LR(1) Parser Example

2011-04-19T05:24:08+08:00

Terminal Symbols: 6个

BOF, EOF, id, -, (, )

Nonterminal Symbols: 3个

S, expr, term

Start Symbol:

S

Production Rules: 5个

0 S BOF expr EOF

1 expr term

2 expr expr - term

3 term id

4 term ( expr )

Total State: 11个 (0 to 11)
Total Transitions: 28个

State Symbol Action

0 BOF shift to state 6

1 ( shift to state 3

1 id shift to state 2

1 term shift to state 8

3 ( shift to state 3

3 expr shift to state 7

3 id shift to state 2

3 term shift to state 4

6 ( shift to state 3

6 expr shift to state 10

6 id shift to state 2

6 term shift to state 4

7 ) shift to state 9

7 - shift to state 1

10 - shift to state 1

10 EOF shift to state 5

2 ) reduce by rule 3

2 - reduce by rule 3

2 EOF reduce by rule 3

4 ) reduce by rule 1

4 - reduce by rule 1

4 EOF reduce by rule 1

8 ) reduce by rule 2

8 - reduce by rule 2

8 EOF reduce by rule 2

9 ) reduce by rule 4

9 - reduce by rule 4

9 EOF reduce by rule 4

String to Parse:

BOF id - ( id ) - id EOF

Parse Step:
蓝色的行是Shift, 灰色的行是Reduce
Reduce的次数取决于Production Rule RHS的长度
当前Symbol所对应的State,

							State Stack (At EOL)	Description
S0							0	Start
BOF	S6						0 6	S0 BOF S6
	id	S2					0 6 2	S6 id S2
	R3	-					0 6	S2 - Reduce by rule #3 (replace id with term)
	term	S4					0 6 4	S6 term S4
	R1	-					0 6	S4 - Reduce by rule #1 (replace term with expr)
	expr	S10					0 6 10	S6 expr S10
		-	S1				0 6 10 1	S10 - S1
			(	S3			0 6 10 1 3	S1 ( S3
				id	S2		0 6 10 1 3 2	S3 id S2
				R3	)		0 6 10 1 3	S2 ) Reduce by rule #3 (replace id with term)
				term	S4		0 6 10 1 3 4	S3 term S4
				R1	)		0 6 10 1 3	S4 ) Reduce by rule #1 (replace term with expr)
				expr	S7		0 6 10 1 3 7	S3 expr S7
					)	S9	0 6 10 1 3 7 9	S7 ) S9
			R4	R4	R4	-	0 6 10 1	S9 - Reduce by rule #4 (repace "( expr )" with term)
			term	S8			0 6 10 1 8	S1 term S8
	R2	R2	R2	-			0 6	S8 - Reduce by rule #2 (replace "expr - term" with expr)
	expr	S10					0 6 10	S6 expr S10
		-	S1				0 6 10 1	S10 - S1
			id	S2			0 6 10 1 2	S1 id S2
			R3	EOF			0 6 10 1	S2 EOF Reduce by rule #3 (replace id with term)
			term	S8			0 6 10 1 8	S1 term S8
	R2	R2	R2	EOF			0 6	S8 EOF Reduce by rule #2 (replace "expr - term" with expr)
	expr	S10					0 6 10	S6 expr S10
		EOF	S5				Final S5	S10 EOF S5

原题来源: http://www.student.cs.uwaterloo.ca/~cs241/parsing/lr1.html

0	S BOF expr EOF
1	expr term
2	expr expr - term
3	term id
4	term ( expr )

State	Symbol	Action
0	BOF	shift to state 6
1	(	shift to state 3
1	id	shift to state 2
1	term	shift to state 8
3	(	shift to state 3
3	expr	shift to state 7
3	id	shift to state 2
3	term	shift to state 4
6	(	shift to state 3
6	expr	shift to state 10
6	id	shift to state 2
6	term	shift to state 4
7	)	shift to state 9
7	-	shift to state 1
10	-	shift to state 1
10	EOF	shift to state 5
2	)	reduce by rule 3
2	-	reduce by rule 3
2	EOF	reduce by rule 3
4	)	reduce by rule 1
4	-	reduce by rule 1
4	EOF	reduce by rule 1
8	)	reduce by rule 2
8	-	reduce by rule 2
8	EOF	reduce by rule 2
9	)	reduce by rule 4
9	-	reduce by rule 4
9	EOF	reduce by rule 4

某储备粮的“学习笔记” - parse

LR(1) Parser Example