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The document appears to provide a detailed breakdown of a parsing algorithm, likely related to LR parsing techniques, with various production rules and shifting/reducing operations listed. It includes examples of parsing expressions involving numbers, addition, and multiplication. Overall, it serves as a technical guide for understanding and implementing LR parsing methods in contextual grammar.

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13 •  • 
14 num + num * num 2 + 3 * 4
15 expr num + num * num 2 + 3 * 4
16 expr expr num + num * num 2 + 3 * 4
17 •  •  LR •  SLR •  LALR •  GLR •  etc...
18 num + * num x > > + < > < * < > > num + num * num
19 num + * num x > > + < > < * < > > num + num * num
20 num > + num + * num x > > + < > < * < > > num + num * num
21 num > + num + * num x > > + < > < * < > > num + num * num
22 num + * num x > > + < > < * < > > num + num * num
23 + < num num + * num x > > + < > < * < > > num + num * num
24 + < num num + * num x > > + < > < * < > > num num + * num
25 num + * num x > > + < > < * < > > num num + * num
26 num > * num + * num x > > + < > < * < > > num num + * num
27 num > * num + * num x > > + < > < * < > > num num + * num
28 num + * num x > > + < > < * < > > + < * num num + * num
29 num + * num x > > + < > < * < > > + < * num num * + num
30 num + * num x > > + < > < * < > > num num * + num
31 num + * num x > > + < > < * < > > * < num num num * + num
32 num + * num x > > + < > < * < > > * < num num num num * +
33 num + * num x > > + < > < * < > > num num num * +
34 num + * num x > > + < > < * < > > num num num * +
35 num + * num x > > + < > < * < > > num num num * +
36 num + * num x > > + < > < * < > > num num num * +
37 LR 1.  E → E + T 2.  E → T 3.  T → T * num 4.  T → num
38 LR 1.  E → E + T 2.  E → T 3.  T → T * num 4.  T → num
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 LR * + num $ E T 0 s3 1 2 0 num + num * num
41 LR * + num $ E T 0 s3 1 2 shift 3 0 num + num * num
42 LR * + num $ E T 0 s3 1 2 shift 3 0 + num * num
43 LR * + num $ E T 0 s3 1 2 shift 3 3 3 0 + num * num
44 LR * + num $ E T 3 r4 r4 r4 3 0 + num * num
45 LR * + num $ E T 3 r4 r4 r4 reduce 4 3 0 + num * num
46 LR * + num $ E T 3 r4 r4 r4 reduce 4 4 4 3 0 + num * num
47 LR * + num $ E T 3 r4 r4 r4 T → num reduce 4 4 3 0 + num * num
48 LR * + num $ E T 3 r4 r4 r4 T → num reduce 4 4 0 + num * num
49 LR * + num $ E T 3 r4 r4 r4 0 s3 1 2 T → num reduce 4 4 0 + num * num
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 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 LR * + num $ E T 2 s5 r2 r2 4 2 0 + num * num
53 LR * + num $ E T 2 s5 r2 r2 reduce 2 4 2 0 + num * num
54 LR * + num $ E T 2 s5 r2 r2 reduce 2 4 2 2 0 + num * num
55 LR * + num $ E T 2 s5 r2 r2 E → T reduce 2 4 2 2 0 + num * num
56 LR * + num $ E T 2 s5 r2 r2 E → T reduce 2 4 2 0 + num * num
57 LR * + num $ E T 2 s5 r2 r2 0 s3 1 2 E → T reduce 2 4 2 0 + num * num
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 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 LR * + num $ E T 1 s4 acc 4 2 1 0 + num * num
61 LR * + num $ E T 1 s4 acc shift 4 4 2 1 0 + num * num
62 LR * + num $ E T 1 s4 acc shift 4 4 2 1 0 num * num
63 LR * + num $ E T 1 s4 acc shift 4 4 4 2 1 0 num * num
64 LR * + num $ E T 4 s3 6 4 4 2 1 0 num * num
65 LR * + num $ E T 4 s3 6 shift 3 4 4 2 1 0 num * num
66 LR * + num $ E T 4 s3 6 shift 3 4 4 2 1 0 * num
67 LR * + num $ E T 4 s3 6 shift 3 3 4 4 2 1 0 * num
68 LR * + num $ E T 3 r4 r4 r4 3 4 4 2 1 0 * num
69 LR * + num $ E T 3 r4 r4 r4 reduce 4 3 4 4 2 1 0 * num
70 LR * + num $ E T 3 r4 r4 r4 reduce 4 T → N 3 4 4 2 4 1 0 * num
71 LR * + num $ E T 3 r4 r4 r4 reduce 4 T → N 4 4 2 4 1 0 * num
72 LR * + num $ E T 3 r4 r4 r4 4 s3 6 reduce 4 T → N 4 4 2 4 1 0 * num
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 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 LR * + num $ E T 6 s5 r1 r1 6 4 4 2 4 1 0 * num
76 LR * + num $ E T 6 s5 r1 r1 shift 5 6 4 4 2 4 1 0 * num
77 LR * + num $ E T 6 s5 r1 r1 shift 5 6 4 4 2 4 1 0 num
78 LR * + num $ E T 6 s5 r1 r1 5 shift 5 6 4 4 2 4 1 0 num
79 LR * + num $ E T 5 s7 5 6 4 4 2 4 1 0 num
80 LR * + num $ E T 5 s7 5 shift 7 6 4 4 2 4 1 0 num
81 LR * + num $ E T 5 s7 5 shift 7 6 4 4 2 4 1 0
82 LR 7 * + num $ E T 5 s7 5 shift 7 6 4 4 2 4 1 0
83 LR 7 * + num $ E T 7 r3 r3 r3 5 6 4 4 2 4 1 0
84 LR 7 * + num $ E T 7 r3 r3 r3 5 reduce 3 6 4 4 2 4 1 0
85 LR 7 * + num $ E T 7 r3 r3 r3 5 reduce 3 6 4 4 2 4 3 1 0
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 LR * + num $ E T 7 r3 r3 r3 reduce 3 4 4 2 4 3 1 0 T → T * N
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 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 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 LR * + num $ E T 6 s5 r1 r1 6 4 4 2 4 3 1 0
92 LR * + num $ E T 6 s5 r1 r1 reduce 1 6 4 4 2 4 3 1 0
93 LR * + num $ E T 6 s5 r1 r1 reduce 1 6 4 4 2 4 3 1 1 0
94 LR * + num $ E T 6 s5 r1 r1 reduce 1 6 4 4 2 4 3 1 1 0 E → E + T
95 LR * + num $ E T 6 s5 r1 r1 reduce 1 4 2 4 3 1 0 E → E + T
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 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 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 LR * + num $ E T 1 s4 acc 4 2 4 3 1 1 0
100 LR * + num $ E T 1 s4 acc accept ! 4 2 4 3 1 1 0
101 GOTO 1.  E → E + T 2.  E → T 3.  T → T * num 4.  T → num
102 GOTO 0. S → E 1.  E → E + T 2.  E → T 3.  T → T * num 4.  T → num
103 GOTO 0. S → E 1.  E → E + T LR(0) 2.  E → T 3.  T → T * num 4.  T → num
104 GOTO 0. S → E 1.  E → E + T LR(0) LR(0) 2.  E → T 3.  T → T * num 4.  T → num
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 LR(0) E → E + T
107 LR(0) E → E + T 1)  E → E+T 2)  E → E +T 3)  E → E + T 4)  E → E + T
108 LR(0) E → E + T 1)  E → E+T 2)  E → E +T 3)  E → E + T 4)  E → E + T
109 0.  S  →  E   3.  T  →  T  *  N   LR(0) 1.  E  →  E  +  T   4.  T  →  N 2.  E  →  T   I0 S  →   E    
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 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 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 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 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 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 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 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 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 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 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 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 LR(0) T I0 I2 I7 num * num E I3 I5 num * + T I1 I4 I6
123 LR(0) * + num E T 0 3 1 2 1 4 2 5 3 4 3 6 5 7 6 5 7
124 GOTO * + num $ E T 0 s3 1 2 1 s4 2 s5 3 4 s3 6 5 s7 6 s5 7
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 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 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 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 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 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 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 shift-reduce conflict (SLR ) 0.  S  →  E   1.  E  →  E  +  T   2.  E  →  T   3.  T  →  T  *  N   4.  T  →  N
133 shift-reduce conflict (SLR ) 0.  S  →  E   1.  E  →  E  +  T   2.  E  →  T   3.  T  →  T  *  N   4.  T  →  N
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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 LR(1) LALR(1) SLR(1) LR(0)
150 expr 2 + 3 * 4
151 expr expr num + 2 + 3 * 4
152 expr expr num + num * num 2 + 3 * 4
153 •  ( ) •  Backtrack parsing •  Packrat parsing
154 E 1.  E    →  T  E’   2.  E’  →  +  E  |  ε   3.  T    →  num  T’   4.  T’  →  *  T  |  ε num + num * num
155 E 1.  E    →  T  E’   LL(1) 2.  E’  →  +  E  |  ε   3.  T    →  num  T’   4.  T’  →  *  T  |  ε num + num * num
156 E 1.  E    →  T  E’   2.  E’  →  +  E  |  ε   3.  T    →  num  T’   4.  T’  →  *  T  |  ε num + num * num
157 E E’ 1.  E    →  T  E’   T 2.  E’  →  +  E  |  ε   3.  T    →  num  T’   4.  T’  →  *  T  |  ε num + num * num
158 E E’ 1.  E    →  T  E’   T 2.  E’  →  +  E  |  ε   3.  T    →  num  T’   4.  T’  →  *  T  |  ε num + num * num
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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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
195 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
196 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
197 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
198 LL(1) •  • 
199 LL(1) E  →  T  +  E  |  T   T  →  num  *  T  |  num  
200 LL(1) E  →  T  +  E  |  T   T  →  num  *  T  |  num   E  →  T  E’   E’→  +  E  |  ε   T  →  num  *  T  |  num  
201 LL(1) E  →  T  +  E  |  T   T  →  num  *  T  |  num   E  →  T  E’   E  →  T  E’   E’→  +  E  |  ε   E’→  +  E  |  ε   T  →  num  T’   T  →  num  *  T  |  num   T’→  *  T  |  ε  
202 LL(1) E  →  T  +  E  |  T   LL(2) T  →  num  *  T  |  num   E  →  T  E’   E  →  T  E’   E’→  +  E  |  ε   E’→  +  E  |  ε   T  →  num  T’   T  →  num  *  T  |  num   T’→  *  T  |  ε  
203 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T 4.  T → num num + num * num
204 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num + num * num
205 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num + num * num
206 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num * T num + num * num
207 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num * T num + num * num
208 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num * T num + num * num
209 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num * T num + num * num
210 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num * T num + num * num
211 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num Backtrack ! num + num * num
212 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num + num * num
213 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num num + num * num
214 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num num + num * num
215 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num num + num * num
216 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num num + num * num
217 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num num + num * num
218 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num num + num * num
219 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num num + num * num
220 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num T + E num + num * num
221 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num T + E num + num * num
222 E Backtrack parsing 1.  E → T + E T + E 2.  E → T 3.  T → num * T num T + E 4.  T → num num * T num + num * num
223 E Backtrack parsing 1.  E → T + E T + E 2.  E → T 3.  T → num * T num T + E 4.  T → num num * T num + num * num
224 E Backtrack parsing 1.  E → T + E T + E 2.  E → T 3.  T → num * T num T + E 4.  T → num num * T num + num * num
225 E Backtrack parsing 1.  E → T + E T + E 2.  E → T 3.  T → num * T num T + E 4.  T → num num * T num + num * num
226 E Backtrack parsing 1.  E → T + E T + E 2.  E → T 3.  T → num * T num T + E 4.  T → num num * T num + num * num
227 E Backtrack parsing 1.  E → T + E T + E 2.  E → T 3.  T → num * T num T + E 4.  T → num num * T num + num * num
228 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num * T num + num * num
229 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num * T num + num * num
230 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num * T num + num * num
231 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num * T num + num * num
232 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num * T num + num * num
233 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num Backtrack ! num + num * num
234 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num + num * num
235 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num num + num * num
236 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num num + num * num
237 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num num + num * num
238 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num num + num * num
239 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num num + num * num
240 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num num + num * num
241 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num num + num * num
242 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num Backtrack ! num + num * num
243 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num num + num * num
244 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num T num + num * num
245 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num T num + num * num
246 E Backtrack parsing 1.  E → T + E T + E 2.  E → T 3.  T → num * T num T 4.  T → num num * T num + num * num
247 E Backtrack parsing 1.  E → T + E T + E 2.  E → T 3.  T → num * T num T 4.  T → num num * T num + num * num
248 E Backtrack parsing 1.  E → T + E T + E 2.  E → T 3.  T → num * T num T 4.  T → num num * T num + num * num
249 E Backtrack parsing 1.  E → T + E T + E 2.  E → T 3.  T → num * T num T 4.  T → num num * T num + num * num
250 E Backtrack parsing 1.  E → T + E T + E 2.  E → T 3.  T → num * T num T 4.  T → num num * T num + num * num
251 E Backtrack parsing 1.  E → T + E T + E 2.  E → T 3.  T → num * T num T 4.  T → num num * T num + num * num
252 T + E Backtrack parsing T 1.  E → T + E num 2.  E → T num * T 3.  T → num * T 4.  T → num num * T num + num * num
253 T + E Backtrack parsing T 1.  E → T + E num 2.  E → T num * T 3.  T → num * T 4.  T → num num * T num + num * num
254 T + E Backtrack parsing T 1.  E → T + E num 2.  E → T num * T 3.  T → num * T 4.  T → num num * T num + num * num
255 T + E Backtrack parsing T 1.  E → T + E num 2.  E → T num * T 3.  T → num * T 4.  T → num num * T num + num * num
256 T + E Backtrack parsing T 1.  E → T + E num 2.  E → T num * T 3.  T → num * T 4.  T → num num * T num + num * num
257 T + E Backtrack parsing T 1.  E → T + E num 2.  E → T num * T 3.  T → num * T 4.  T → num Backtrack ! num + num * num
258 T + E Backtrack parsing T 1.  E → T + E num 2.  E → T num * T 3.  T → num * T 4.  T → num num + num * num
259 T + E Backtrack parsing T 1.  E → T + E num 2.  E → T num * T 3.  T → num * T 4.  T → num num num + num * num
260 T + E Backtrack parsing T 1.  E → T + E num 2.  E → T num * T 3.  T → num * T 4.  T → num num num + num * num
261 T + E Backtrack parsing T 1.  E → T + E num 2.  E → T num * T 3.  T → num * T 4.  T → num num num + num * num
262 T + E Backtrack parsing T 1.  E → T + E num 2.  E → T num * T 3.  T → num * T 4.  T → num num num + num * num
263 T + E Backtrack parsing T 1.  E → T + E num 2.  E → T num * T 3.  T → num * T 4.  T → num num num + num * num
264 E Backtrack parsing 1.  E → T + E T + E 2.  E → T T 3.  T → num * T num 4.  T → num num * T num num + num * num
265 E Backtrack parsing 1.  E → T + E T + E 2.  E → T T 3.  T → num * T num 4.  T → num num * T num num + num * num
266 E 1.   E  →  E  +  T   2.   E  →  T   3.   T  →  T  *  num   4.   T  →  num
267 E 1.   E  →  E  +  T   E + T 2.   E  →  T   3.   T  →  T  *  num   4.   T  →  num
268 E 1.   E  →  E  +  T   E + T 2.   E  →  T   3.   T  →  T  *  num   4.   T  →  num
269 E 1.   E  →  E  +  T   E + T 2.   E  →  T   3.   T  →  T  *  num   E + T 4.   T  →  num
270 E 1.   E  →  E  +  T   E + T 2.   E  →  T   3.   T  →  T  *  num   E + T 4.   T  →  num
271 E 1.   E  →  E  +  T   E + T 2.   E  →  T   3.   T  →  T  *  num   E + T 4.   T  →  num E + T
272 E 1.   E  →  E  +  T   E + T 2.   E  →  T   3.   T  →  T  *  num   E + T 4.   T  →  num E + T
273 E 1.   E  →  E  +  T   E + T 2.   E  →  T   3.   T  →  T  *  num   E + T 4.   T  →  num E + T E + T
274 E 1.   E  →  E  +  T   E + T 2.   E  →  T   3.   T  →  T  *  num   E + T 4.   T  →  num E + T E + T
275 E 1.   E  →  E  +  T   E + T 2.   E  →  T   3.   T  →  T  *  num   E + T 4.   T  →  num E + T E + T
276  E  →  E  +  T  |  T    T  →  T  *  num  |  num  
277  E  →  E  +  T  |  T    T  →  T  *  num  |  num    E  →  T  E’    E’→  +  T  E’  |  ε    T  →  T  *  num  |  num  
278  E  →  E  +  T  |  T    T  →  T  *  num  |  num    E  →  T  E’    E’→  +  T  E’  |  ε    T  →  T  *  num  |  num  
279 E  → T  {  +  T  }   T  →  num  {  *  num  }     OK  E  →  E  +  T  |  T    T  →  T  *  num  |  num    E  →  T  E’    E  →  T  E’    E’→  +  T  E’  |  ε    E’→  +  T  E’  |  ε    T  →  num  T’    T  →  T  *  num  |  num    T’→  *  num  T’  |  ε  
280 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E num + num * num
281 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E T + E num + num * num
282 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E T + E num + num * num
283 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E T + E num * T num + num * num
284 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E T + E num * T num + num * num
285 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num T + E num * T num + num * num
286 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num T + E num * T num + num * num
287 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num T + E Backtrack ! num + num * num
288 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num T + E num + num * num
289 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num T + E num num + num * num
290 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num T + E num num + num * num
291 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num T + E num num + num * num
292 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num T + E num num + num * num
293 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num 0 - 1 T T(num) T + E num num + num * num
294 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num 0 - 1 T T(num) T + E num num + num * num
295 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + T + E num num + num * num
296 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + T + E num num + num * num
297 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + T + E num T + E num + num * num
298 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + T + E num T + E num + num * num
299 E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num T + E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + num T + E num * T num + num * num
300 E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num T + E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + num T + E num * T num + num * num
301 E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num T + E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + num T + E 2 - 3 num num num * T num + num * num
302 E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num T + E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + num T + E 2 - 3 num num num * T num + num * num
303 E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num T + E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + num T + E 2 - 3 num num 3 - 4 * * num * T num + num * num
304 E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num T + E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + num T + E 2 - 3 num num 3 - 4 * * num * T num + num * num
305 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * num * T num + num * num
306 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * num * T num + num * num
307 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * 4 - 5 num num num * T num + num * num
308 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * 4 - 5 num num num * T num + num * num
309 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * 4 - 5 num num num * T num + num * num
310 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * 4 - 5 num num Backtrack ! num + num * num
311 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * 4 - 5 num num num + num * num
312 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * 4 - 5 num num num num + num * num
313 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * 4 - 5 num num num num + num * num
314 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * 4 - 5 num num num num + num * num
315 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * 4 - 5 num num num 4 - 5 T T(num) num + num * num
316 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * 4 - 5 num num num 4 - 5 T T(num) 2 - 5 T T(num, *, T) num + num * num
317 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * 4 - 5 num num num 4 - 5 T T(num) 2 - 5 T T(num, *, T) num + num * num
318 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * 4 - 5 num num num 4 - 5 T T(num) 2 - 5 T T(num, *, T) num + num * num
319 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + T + E 2 - 3 num num 3 - 4 * * 4 - 5 num num num Backtrack ! 4 - 5 T T(num) 2 - 5 T T(num, *, T) num + num * num
320 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + T + E 2 - 3 num num 3 - 4 * * 4 - 5 num num 4 - 5 T T(num) num 2 - 5 T T(num, *, T) num + num * num
321 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + T + E 2 - 3 num num 3 - 4 * * 4 - 5 num num 4 - 5 T T(num) num T 2 - 5 T T(num, *, T) num + num * num
322 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + T + E 2 - 3 num num 3 - 4 * * 4 - 5 num num 4 - 5 T T(num) num T 2 - 5 T T(num, *, T) num + num * num
323 E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num T + E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + num T 2 - 3 num num 3 - 4 * * 4 - 5 num num num * T 4 - 5 T T(num) 2 - 5 T T(num, *, T) num + num * num num
324 E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num T + E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + num T 2 - 3 num num 3 - 4 * * 4 - 5 num num num * T 4 - 5 T T(num) 2 - 5 T T(num, *, T) 2 - 5 E E(T) num + num * num num
325 E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num T + E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + num T 2 - 3 num num 3 - 4 * * 4 - 5 num num num * T 4 - 5 T T(num) 2 - 5 T T(num, *, T) 2 - 5 E E(T) num + num 0 - 5 * E num + E) E(T num
326 Packrat parsing •  (PEG) •  ☓
327 E→E+T|T Packrat parsing + T → T * num | num E num + num * num
328 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL FAIL num + num * num
329 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL E + T num + num * num
330 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL E + T num + num * num
331 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL E + T num + num * num
332 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL E + T num + num * num
333 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL num + num * num
334 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL T num + num * num
335 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL 0 - 0 T FAIL T FAIL num + num * num
336 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL 0 - 0 T FAIL T T * num num + num * num
337 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL 0 - 0 T FAIL T T * num num + num * num
338 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL 0 - 0 T FAIL T T * num num + num * num
339 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL 0 - 0 T FAIL T T * num num + num * num
340 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL 0 - 0 T FAIL T num + num * num
341 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL 0 - 0 T FAIL T num num + num * num
342 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL 0 - 0 T FAIL T num num + num * num
343 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL 0 - 0 T FAIL T 0 - 1 num num num num + num * num
344 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL 0 - 1 T T(num) T 0 - 1 num num num num + num * num
345 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 0 - 1 T T(num) T 0 - 1 num num Backtrack ! num + num * num
346 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 0 - 1 T T(num) T 0 - 1 num num T * num num + num * num
347 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 0 - 1 T T(num) T 0 - 1 num num T * num num + num * num
348 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 ! 0 - 1 T T(num) T 0 - 1 num num T * num num + num * num
349 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 ! 0 - 1 T T(num) T 0 - 1 num num T * num num num + num * num
350 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 0 - 1 T T(num) T 0 - 1 num num T * num num num + num * num
351 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 0 - 1 T T(num) T 0 - 1 num num T * num num num + num * num
352 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 0 - 1 T T(num) T 0 - 1 num num Backtrack ! num + num * num
353 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 0 - 1 T T(num) T 0 - 1 num num num num + num * num
354 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 0 - 1 T T(num) T 0 - 1 num num num num + num * num
355 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 0 - 1 T T(num) T ! 0 - 1 num num num num + num * num
356 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 0 - 1 T T(num) T ! 0 - 1 num num num num + num * num
357 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 0 - 1 T T(num) T 0 - 1 num num num num + num * num
358 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 0 - 1 T T(num) T 0 - 1 num num ! num + num * num
359 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL 0 - 1 T T(num) T 0 - 1 num num num num + num * num
360 E→E+T|T Packrat parsing + T → T * num | num E 0 - 1 E E(T(num)) 0 - 1 T T(num) T 0 - 1 num num num num + num * num
361 E→E+T|T Packrat parsing + T → T * num | num : 1 E 0 - 1 E E(T(num)) 0 - 1 T T(num) 0 - 1 num num Backtrack ! num + num * num
362 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num num + num * num
363 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num num + num * num
364 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T ! 0 - 1 num num num + num * num
365 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T ! 0 - 1 num num T num num + num * num
366 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num T num num + num * num
367 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T num num + num * num
368 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T num num + num * num
369 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T 2 - 2 T FAIL FAIL num num + num * num
370 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T 2 - 2 T FAIL T * num num num + num * num
371 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T 2 - 2 T FAIL T * num num num + num * num
372 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T 2 - 2 T FAIL T * num num num + num * num
373 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T 2 - 2 T FAIL T * num num num + num * num
374 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T 2 - 2 T FAIL num num + num * num
375 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T num 2 - 2 T FAIL num num + num * num
376 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T num 2 - 2 T FAIL num num + num * num
377 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T num 2 - 2 T FAIL 2 - 3 num num num num + num * num
378 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T num 2 - 3 T T(num) 2 - 3 num num num num + num * num
379 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 3 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T 2 - 3 T T(num) 2 - 3 num num num Backtrack ! num + num * num
380 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 3 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 3 T T(num) 2 - 3 num num num num + num * num
381 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 3 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 3 T T(num) 2 - 3 num num num num + num * num
382 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 3 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 3 T T(num) 2 - 3 num num ! num num + num * num
383 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 3 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 3 T T(num) 2 - 3 num num ! num num num + num * num
384 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 3 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 3 T T(num) 2 - 3 num num num num num + num * num
385 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 3 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 3 T T(num) 2 - 3 num num 3 - 4 * * num num num + num * num
386 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 3 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 3 T T(num) 2 - 3 num num 3 - 4 * * num num num + num * num
387 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 3 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 3 T T(num) 2 - 3 num num 3 - 4 * * num num 4 - 5 num num num + num * num
388 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 3 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 3 T T(num) 2 - 3 num num 3 - 4 * * num num 4 - 5 num num num + num * num
389 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 3 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * num num 4 - 5 num num num + num * num
390 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T 2 - 5 T T(T(num)*num) 2 - 3 num num Backtrack ! 3 - 4 * * num 4 - 5 num num num + num * num
391 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * num 4 - 5 num num num + num * num
392 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * num 4 - 5 num num num + num * num
393 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * ! 4 - 5 num num num num + num * num
394 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * T * num ! 4 - 5 num num num num num + num * num
395 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * T * num num 4 - 5 num num num num + num * num
396 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * T * num num 4 - 5 num num num num + num * num
397 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T 2 - 5 T T(T(num)*num) 2 - 3 num num Backtrack ! 3 - 4 * * num 4 - 5 num num num + num * num
398 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * num 4 - 5 num num num + num * num
399 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * num 4 - 5 num num num + num * num
400 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * ! 4 - 5 num num num num + num * num
401 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * ! 4 - 5 num num num num + num * num
402 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * num 4 - 5 num num num + num * num
403 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num ! 1 - 2 + + T 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * num 4 - 5 num num num + num * num
404 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * num num 4 - 5 num num num + num * num
405 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * num num 4 - 5 num num num + num * num
406 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * num num 4 - 5 num num num + num * num
407 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) 0 - 1 num num 1 - 2 + + 2 - 5 T T(T(num)*num) 2 - 3 num num Backtrack ! 3 - 4 * * 4 - 5 num num num + num * num
408 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * 4 - 5 num num num + num * num
409 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * 4 - 5 num num num + num * num
410 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) E + T ! 0 - 1 num num 1 - 2 + + 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * 4 - 5 num num num + num * num
411 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) E + T ! 0 - 1 num num 1 - 2 + + E + T 2 - 5 T T(T(num)*num) 2 - 3 num num T T * num 3 - 4 * * 4 - 5 num num num num num + num * num
412 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + E + T 2 - 5 T T(T(num)*num) 2 - 3 num num T T * num 3 - 4 * * 4 - 5 num num num num num + num * num
413 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + E + T 2 - 5 T T(T(num)*num) 2 - 3 num num T T * num 3 - 4 * * 4 - 5 num num num num num + num * num
414 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) 0 - 1 num num 1 - 2 + + 2 - 5 T T(T(num)*num) 2 - 3 num num Backtrack ! 3 - 4 * * 4 - 5 num num num + num * num
415 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) T 0 - 1 num num 1 - 2 + + 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * 4 - 5 num num num + num * num
416 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) T 0 - 1 num num 1 - 2 + + 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * 4 - 5 num num num + num * num
417 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) T ! 0 - 1 num num 1 - 2 + + 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * 4 - 5 num num num + num * num
418 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) T ! 0 - 1 num num 1 - 2 + + 2 - 5 T T(T(num)*num) num 2 - 3 num num 3 - 4 * * 4 - 5 num num num + num * num
419 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) T 0 - 1 num num 1 - 2 + + 2 - 5 T T(T(num)*num) num 2 - 3 num num 3 - 4 * * 4 - 5 num num num + num * num
420 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) ! 0 - 1 num num 1 - 2 + + 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * 4 - 5 num num num + num * num
421 E→E+T|T Packrat parsing + T → T * num | num E 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * num num 4 - 5 num num num + num * num
422 LL(k) Backtrack Packrat Rats! Packrat + LR CFG&PEG ?
423 LL(k)
424 •  – p.14 •  – p.18 •  LR – p.37 •  – p.148 •  – p.150 •  – p.154 •  Backtrack parsing – p.203 •  Packrat parsing – p.280 •  Packrat parsing + – p.327 •  – p.422

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ビジュアル構文解析

  • 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
  • 195. 195 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
  • 196. 196 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
  • 197. 197 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
  • 198. 198 LL(1) •  • 
  • 199. 199 LL(1) E  →  T  +  E  |  T   T  →  num  *  T  |  num  
  • 200. 200 LL(1) E  →  T  +  E  |  T   T  →  num  *  T  |  num   E  →  T  E’   E’→  +  E  |  ε   T  →  num  *  T  |  num  
  • 201. 201 LL(1) E  →  T  +  E  |  T   T  →  num  *  T  |  num   E  →  T  E’   E  →  T  E’   E’→  +  E  |  ε   E’→  +  E  |  ε   T  →  num  T’   T  →  num  *  T  |  num   T’→  *  T  |  ε  
  • 202. 202 LL(1) E  →  T  +  E  |  T   LL(2) T  →  num  *  T  |  num   E  →  T  E’   E  →  T  E’   E’→  +  E  |  ε   E’→  +  E  |  ε   T  →  num  T’   T  →  num  *  T  |  num   T’→  *  T  |  ε  
  • 203. 203 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T 4.  T → num num + num * num
  • 204. 204 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num + num * num
  • 205. 205 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num + num * num
  • 206. 206 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num * T num + num * num
  • 207. 207 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num * T num + num * num
  • 208. 208 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num * T num + num * num
  • 209. 209 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num * T num + num * num
  • 210. 210 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num * T num + num * num
  • 211. 211 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num Backtrack ! num + num * num
  • 212. 212 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num + num * num
  • 213. 213 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num num + num * num
  • 214. 214 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num num + num * num
  • 215. 215 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num num + num * num
  • 216. 216 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num num + num * num
  • 217. 217 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num num + num * num
  • 218. 218 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num num + num * num
  • 219. 219 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num num + num * num
  • 220. 220 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num T + E num + num * num
  • 221. 221 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num T + E num + num * num
  • 222. 222 E Backtrack parsing 1.  E → T + E T + E 2.  E → T 3.  T → num * T num T + E 4.  T → num num * T num + num * num
  • 223. 223 E Backtrack parsing 1.  E → T + E T + E 2.  E → T 3.  T → num * T num T + E 4.  T → num num * T num + num * num
  • 224. 224 E Backtrack parsing 1.  E → T + E T + E 2.  E → T 3.  T → num * T num T + E 4.  T → num num * T num + num * num
  • 225. 225 E Backtrack parsing 1.  E → T + E T + E 2.  E → T 3.  T → num * T num T + E 4.  T → num num * T num + num * num
  • 226. 226 E Backtrack parsing 1.  E → T + E T + E 2.  E → T 3.  T → num * T num T + E 4.  T → num num * T num + num * num
  • 227. 227 E Backtrack parsing 1.  E → T + E T + E 2.  E → T 3.  T → num * T num T + E 4.  T → num num * T num + num * num
  • 228. 228 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num * T num + num * num
  • 229. 229 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num * T num + num * num
  • 230. 230 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num * T num + num * num
  • 231. 231 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num * T num + num * num
  • 232. 232 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num * T num + num * num
  • 233. 233 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num Backtrack ! num + num * num
  • 234. 234 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num + num * num
  • 235. 235 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num num + num * num
  • 236. 236 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num num + num * num
  • 237. 237 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num num + num * num
  • 238. 238 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num num + num * num
  • 239. 239 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num num + num * num
  • 240. 240 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num num + num * num
  • 241. 241 T + E Backtrack parsing 1.  E → T + E num T + E 2.  E → T num * T 3.  T → num * T 4.  T → num num num + num * num
  • 242. 242 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num Backtrack ! num + num * num
  • 243. 243 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num num + num * num
  • 244. 244 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num T num + num * num
  • 245. 245 Backtrack parsing 1.  E → T + E E 2.  E → T 3.  T → num * T T + E 4.  T → num num T num + num * num
  • 246. 246 E Backtrack parsing 1.  E → T + E T + E 2.  E → T 3.  T → num * T num T 4.  T → num num * T num + num * num
  • 247. 247 E Backtrack parsing 1.  E → T + E T + E 2.  E → T 3.  T → num * T num T 4.  T → num num * T num + num * num
  • 248. 248 E Backtrack parsing 1.  E → T + E T + E 2.  E → T 3.  T → num * T num T 4.  T → num num * T num + num * num
  • 249. 249 E Backtrack parsing 1.  E → T + E T + E 2.  E → T 3.  T → num * T num T 4.  T → num num * T num + num * num
  • 250. 250 E Backtrack parsing 1.  E → T + E T + E 2.  E → T 3.  T → num * T num T 4.  T → num num * T num + num * num
  • 251. 251 E Backtrack parsing 1.  E → T + E T + E 2.  E → T 3.  T → num * T num T 4.  T → num num * T num + num * num
  • 252. 252 T + E Backtrack parsing T 1.  E → T + E num 2.  E → T num * T 3.  T → num * T 4.  T → num num * T num + num * num
  • 253. 253 T + E Backtrack parsing T 1.  E → T + E num 2.  E → T num * T 3.  T → num * T 4.  T → num num * T num + num * num
  • 254. 254 T + E Backtrack parsing T 1.  E → T + E num 2.  E → T num * T 3.  T → num * T 4.  T → num num * T num + num * num
  • 255. 255 T + E Backtrack parsing T 1.  E → T + E num 2.  E → T num * T 3.  T → num * T 4.  T → num num * T num + num * num
  • 256. 256 T + E Backtrack parsing T 1.  E → T + E num 2.  E → T num * T 3.  T → num * T 4.  T → num num * T num + num * num
  • 257. 257 T + E Backtrack parsing T 1.  E → T + E num 2.  E → T num * T 3.  T → num * T 4.  T → num Backtrack ! num + num * num
  • 258. 258 T + E Backtrack parsing T 1.  E → T + E num 2.  E → T num * T 3.  T → num * T 4.  T → num num + num * num
  • 259. 259 T + E Backtrack parsing T 1.  E → T + E num 2.  E → T num * T 3.  T → num * T 4.  T → num num num + num * num
  • 260. 260 T + E Backtrack parsing T 1.  E → T + E num 2.  E → T num * T 3.  T → num * T 4.  T → num num num + num * num
  • 261. 261 T + E Backtrack parsing T 1.  E → T + E num 2.  E → T num * T 3.  T → num * T 4.  T → num num num + num * num
  • 262. 262 T + E Backtrack parsing T 1.  E → T + E num 2.  E → T num * T 3.  T → num * T 4.  T → num num num + num * num
  • 263. 263 T + E Backtrack parsing T 1.  E → T + E num 2.  E → T num * T 3.  T → num * T 4.  T → num num num + num * num
  • 264. 264 E Backtrack parsing 1.  E → T + E T + E 2.  E → T T 3.  T → num * T num 4.  T → num num * T num num + num * num
  • 265. 265 E Backtrack parsing 1.  E → T + E T + E 2.  E → T T 3.  T → num * T num 4.  T → num num * T num num + num * num
  • 266. 266 E 1.   E  →  E  +  T   2.   E  →  T   3.   T  →  T  *  num   4.   T  →  num
  • 267. 267 E 1.   E  →  E  +  T   E + T 2.   E  →  T   3.   T  →  T  *  num   4.   T  →  num
  • 268. 268 E 1.   E  →  E  +  T   E + T 2.   E  →  T   3.   T  →  T  *  num   4.   T  →  num
  • 269. 269 E 1.   E  →  E  +  T   E + T 2.   E  →  T   3.   T  →  T  *  num   E + T 4.   T  →  num
  • 270. 270 E 1.   E  →  E  +  T   E + T 2.   E  →  T   3.   T  →  T  *  num   E + T 4.   T  →  num
  • 271. 271 E 1.   E  →  E  +  T   E + T 2.   E  →  T   3.   T  →  T  *  num   E + T 4.   T  →  num E + T
  • 272. 272 E 1.   E  →  E  +  T   E + T 2.   E  →  T   3.   T  →  T  *  num   E + T 4.   T  →  num E + T
  • 273. 273 E 1.   E  →  E  +  T   E + T 2.   E  →  T   3.   T  →  T  *  num   E + T 4.   T  →  num E + T E + T
  • 274. 274 E 1.   E  →  E  +  T   E + T 2.   E  →  T   3.   T  →  T  *  num   E + T 4.   T  →  num E + T E + T
  • 275. 275 E 1.   E  →  E  +  T   E + T 2.   E  →  T   3.   T  →  T  *  num   E + T 4.   T  →  num E + T E + T
  • 276. 276  E  →  E  +  T  |  T    T  →  T  *  num  |  num  
  • 277. 277  E  →  E  +  T  |  T    T  →  T  *  num  |  num    E  →  T  E’    E’→  +  T  E’  |  ε    T  →  T  *  num  |  num  
  • 278. 278  E  →  E  +  T  |  T    T  →  T  *  num  |  num    E  →  T  E’    E’→  +  T  E’  |  ε    T  →  T  *  num  |  num  
  • 279. 279 E  → T  {  +  T  }   T  →  num  {  *  num  }     OK  E  →  E  +  T  |  T    T  →  T  *  num  |  num    E  →  T  E’    E  →  T  E’    E’→  +  T  E’  |  ε    E’→  +  T  E’  |  ε    T  →  num  T’    T  →  T  *  num  |  num    T’→  *  num  T’  |  ε  
  • 280. 280 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E num + num * num
  • 281. 281 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E T + E num + num * num
  • 282. 282 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E T + E num + num * num
  • 283. 283 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E T + E num * T num + num * num
  • 284. 284 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E T + E num * T num + num * num
  • 285. 285 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num T + E num * T num + num * num
  • 286. 286 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num T + E num * T num + num * num
  • 287. 287 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num T + E Backtrack ! num + num * num
  • 288. 288 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num T + E num + num * num
  • 289. 289 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num T + E num num + num * num
  • 290. 290 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num T + E num num + num * num
  • 291. 291 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num T + E num num + num * num
  • 292. 292 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num T + E num num + num * num
  • 293. 293 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num 0 - 1 T T(num) T + E num num + num * num
  • 294. 294 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num 0 - 1 T T(num) T + E num num + num * num
  • 295. 295 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + T + E num num + num * num
  • 296. 296 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + T + E num num + num * num
  • 297. 297 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + T + E num T + E num + num * num
  • 298. 298 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + T + E num T + E num + num * num
  • 299. 299 E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num T + E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + num T + E num * T num + num * num
  • 300. 300 E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num T + E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + num T + E num * T num + num * num
  • 301. 301 E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num T + E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + num T + E 2 - 3 num num num * T num + num * num
  • 302. 302 E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num T + E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + num T + E 2 - 3 num num num * T num + num * num
  • 303. 303 E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num T + E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + num T + E 2 - 3 num num 3 - 4 * * num * T num + num * num
  • 304. 304 E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num T + E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + num T + E 2 - 3 num num 3 - 4 * * num * T num + num * num
  • 305. 305 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * num * T num + num * num
  • 306. 306 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * num * T num + num * num
  • 307. 307 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * 4 - 5 num num num * T num + num * num
  • 308. 308 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * 4 - 5 num num num * T num + num * num
  • 309. 309 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * 4 - 5 num num num * T num + num * num
  • 310. 310 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * 4 - 5 num num Backtrack ! num + num * num
  • 311. 311 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * 4 - 5 num num num + num * num
  • 312. 312 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * 4 - 5 num num num num + num * num
  • 313. 313 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * 4 - 5 num num num num + num * num
  • 314. 314 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * 4 - 5 num num num num + num * num
  • 315. 315 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * 4 - 5 num num num 4 - 5 T T(num) num + num * num
  • 316. 316 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * 4 - 5 num num num 4 - 5 T T(num) 2 - 5 T T(num, *, T) num + num * num
  • 317. 317 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * 4 - 5 num num num 4 - 5 T T(num) 2 - 5 T T(num, *, T) num + num * num
  • 318. 318 T + E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num num T + E 0 - 1 num num 0 - 1 T T(num) num * T 1 - 2 + + 2 - 3 num num 3 - 4 * * 4 - 5 num num num 4 - 5 T T(num) 2 - 5 T T(num, *, T) num + num * num
  • 319. 319 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + T + E 2 - 3 num num 3 - 4 * * 4 - 5 num num num Backtrack ! 4 - 5 T T(num) 2 - 5 T T(num, *, T) num + num * num
  • 320. 320 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + T + E 2 - 3 num num 3 - 4 * * 4 - 5 num num 4 - 5 T T(num) num 2 - 5 T T(num, *, T) num + num * num
  • 321. 321 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + T + E 2 - 3 num num 3 - 4 * * 4 - 5 num num 4 - 5 T T(num) num T 2 - 5 T T(num, *, T) num + num * num
  • 322. 322 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + T + E 2 - 3 num num 3 - 4 * * 4 - 5 num num 4 - 5 T T(num) num T 2 - 5 T T(num, *, T) num + num * num
  • 323. 323 E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num T + E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + num T 2 - 3 num num 3 - 4 * * 4 - 5 num num num * T 4 - 5 T T(num) 2 - 5 T T(num, *, T) num + num * num num
  • 324. 324 E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num T + E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + num T 2 - 3 num num 3 - 4 * * 4 - 5 num num num * T 4 - 5 T T(num) 2 - 5 T T(num, *, T) 2 - 5 E E(T) num + num * num num
  • 325. 325 E 1.  E → T + E 3.  T → num * T Packrat parsing 2.  E → T 4.  T → num T + E 0 - 1 num num 0 - 1 T T(num) 1 - 2 + + num T 2 - 3 num num 3 - 4 * * 4 - 5 num num num * T 4 - 5 T T(num) 2 - 5 T T(num, *, T) 2 - 5 E E(T) num + num 0 - 5 * E num + E) E(T num
  • 326. 326 Packrat parsing •  (PEG) •  ☓
  • 327. 327 E→E+T|T Packrat parsing + T → T * num | num E num + num * num
  • 328. 328 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL FAIL num + num * num
  • 329. 329 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL E + T num + num * num
  • 330. 330 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL E + T num + num * num
  • 331. 331 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL E + T num + num * num
  • 332. 332 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL E + T num + num * num
  • 333. 333 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL num + num * num
  • 334. 334 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL T num + num * num
  • 335. 335 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL 0 - 0 T FAIL T FAIL num + num * num
  • 336. 336 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL 0 - 0 T FAIL T T * num num + num * num
  • 337. 337 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL 0 - 0 T FAIL T T * num num + num * num
  • 338. 338 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL 0 - 0 T FAIL T T * num num + num * num
  • 339. 339 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL 0 - 0 T FAIL T T * num num + num * num
  • 340. 340 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL 0 - 0 T FAIL T num + num * num
  • 341. 341 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL 0 - 0 T FAIL T num num + num * num
  • 342. 342 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL 0 - 0 T FAIL T num num + num * num
  • 343. 343 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL 0 - 0 T FAIL T 0 - 1 num num num num + num * num
  • 344. 344 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL 0 - 1 T T(num) T 0 - 1 num num num num + num * num
  • 345. 345 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 0 - 1 T T(num) T 0 - 1 num num Backtrack ! num + num * num
  • 346. 346 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 0 - 1 T T(num) T 0 - 1 num num T * num num + num * num
  • 347. 347 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 0 - 1 T T(num) T 0 - 1 num num T * num num + num * num
  • 348. 348 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 ! 0 - 1 T T(num) T 0 - 1 num num T * num num + num * num
  • 349. 349 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 ! 0 - 1 T T(num) T 0 - 1 num num T * num num num + num * num
  • 350. 350 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 0 - 1 T T(num) T 0 - 1 num num T * num num num + num * num
  • 351. 351 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 0 - 1 T T(num) T 0 - 1 num num T * num num num + num * num
  • 352. 352 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 0 - 1 T T(num) T 0 - 1 num num Backtrack ! num + num * num
  • 353. 353 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 0 - 1 T T(num) T 0 - 1 num num num num + num * num
  • 354. 354 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 0 - 1 T T(num) T 0 - 1 num num num num + num * num
  • 355. 355 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 0 - 1 T T(num) T ! 0 - 1 num num num num + num * num
  • 356. 356 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 0 - 1 T T(num) T ! 0 - 1 num num num num + num * num
  • 357. 357 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 0 - 1 T T(num) T 0 - 1 num num num num + num * num
  • 358. 358 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL : 1 0 - 1 T T(num) T 0 - 1 num num ! num + num * num
  • 359. 359 E→E+T|T Packrat parsing + T → T * num | num E 0 - 0 E FAIL 0 - 1 T T(num) T 0 - 1 num num num num + num * num
  • 360. 360 E→E+T|T Packrat parsing + T → T * num | num E 0 - 1 E E(T(num)) 0 - 1 T T(num) T 0 - 1 num num num num + num * num
  • 361. 361 E→E+T|T Packrat parsing + T → T * num | num : 1 E 0 - 1 E E(T(num)) 0 - 1 T T(num) 0 - 1 num num Backtrack ! num + num * num
  • 362. 362 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num num + num * num
  • 363. 363 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num num + num * num
  • 364. 364 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T ! 0 - 1 num num num + num * num
  • 365. 365 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T ! 0 - 1 num num T num num + num * num
  • 366. 366 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num T num num + num * num
  • 367. 367 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T num num + num * num
  • 368. 368 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T num num + num * num
  • 369. 369 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T 2 - 2 T FAIL FAIL num num + num * num
  • 370. 370 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T 2 - 2 T FAIL T * num num num + num * num
  • 371. 371 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T 2 - 2 T FAIL T * num num num + num * num
  • 372. 372 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T 2 - 2 T FAIL T * num num num + num * num
  • 373. 373 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T 2 - 2 T FAIL T * num num num + num * num
  • 374. 374 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T 2 - 2 T FAIL num num + num * num
  • 375. 375 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T num 2 - 2 T FAIL num num + num * num
  • 376. 376 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T num 2 - 2 T FAIL num num + num * num
  • 377. 377 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T num 2 - 2 T FAIL 2 - 3 num num num num + num * num
  • 378. 378 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T num 2 - 3 T T(num) 2 - 3 num num num num + num * num
  • 379. 379 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 3 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T 2 - 3 T T(num) 2 - 3 num num num Backtrack ! num + num * num
  • 380. 380 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 3 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 3 T T(num) 2 - 3 num num num num + num * num
  • 381. 381 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 3 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 3 T T(num) 2 - 3 num num num num + num * num
  • 382. 382 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 3 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 3 T T(num) 2 - 3 num num ! num num + num * num
  • 383. 383 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 3 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 3 T T(num) 2 - 3 num num ! num num num + num * num
  • 384. 384 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 3 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 3 T T(num) 2 - 3 num num num num num + num * num
  • 385. 385 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 3 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 3 T T(num) 2 - 3 num num 3 - 4 * * num num num + num * num
  • 386. 386 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 3 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 3 T T(num) 2 - 3 num num 3 - 4 * * num num num + num * num
  • 387. 387 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 3 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 3 T T(num) 2 - 3 num num 3 - 4 * * num num 4 - 5 num num num + num * num
  • 388. 388 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 3 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 3 T T(num) 2 - 3 num num 3 - 4 * * num num 4 - 5 num num num + num * num
  • 389. 389 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 3 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * num num 4 - 5 num num num + num * num
  • 390. 390 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T 2 - 5 T T(T(num)*num) 2 - 3 num num Backtrack ! 3 - 4 * * num 4 - 5 num num num + num * num
  • 391. 391 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * num 4 - 5 num num num + num * num
  • 392. 392 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * num 4 - 5 num num num + num * num
  • 393. 393 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * ! 4 - 5 num num num num + num * num
  • 394. 394 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * T * num ! 4 - 5 num num num num num + num * num
  • 395. 395 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * T * num num 4 - 5 num num num num + num * num
  • 396. 396 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * T * num num 4 - 5 num num num num + num * num
  • 397. 397 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T 2 - 5 T T(T(num)*num) 2 - 3 num num Backtrack ! 3 - 4 * * num 4 - 5 num num num + num * num
  • 398. 398 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * num 4 - 5 num num num + num * num
  • 399. 399 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * num 4 - 5 num num num + num * num
  • 400. 400 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * ! 4 - 5 num num num num + num * num
  • 401. 401 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * ! 4 - 5 num num num num + num * num
  • 402. 402 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * num 4 - 5 num num num + num * num
  • 403. 403 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) : 5 0 - 1 T T(num) E + T 0 - 1 num num ! 1 - 2 + + T 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * num 4 - 5 num num num + num * num
  • 404. 404 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * num num 4 - 5 num num num + num * num
  • 405. 405 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 1 E E(T(num)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * num num 4 - 5 num num num + num * num
  • 406. 406 E→E+T|T Packrat parsing + T → T * num | num E : 1 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * num num 4 - 5 num num num + num * num
  • 407. 407 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) 0 - 1 num num 1 - 2 + + 2 - 5 T T(T(num)*num) 2 - 3 num num Backtrack ! 3 - 4 * * 4 - 5 num num num + num * num
  • 408. 408 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * 4 - 5 num num num + num * num
  • 409. 409 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * 4 - 5 num num num + num * num
  • 410. 410 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) E + T ! 0 - 1 num num 1 - 2 + + 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * 4 - 5 num num num + num * num
  • 411. 411 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) E + T ! 0 - 1 num num 1 - 2 + + E + T 2 - 5 T T(T(num)*num) 2 - 3 num num T T * num 3 - 4 * * 4 - 5 num num num num num + num * num
  • 412. 412 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + E + T 2 - 5 T T(T(num)*num) 2 - 3 num num T T * num 3 - 4 * * 4 - 5 num num num num num + num * num
  • 413. 413 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + E + T 2 - 5 T T(T(num)*num) 2 - 3 num num T T * num 3 - 4 * * 4 - 5 num num num num num + num * num
  • 414. 414 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) 0 - 1 num num 1 - 2 + + 2 - 5 T T(T(num)*num) 2 - 3 num num Backtrack ! 3 - 4 * * 4 - 5 num num num + num * num
  • 415. 415 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) T 0 - 1 num num 1 - 2 + + 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * 4 - 5 num num num + num * num
  • 416. 416 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) T 0 - 1 num num 1 - 2 + + 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * 4 - 5 num num num + num * num
  • 417. 417 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) T ! 0 - 1 num num 1 - 2 + + 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * 4 - 5 num num num + num * num
  • 418. 418 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) T ! 0 - 1 num num 1 - 2 + + 2 - 5 T T(T(num)*num) num 2 - 3 num num 3 - 4 * * 4 - 5 num num num + num * num
  • 419. 419 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) T 0 - 1 num num 1 - 2 + + 2 - 5 T T(T(num)*num) num 2 - 3 num num 3 - 4 * * 4 - 5 num num num + num * num
  • 420. 420 E→E+T|T Packrat parsing + T → T * num | num E : 5 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) ! 0 - 1 num num 1 - 2 + + 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * 4 - 5 num num num + num * num
  • 421. 421 E→E+T|T Packrat parsing + T → T * num | num E 0 - 5 E E(E(...)+T(...)) 0 - 1 T T(num) E + T 0 - 1 num num 1 - 2 + + T T * num 2 - 5 T T(T(num)*num) 2 - 3 num num 3 - 4 * * num num 4 - 5 num num num + num * num
  • 422. 422 LL(k) Backtrack Packrat Rats! Packrat + LR CFG&PEG ?
  • 423. 423 LL(k)
  • 424. 424 •  – p.14 •  – p.18 •  LR – p.37 •  – p.148 •  – p.150 •  – p.154 •  Backtrack parsing – p.203 •  Packrat parsing – p.280 •  Packrat parsing + – p.327 •  – p.422