+
num
$
E
T
1
s4
acc
accept !
4
2
4
3
1
1
0

101. 101
GOTO
1. E → E + T
2. E → T
3. T → T * num
4. T → num

102. 102
GOTO
0. S → E
1. E → E + T
2. E → T
3. T → T * num
4. T → num

103. 103
GOTO
0. S → E
1. E → E + T
LR(0)
2. E → T
3. T → T * num
4. T → num

104. 104
GOTO
0. S → E
1. E → E + T
LR(0) LR(0)
2. E → T
3. T → T * num
4. T → num

105. 105
GOTO
0. S → E
1. E → E + T
LR(0) LR(0)
2. E → T
3. T → T * num
4. T → num
GOTO

106. 106
LR(0)
E → E + T

107. 107
LR(0)
E → E + T
1) E → E+T
2) E → E +T
3) E → E + T
4) E → E + T

108. 108
LR(0)
E → E + T
1) E → E+T
2) E → E +T
3) E → E + T
4) E → E + T

109. 109
0.
S
→
E
3. T
→
T
*
N
LR(0)
1. E
→
E
+
T
4. T
→
N
2. E
→
T
I0
S
→
E

110. 110
0.
S
→
E
3. T
→
T
*
N
LR(0)
1. E
→
E
+
T
4. T
→
N
2. E
→
T
I0
S
→
E
E
→
E
+
T
E
→
T

111. 111
0.
S
→
E
3. T
→
T
*
N
LR(0)
1. E
→
E
+
T
4. T
→
N
2. E
→
T
I0
S
→
E
E
→
E
+
T
E
→
T
T
→
T
*
num
T
→
num

112. 112
0.
S
→
E
3. T
→
T
*
N
LR(0)
1. E
→
E
+
T
4. T
→
N
2. E
→
T
I0
S
→
E
E
→
E
+
T
E
→
T
T
→
T
*
num
T
→
num
E
I1
S
→
E
E
→
E
+
T

113. 113
0.
S
→
E
3. T
→
T
*
N
LR(0)
1. E
→
E
+
T
4. T
→
N
2. E
→
T
I0
I2
S
→
E
E
→
T
E
→
E
+
T
T
→
T
*
num
T
E
→
T
T
→
T
*
num
T
→
num
E
I1
S
→
E
E
→
E
+
T

114. 114
0.
S
→
E
3. T
→
T
*
N
LR(0)
1. E
→
E
+
T
4. T
→
N
2. E
→
T
I0
I2
S
→
E
E
→
T
E
→
E
+
T
T
→
T
*
num
T
E
→
T
T
→
T
*
num
T
→
num
num
I3
E
T
→
num
I1
S
→
E
E
→
E
+
T

115. 115
0.
S
→
E
3. T
→
T
*
N
LR(0)
1. E
→
E
+
T
4. T
→
N
2. E
→
T
I0
I2
S
→
E
E
→
T
E
→
E
+
T
T
→
T
*
num
T
E
→
T
T
→
T
*
num
T
→
num
num
I3
E
T
→
num
E
→
E
+
T
I1
S
→
E
I4
+
E
→
E
+
T

116. 116
0.
S
→
E
3. T
→
T
*
N
LR(0)
1. E
→
E
+
T
4. T
→
N
2. E
→
T
I0
I2
S
→
E
E
→
T
E
→
E
+
T
T
→
T
*
num
T
E
→
T
T
→
T
*
num
T
→
num
num
I3
E
T
→
num
E
→
E
+
T
T
→
T
*
num
I1
T
→
num
S
→
E
I4
+
E
→
E
+
T

117. 117
0.
S
→
E
3. T
→
T
*
N
LR(0)
1. E
→
E
+
T
4. T
→
N
2. E
→
T
I0
I2
S
→
E
E
→
T
E
→
E
+
T
T
→
T
*
num
T
E
→
T
T
→
T
*
num
T
→
num
num
I3
E
T
→
num
E
→
E
+
T
num
T
→
T
*
num
I1
T
→
num
S
→
E
I4
+
E
→
E
+
T

118. 118
0.
S
→
E
3. T
→
T
*
N
LR(0)
1. E
→
E
+
T
4. T
→
N
2. E
→
T
I0
I2
S
→
E
E
→
T
E
→
E
+
T
T
→
T
*
num
T
E
→
T
I5
*
T
→
T
*
num
T
→
num
T
→
T
*
num
num
I3
E
T
→
num
E
→
E
+
T
num
T
→
T
*
num
I1
T
→
num
S
→
E
I4
+
E
→
E
+
T

119. 119
0.
S
→
E
3. T
→
T
*
N
LR(0)
1. E
→
E
+
T
4. T
→
N
2. E
→
T
I0
I2
S
→
E
E
→
T
E
→
E
+
T
T
→
T
*
num
T
E
→
T
I5
*
T
→
T
*
num
T
→
num
T
→
T
*
num
num
I6
I3
E
→
E
+
T
E
T
→
num
E
→
E
+
T
T
→
T
*
num
num
T
→
T
*
num
T
I1
T
→
num
S
→
E
I4
+
E
→
E
+
T

120. 120
0.
S
→
E
3. T
→
T
*
N
LR(0)
1. E
→
E
+
T
4. T
→
N
2. E
→
T
I0
I2
S
→
E
E
→
T
E
→
E
+
T
T
→
T
*
num
T
E
→
T
I5
*
T
→
T
*
num
T
→
num
T
→
T
*
num
num
*
I6
I3
E
→
E
+
T
E
T
→
num
E
→
E
+
T
T
→
T
*
num
num
T
→
T
*
num
T
I1
T
→
num
S
→
E
I4
+
E
→
E
+
T

121. 121
0.
S
→
E
3. T
→
T
*
N
LR(0)
1. E
→
E
+
T
4. T
→
N
2. E
→
T
I0
I2
S
→
E
E
→
T
E
→
E
+
T
T
→
T
*
num
I7
T
E
→
T
T
→
T
*
num
I5
*
T
→
T
*
num
T
→
num
num
T
→
T
*
num
num
*
I6
I3
E
→
E
+
T
E
T
→
num
E
→
E
+
T
T
→
T
*
num
num
T
→
T
*
num
T
I1
T
→
num
S
→
E
I4
+
E
→
E
+
T

122. 122
LR(0)
T
I0
I2
I7
num
*
num
E
I3
I5
num
*
+
T
I1
I4
I6

123. 123
LR(0)
*
+
num
E
T
0
3
1
2
1
4
2
5
3
4
3
6
5
7
6
5
7

124. 124
GOTO
*
+
num
$
E
T
0
s3
1
2
1
s4
2
s5
3
4
s3
6
5
s7
6
s5
7

125. 125
GOTO
*
+
num
$
E
T
0
s3
1
2
I1
1
s4
S
→
E
2
s5
E
→
E
+
T
3
4
s3
6
5
s7
6
s5
7

126. 126
GOTO
*
+
num
$
E
T
0
s3
1
2
I1
1
s4
acc
S
→
E
2
s5
E
→
E
+
T
3
4
s3
6
5
s7
6
s5
7

127. 127
GOTO
I2
*
+
num
$
E
T
E
→
T
0
s3
1
2
T
→
T
*
num
1
s4
acc
2
s5
3
4
s3
6
5
s7
6
s5
7

128. 128
GOTO
2
I2
*
+
num
$
E
T
E
→
T
0
s3
1
2
T
→
T
*
num
1
s4
acc
2
s5
3
4
s3
6
5
s7
6
s5
7

129. 129
GOTO
reduce 2
I2
*
+
num
$
E
T
E
→
T
0
s3
1
2
T
→
T
*
num
1
s4
acc
2
s5
3
4
s3
6
5
s7
6
s5
7

130. 130
GOTO
reduce 2
I2
*
+
num
$
E
T
E
→
T
0
s3
1
2
T
→
T
*
num
1
s4
acc
2
s5
3
shift 5
4
s3
6
5
s7
6
s5
7

131. 131
GOTO
reduce 2
I2
*
+
num
$
E
T
E
→
T
0
s3
1
2
T
→
T
*
num
1
s4
acc
2
s5
3
shift 5
4
s3
6
5
s7
shift-reduce
6
s5
conflict
7

132. 132
shift-reduce conflict (SLR )
0.
S
→
E
1. E
→
E
+
T
2. E
→
T
3. T
→
T
*
N
4. T
→
N

133. 133
shift-reduce conflict (SLR )
0.
S
→
E
1. E
→
E
+
T
2. E
→
T
3. T
→
T
*
N
4. T
→
N

134. 134
shift-reduce conflict (SLR )
0.
S
→
E
E
1. E
→
E
+
T
+ $
2. E
→
T
3. T
→
T
*
N
4. T
→
N
• + $ reduce
• * shift

135. 135
GOTO
reduce 2
I2
*
+
num
$
E
T
E
→
T
0
s3
1
2
T
→
T
*
num
1
s4
acc
2
s5
r2
r2
3
shift 5
4
s3
6
5
s7
shift reduce
6
s5
conflict
7

136. 136
GOTO
I3
*
+
num
$
E
T
T
→
num
0
s3
1
2
1
s4
acc
2
s5
r2
r2
3
4
s3
6
5
s7
6
s5
7

137. 137
GOTO
reduce 4
I3
*
+
num
$
E
T
T
→
num
0
s3
1
2
1
s4
acc
2
s5
r2
r2
3
4
s3
6
5
s7
6
s5
7

138. 138
GOTO
reduce 4
I3
*
+
num
$
E
T
T
→
num
0
s3
1
2
1
s4
acc
2
s5
r2
r2
3
r4
r4
r4
4
s3
6
5
s7
6
s5
7

139. 139
GOTO
I6
*
+
num
$
E
T
E
→
E
+
T
0
s3
1
2
T
→
T
*
num
1
s4
acc
2
s5
r2
r2
3
r4
r4
r4
4
s3
6
5
s7
6
s5
7

140. 140
GOTO
reduce 1
I6
*
+
num
$
E
T
E
→
E
+
T
0
s3
1
2
T
→
T
*
num
1
s4
acc
2
s5
r2
r2
3
r4
r4
r4
4
s3
6
5
s7
6
s5
7

141. 141
GOTO
reduce 1
I6
*
+
num
$
E
T
E
→
E
+
T
0
s3
1
2
T
→
T
*
num
1
s4
acc
2
s5
r2
r2
3
r4
r4
r4
shift 5
4
s3
6
5
s7
6
s5
7

142. 142
GOTO
reduce 1
I6
*
+
num
$
E
T
E
→
E
+
T
0
s3
1
2
T
→
T
*
num
1
s4
acc
2
s5
r2
r2
3
r4
r4
r4
shift 5
4
s3
6
5
s7
6
s5
E
7
+ $

143. 143
GOTO
reduce 1
I6
*
+
num
$
E
T
E
→
E
+
T
0
s3
1
2
T
→
T
*
num
1
s4
acc
2
s5
r2
r2
3
r4
r4
r4
shift 5
4
s3
6
5
s7
6
s5
r1
r1
E
7
+ $

144. 144
GOTO
I7
*
+
num
$
E
T
T
→
T
*
num
0
s3
1
2
1
s4
acc
2
s5
r2
r2
3
r4
r4
r4
4
s3
6
5
s7
6
s5
r1
r1
7

145. 145
GOTO
reduce 3
I7
*
+
num
$
E
T
T
→
T
*
num
0
s3
1
2
1
s4
acc
2
s5
r2
r2
3
r4
r4
r4
4
s3
6
5
s7
6
s5
r1
r1
7

146. 146
GOTO
reduce 3
I7
*
+
num
$
E
T
T
→
T
*
num
0
s3
1
2
1
s4
acc
2
s5
r2
r2
3
r4
r4
r4
4
s3
6
5
s7
6
s5
r1
r1
7
r3
r3
r3

147. 147
GOTO
*
+
num
$
E
T
0
s3
1
2
1
s4
acc
2
s5
r2
r2
3
r4
r4
r4
4
s3
6
5
s7
6
s5
r1
r1
7
r3
r3
r3

148. 148
O(n)
LR(0)
O(n)
LR(0)
SLR(1)
O(n)
SLR(1)
LALR(1)
O(n)
LALR(1)
LR(1) O(n)
LR(1)
GLR O(n3)
SDF
O(n)

149. 149
LR(1)
LALR(1)
SLR(1)
LR(0)

150. 150
expr
2 + 3 * 4

151. 151
expr
expr
num
+
2 + 3 * 4

152. 152
expr
expr
num
+
num
*
num
2 + 3 * 4

153. 153
• ( )
• Backtrack parsing
• Packrat parsing

154. 154
E
1. E
→
T
E’
2. E’
→
+
E
|
ε
3. T
→
num
T’
4. T’
→
*
T
|
ε
num
+
num
*
num

155. 155
E
1. E
→
T
E’
LL(1)
2. E’
→
+
E
|
ε
3. T
→
num
T’
4. T’
→
*
T
|
ε
num
+
num
*
num

156. 156
E
1. E
→
T
E’
2. E’
→
+
E
|
ε
3. T
→
num
T’
4. T’
→
*
T
|
ε
num
+
num
*
num

157. 157
E
E’
1. E
→
T
E’
T
2. E’
→
+
E
|
ε
3. T
→
num
T’
4. T’
→
*
T
|
ε
num
+
num
*
num

158. 158
E
E’
1. E
→
T
E’
T
2. E’
→
+
E
|
ε
3. T
→
num
T’
4. T’
→
*
T
|
ε
num
+
num
*
num

159. 159
E
E’
1. E
→
T
E’
T
2. E’
→
+
E
|
ε
num
T’
3. T
→
num
T’
4. T’
→
*
T
|
ε
num
+
num
*
num

160. 160
E
E’
1. E
→
T
E’
T
2. E’
→
+
E
|
ε
num
T’
3. T
→
num
T’
4. T’
→
*
T
|
ε
num
+
num
*
num

161. 161
E
E’
1. E
→
T
E’
T
2. E’
→
+
E
|
ε
num
T’
3. T
→
num
T’
4. T’
→
*
T
|
ε
num
+
num
*
num

162. 162
E
E’
1. E
→
T
E’
T
2. E’
→
+
E
|
ε
num
T’
3. T
→
num
T’
4. T’
→
*
T
|
ε
num
+
num
*
num

163. 163
E
E’
1. E
→
T
E’
T
2. E’
→
+
E
|
ε
num
T’
3. T
→
num
T’
4. T’
→
*
T
|
ε
1 +
num
+
num
*
num

164. 164
E
E’
1. E
→
T
E’
T
2. E’
→
+
E
|
ε
num
T’
3. T
→
num
T’
4. T’
→
*
T
|
ε
ε
num
+
num
*
num

165. 165
E
E’
1. E
→
T
E’
T
2. E’
→
+
E
|
ε
num
T’
3. T
→
num
T’
4. T’
→
*
T
|
ε
ε
num
+
num
*
num

166. 166
E
E’
1. E
→
T
E’
T
2. E’
→
+
E
|
ε
num
T’
3. T
→
num
T’
4. T’
→
*
T
|
ε
ε
num
+
num
*
num

167. 167
E
E’
1. E
→
T
E’
T
2. E’
→
+
E
|
ε
num
T’
3. T
→
num
T’
4. T’
→
*
T
|
ε
ε
1 +
num
+
num
*
num

168. 168
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
3. T
→
num
T’
4. T’
→
*
T
|
ε
ε
num
+
num
*
num

169. 169
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
3. T
→
num
T’
4. T’
→
*
T
|
ε
ε
num
+
num
*
num

170. 170
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
3. T
→
num
T’
4. T’
→
*
T
|
ε
ε
num
+
num
*
num

171. 171
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
3. T
→
num
T’
4. T’
→
*
T
|
ε
ε
num
+
num
*
num

172. 172
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
T
E’
3. T
→
num
T’
4. T’
→
*
T
|
ε
ε
num
+
num
*
num

173. 173
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
T
E’
3. T
→
num
T’
4. T’
→
*
T
|
ε
ε
num
+
num
*
num

174. 174
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
T
E’
3. T
→
num
T’
num
T’
4. T’
→
*
T
|
ε
ε
num
+
num
*
num

175. 175
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
T
E’
3. T
→
num
T’
num
T’
4. T’
→
*
T
|
ε
ε
num
+
num
*
num

176. 176
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
T
E’
3. T
→
num
T’
num
T’
4. T’
→
*
T
|
ε
ε
num
+
num
*
num

177. 177
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
T
E’
3. T
→
num
T’
num
T’
4. T’
→
*
T
|
ε
ε
num
+
num
*
num

178. 178
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
T
E’
3. T
→
num
T’
num
T’
4. T’
→
*
T
|
ε
ε
1 *
num
+
num
*
num

179. 179
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
T
E’
3. T
→
num
T’
num
T’
4. T’
→
*
T
|
ε
ε
*
T
num
+
num
*
num

180. 180
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
T
E’
3. T
→
num
T’
num
T’
4. T’
→
*
T
|
ε
ε
*
T
num
+
num
*
num

181. 181
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
T
E’
3. T
→
num
T’
num
T’
4. T’
→
*
T
|
ε
ε
*
T
num
+
num
*
num

182. 182
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
T
E’
3. T
→
num
T’
num
T’
4. T’
→
*
T
|
ε
ε
*
T
num
+
num
*
num

183. 183
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
T
E’
3. T
→
num
T’
num
T’
4. T’
→
*
T
|
ε
ε
*
T
num
T’
num
+
num
*
num

184. 184
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
T
E’
3. T
→
num
T’
num
T’
4. T’
→
*
T
|
ε
ε
*
T
num
T’
num
+
num
*
num

185. 185
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
T
E’
3. T
→
num
T’
num
T’
4. T’
→
*
T
|
ε
ε
*
T
num
T’
num
+
num
*
num

186. 186
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
T
E’
3. T
→
num
T’
num
T’
4. T’
→
*
T
|
ε
ε
*
T
num
T’
num
+
num
*
num

187. 187
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
T
E’
3. T
→
num
T’
num
T’
4. T’
→
*
T
|
ε
ε
1 *
T
num
T’
num
+
num
*
num

188. 188
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
T
E’
3. T
→
num
T’
num
T’
4. T’
→
*
T
|
ε
ε
*
T
num
T’
num
+
num
*
num
ε

189. 189
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
T
E’
3. T
→
num
T’
num
T’
4. T’
→
*
T
|
ε
ε
*
T
num
T’
num
+
num
*
num
ε

190. 190
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
T
E’
3. T
→
num
T’
num
T’
4. T’
→
*
T
|
ε
ε
*
T
num
T’
num
+
num
*
num
ε

191. 191
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
T
E’
3. T
→
num
T’
num
T’
4. T’
→
*
T
|
ε
ε
*
T
num
T’
num
+
num
*
num
ε

192. 192
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
T
E’
3. T
→
num
T’
num
T’
4. T’
→
*
T
|
ε
ε
*
T
num
T’
num
+
num
*
num
ε

193. 193
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
T
E’
3. T
→
num
T’
num
T’
4. T’
→
*
T
|
ε
ε
1 *
T
num
T’
num
+
num
*
num
ε

194. 194
E
E’
1. E
→
T
E’
T
+
E
2. E’
→
+
E
|
ε
num
T’
T
E’
3. T
→
num
T’
num
T’
ε
4. T’
→
*
T
|
ε
ε
*
T
num
T’
num
+
num
*
num
ε