shift-reduceparsers61移位歸約解析器

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1、1,1,Outline,6.0 Introduction 6.1 Shift-Reduce Parsers 6.2 LR Parsers 6.3 LR(1) Parsing 6.4 SLR(1)Parsing 6.5 LALR(1) 6.6 Calling Semantic Routines in Shift-Reduce Parsers 6.7 Using a Parser Generator (TA course) 6.8 Optimizing Parse Tables 6.9 Practical LR(1) Parsers 6.10 Properties of LR Parsing 6.

2、11 LL(1) or LAlR(1) , That is the question 6.12 Other Shift-Reduce Technique,2,LR(1) Parsing (1),An LR(1) configuration, or item is of the form AX1X2Xi Xi+1 Xj, l where l Vt The look ahead component l represents a possible look-ahead after the entire right-hand side has been matched The appears as l

3、ook-ahead only for the augmenting production because there is no look-ahead after the end-marker We use the following notation to represent the set of LR(1) configurations that shared the same dotted production AX1X2Xi Xi+1 Xj, l1lm =AX1X2Xi Xi+1 Xj, l1 AX1X2Xi Xi+1 Xj, l2 AX1X2Xi Xi+1 Xj, lm,3,LR

4、(1) Parsing (2),LR(1) There are many more distinct LR(1) configurations than LR(0) configurations. In fact, the major difficulty with LR(1) parsers is not their power but rather finding ways to represent them in storage-efficient ways. Parsing begins with the configuration : closure1(S $, ),Configu

5、ration_set closure1 (configuration_set s) configuration_set s = s ; do if( B A , l s for A Vn ) /* * Predict productions with A as the left-hand side. * Possible lookaheads are First(l ) */ Add all configurations of the form A , u where u First(l ) to s while (more new config

6、urations can be added) ; return s; ,for grammar G2 : 1. SE$ 2.EE+T 3.ET 4.T id 5.T (E),closure1(S E$, )= S E$, E E+T,$+ E T,$+ T id,$+ T (E),$+ ,4,LR(1) Parsing (3),Tracing Example,for grammar G2 : 1. SE$ 2.EE+T 3.ET 4.T id 5.T (E),closure1(S E$, ),S E$,,,E E+T,$ E T,$,,T id,$ T (E),$,,E

7、E+T,+ E T,+,,T id,+ T (E),+,,closure1(S E$, )= S E$, E E+T,$+ E T,$+ T id,$+ T (E),$+ ,5,LR(1) Parsing (4),Given an LR(1) configuration set s We compute its successor, s, under a symbol X go_to1(s,X),Configuration_set goto1 (configuration_set s , symbol x) Sb = ; for (each configuration c s

8、) if( c is of the form A x , l) //In goto0 if( each configuration c s) Add A x , l to sb ; /* * That is, we advance the past the symbol X, * if possible. Configurations not having a * dot preceding an X are not included in sb . */ /* Add new predictions to sb via closure1. */ return closure

9、1(sb) ; ,6,LR(1) Parsing (5),LR(1) We can build a finite automata that is analogue of the LR(0) CFSM LR(1) FSM, LR(1) machine The relationship between CFSM and LR(1) macine By merging LR(1) machines configuration sets, we can obtain CFSM,void_build_LR1(void) Create the Start State of FSM; Label it

10、with s0 Put s0 into an initially empty set , S. while (S is nonempty) Remove a configuration set s from S; /* Consider both terminals and non-terminals */ for ( X in Symbols) if(go_to1(s,X) does not label a FSM state) Create a new FSM state and label it with go_to1(s , X) into S; Put go_

11、to1(s , X) into S; Create a transition under X from the state s labels to the state go_to1 (s , X) labels; ,Tracing Example: for grammar G3 : 1.S E $ 2.E E + T 3.E T 4.T T * P 5.T P 6.P id 7.P ( E ),7,state 0 S E$ , E E+T,$+ E T ,$+ T T*P ,$+* T P ,$+* P id ,$+* P (E) ,$+*,E,,P,,id

12、,,,T,,(,8,state 0 S E$ , E E+T,$+ E T ,$+ T T*P ,$+* T P ,$+* P id ,$+* P (E) ,$+*,E,,P,,id,,,T,state 1 S E $ , E E +T,$+,,(,9,state 0 S E$ , E E+T,$+ E T ,$+ T T*P ,$+* T P ,$+* P id ,$+* P (E) ,$+*,E,,P,,id,,,T,state 1 S E $ , E E +T,$+,,$,state 2 //Accept S E $ ,,,(,10,state

13、0 S E$ , E E+T,$+ E T ,$+ T T*P ,$+* T P ,$+* P id ,$+* P (E) ,$+*,E,,P,,id,,,T,state 1 S E $ , E E +T,$+,,+,$,state 2 //Accept S E $ ,,,state 3 E E+ T,$+ T T*P ,$+* T P ,$+* P id ,$+* P (E) ,$+*,,,,,P,T,id,(,,(,11,state 0 S E$ , E E+T,$+ E T ,$+ T T*P ,$+* T P ,$+* P id ,$+*

14、 P (E) ,$+*,E,,P,,id,,,T,state 1 S E $ , E E +T,$+,,+,$,state 2 //Accept S E $ ,,,state 3 E E+ T,$+ T T*P ,$+* T P ,$+* P id ,$+* P (E) ,$+*,,,,,P,T,id,(,state 4 T P ,$+*,,(,12,state 0 S E$ , E E+T,$+ E T ,$+ T T*P ,$+* T P ,$+* P id ,$+* P (E) ,$+*,E,,P,,id,,,T,state 1 S E $ , E

15、E +T,$+,,+,$,state 2 //Accept S E $ ,,,state 3 E E+ T,$+ T T*P ,$+* T P ,$+* P id ,$+* P (E) ,$+*,,,,P,T,id,(,state 4 T P ,$+*,state 5 P id ,$+*,,,(,13,state 0 S E$ , E E+T,$+ E T ,$+ T T*P ,$+* T P ,$+* P id ,$+* P (E) ,$+*,E,,P,,id,,,T,state 1 S E $ , E E +T,$+,,+,$,state 2 //Acc

16、ept S E $ ,,,state 3 E E+ T,$+ T T*P ,$+* T P ,$+* P id ,$+* P (E) ,$+*,,,P,T,id,(,state 4 T P ,$+*,state 5 P id ,$+*,,state 6 P ( E) ,$+* E E+T,)+ E T ,)+ T T*P ,)+* T P ,)+* P id ,)+* P (E) ,)+*,,,(,,E,,T,,P,,id,,(,,Be careful of look-ahead !!,14,state 0 S E$ , E E+T,$+ E T ,$+

17、 T T*P ,$+* T P ,$+* P id ,$+* P (E) ,$+*,E,,P,,id,,,T,state 1 S E $ , E E +T,$+,,+,$,state 2 //Accept S E $ ,,,state 3 E E+ T,$+ T T*P ,$+* T P ,$+* P id ,$+* P (E) ,$+*,,,P,T,id,(,state 4 T P ,$+*,state 5 P id ,$+*,,state 6 P ( E) ,$+* E E+T,)+ E T ,)+ T T*P ,)+* T P ,)+* P id ,

18、)+* P (E) ,)+*,,,(,state 7 E T ,$+ T T *P,$+*,,E,,T,,P,,id,,(,,*,15,state 0 S E$ , E E+T,$+ E T ,$+ T T*P ,$+* T P ,$+* P id ,$+* P (E) ,$+*,E,,P,,id,,,T,state 1 S E $ , E E +T,$+,,+,$,state 2 //Accept S E $ ,,,state 3 E E+ T,$+ T T*P ,$+* T P ,$+* P id ,$+* P (E) ,$+*,,,P,T,id,(,st

19、ate 4 T P ,$+*,state 5 P id ,$+*,,state 6 P ( E) ,$+* E E+T,)+ E T ,)+ T T*P ,)+* T P ,)+* P id ,)+* P (E) ,)+*,,,(,state 7 E T ,$+ T T *P,$+*,,E,,T,,P,,id,,(,,*,state 8 T T* P,$+* P id ,$+* P (E) ,$+*,,id,,P,,(,16,state 0 S E$ , E E+T,$+ E T ,$+ T T*P ,$+* T P ,$+* P id ,$+* P

20、(E) ,$+*,E,,P,,id,,,T,state 1 S E $ , E E +T,$+,,+,$,state 2 //Accept S E $ ,,,state 3 E E+ T,$+ T T*P ,$+* T P ,$+* P id ,$+* P (E) ,$+*,,,P,T,id,(,state 4 T P ,$+*,state 5 P id ,$+*,,state 6 P ( E) ,$+* E E+T,)+ E T ,)+ T T*P ,)+* T P ,)+* P id ,)+* P (E) ,)+*,,,(,state 7 E T ,$+ T

21、 T *P,$+*,,E,,T,,P,,id,,(,,*,state 8 T T* P,$+* P id ,$+* P (E) ,$+*,,id,,P,,(,state 9 T T* P ,$+*,17,state 0 S E$ , E E+T,$+ E T ,$+ T T*P ,$+* T P ,$+* P id ,$+* P (E) ,$+*,E,,P,,id,,,T,state 1 S E $ , E E +T,$+,,+,$,state 2 //Accept S E $ ,,,state 3 E E+ T,$+ T T*P ,$+* T P ,$+*

22、 P id ,$+* P (E) ,$+*,,,P,T,id,(,state 4 T P ,$+*,state 5 P id ,$+*,,state 6 P ( E) ,$+* E E+T,)+ E T ,)+ T T*P ,)+* T P ,)+* P id ,)+* P (E) ,)+*,,,(,state 7 E T ,$+ T T *P,$+*,,E,,T,,P,,,*,state 8 T T* P,$+* P id ,$+* P (E) ,$+*,,id,,P,,(,state 9 T T* P ,$+*,state 10 P id ,)+*,(,,,

23、,,id,18,state 0 S E$ , E E+T,$+ E T ,$+ T T*P ,$+* T P ,$+* P id ,$+* P (E) ,$+*,E,,P,,id,,,T,state 1 S E $ , E E +T,$+,,+,$,state 2 //Accept S E $ ,,,state 3 E E+ T,$+ T T*P ,$+* T P ,$+* P id ,$+* P (E) ,$+*,,,P,T,id,(,state 4 T P ,$+*,state 5 P id ,$+*,,state 6 P ( E) ,$+* E E

24、+T,)+ E T ,)+ T T*P ,)+* T P ,)+* P id ,)+* P (E) ,)+*,,,(,state 7 E T ,$+ T T *P,$+*,,E,,T,,P,,,*,state 8 T T* P,$+* P id ,$+* P (E) ,$+*,,id,,P,,(,state 9 T T* P ,$+*,state 10 P id ,)+*,(,,,,,id,state 11 E E+ T ,$+ T T *P,$+*,,,*,State 8,19,state 0 S E$ , E E+T,$+ E T ,$+ T T*P ,$

25、+* T P ,$+* P id ,$+* P (E) ,$+*,E,,P,,id,,,T,state 1 S E $ , E E +T,$+,,+,$,state 2 //Accept S E $ ,,,state 3 E E+ T,$+ T T*P ,$+* T P ,$+* P id ,$+* P (E) ,$+*,,,P,T,id,(,state 4 T P ,$+*,state 5 P id ,$+*,,state 6 P ( E) ,$+* E E+T,)+ E T ,)+ T T*P ,)+* T P ,)+* P id ,)+* P (E)

26、 ,)+*,,,(,state 7 E T ,$+ T T *P,$+*,,E,,T,,P,,,*,state 8 T T* P,$+* P id ,$+* P (E) ,$+*,,id,,P,,(,state 9 T T* P ,$+*,state 10 P id ,)+*,(,,,,,id,state 11 E E+ T ,$+ T T *P,$+*,,,*,State 8,state 12 P (E ) ,$+* E E +T,)+,,+,,),20,state 0 S E$ , E E+T,$+ E T ,$+ T T*P ,$+* T P ,$+* P

27、id ,$+* P (E) ,$+*,E,,P,,id,,,T,state 1 S E $ , E E +T,$+,,+,$,state 2 //Accept S E $ ,,,state 3 E E+ T,$+ T T*P ,$+* T P ,$+* P id ,$+* P (E) ,$+*,,,P,T,id,(,state 4 T P ,$+*,state 5 P id ,$+*,,state 6 P ( E) ,$+* E E+T,)+ E T ,)+ T T*P ,)+* T P ,)+* P id ,)+* P (E) ,)+*,,,(,state

28、7 E T ,$+ T T *P,$+*,,E,,T,,P,,,*,state 8 T T* P,$+* P id ,$+* P (E) ,$+*,,id,,P,,(,state 9 T T* P ,$+*,state 10 P id ,)+*,(,,,,,id,state 11 E E+ T ,$+ T T *P,$+*,,,*,State 8,state 12 P (E ) ,$+* E E +T,)+,+,,),state 13 P (E ) ,$+*,,,21,state 0 S E$ , E E+T,$+ E T ,$+ T T*P ,$+* T P ,

29、$+* P id ,$+* P (E) ,$+*,E,,P,,id,,,T,state 1 S E $ , E E +T,$+,,+,$,state 2 //Accept S E $ ,,,state 3 E E+ T,$+ T T*P ,$+* T P ,$+* P id ,$+* P (E) ,$+*,,,P,T,id,(,state 4 T P ,$+*,state 5 P id ,$+*,,state 6 P ( E) ,$+* E E+T,)+ E T ,)+ T T*P ,)+* T P ,)+* P id ,)+* P (E) ,)+*,,,(

30、,state 7 E T ,$+ T T *P,$+*,,E,,T,,,*,state 8 T T* P,$+* P id ,$+* P (E) ,$+*,,id,,P,,(,state 9 T T* P ,$+*,state 10 P id ,)+*,,,,,id,state 11 E E+ T ,$+ T T *P,$+*,,,*,State 8,state 12 P (E ) ,$+* E E +T,)+,+,,),state 13 P (E ) ,$+*,,,(,state 14 T P ,)+*,,,,,P,22,state 0 S E$ , E E+T,$

31、+ E T ,$+ T T*P ,$+* T P ,$+* P id ,$+* P (E) ,$+*,E,,P,,id,,,T,state 1 S E $ , E E +T,$+,,+,$,state 2 //Accept S E $ ,,,state 3 E E+ T,$+ T T*P ,$+* T P ,$+* P id ,$+* P (E) ,$+*,,,P,T,id,(,state 4 T P ,$+*,state 5 P id ,$+*,,state 6 P ( E) ,$+* E E+T,)+ E T ,)+ T T*P ,)+* T P ,)

32、+* P id ,)+* P (E) ,)+*,,,(,state 7 E T ,$+ T T *P,$+*,,E,,T,,,*,state 8 T T* P,$+* P id ,$+* P (E) ,$+*,,id,,P,,(,state 9 T T* P ,$+*,state 10 P id ,)+*,,,,,id,state 11 E E+ T ,$+ T T *P,$+*,,,*,State 8,state 12 P (E ) ,$+* E E +T,)+,+,,),state 13 P (E ) ,$+*,,,(,state 14 T P ,)+*,,,,,P,

33、state 18 P ( E) ,)+* E E+T,)+ E T ,)+ T T*P ,)+* T P ,)+* P id ,)+* P (E) ,)+*,,id,,P,,,,(,,T,,E,,23,state 18 P ( E) ,)+* E E+T,)+ E T ,)+ T T*P ,)+* T P ,)+* P id ,)+* P (E) ,)+*,,T,,(,,id,,P,,,State 14,State 10,,E,state 16 P (E ) ,)+* E E +T,)+,,,,(,+,LR(1) Parsing (16),24,state 18

34、 P ( E) ,)+* E E+T,)+ E T ,)+ T T*P ,)+* T P ,)+* P id ,)+* P (E) ,)+*,,T,,(,,id,,P,,,State 14,State 10,,E,state 16 P (E ) ,)+* E E +T,)+,,,,(,+,state 15 P (E ) ,)+*,LR(1) Parsing (17),25,state 18 P ( E) ,)+* E E+T,)+ E T ,)+ T T*P ,)+* T P ,)+* P id ,)+* P (E) ,)+*,,T,,(,,id,,P,,,Sta

35、te 14,State 10,,E,state 16 P (E ) ,)+* E E +T,)+,,,(,+,state 15 P (E ) ,)+*,state 17 E E +T,)+ T T*P ,)+* T P ,)+* P id ,)+* P (E) ,)+*,,,,P,,,id,,(,,T,LR(1) Parsing (18),Renew state 12 -+ to state 17,,26,state 18 P ( E) ,)+* E E+T,)+ E T ,)+ T T*P ,)+* T P ,)+* P id ,)+* P (E) ,)+*,,T

36、,,(,,id,,P,,,State 14,State 10,,E,state 16 P (E ) ,)+* E E +T,)+,,,(,+,state 15 P (E ) ,)+*,state 17 E E +T,)+ T T*P ,)+* T P ,)+* P id ,)+* P (E) ,)+*,,,,P,,,id,,(,,T,state 19 E T ,)+ T T *P ,)+*,,*,Renew state 6 -T to state 19,LR(1) Parsing (19),,27,state 18 P ( E) ,)+* E E+T,)+ E T ,)+

37、 T T*P ,)+* T P ,)+* P id ,)+* P (E) ,)+*,,T,,(,,id,,P,,,State 14,State 10,,E,state 16 P (E ) ,)+* E E +T,)+,,,(,+,state 15 P (E ) ,)+*,state 17 E E +T,)+ T T*P ,)+* T P ,)+* P id ,)+* P (E) ,)+*,,,,P,,,id,,(,,T,state 19 E T ,)+ T T *P ,)+*,state 20 E E +T,)+ T T *P ,)+*,,*,,*,LR(1) Par

38、sing (20),28,state 18 P ( E) ,)+* E E+T,)+ E T ,)+ T T*P ,)+* T P ,)+* P id ,)+* P (E) ,)+*,,T,,(,,id,,P,,,State 14,State 10,,E,state 16 P (E ) ,)+* E E +T,)+,,,(,+,state 15 P (E ) ,)+*,state 17 E E +T,)+ T T*P ,)+* T P ,)+* P id ,)+* P (E) ,)+*,,,,P,,,id,,(,,T,state 19 E T ,)+ T T *P

39、 ,)+*,state 20 E E +T,)+ T T *P ,)+*,,*,state 21 T T * P,)+* P id ,)+* P (E) ,)+*,*,,,,,(,,,id,,P,LR(1) Parsing (21),29,state 18 P ( E) ,)+* E E+T,)+ E T ,)+ T T*P ,)+* T P ,)+* P id ,)+* P (E) ,)+*,,T,,(,,id,,P,,,State 14,State 10,,E,state 16 P (E ) ,)+* E E +T,)+,,,(,+,state 15 P (E )

40、 ,)+*,state 17 E E +T,)+ T T*P ,)+* T P ,)+* P id ,)+* P (E) ,)+*,,,,P,,,id,,(,,T,state 19 E T ,)+ T T *P ,)+*,state 20 E E +T,)+ T T *P ,)+*,,*,state 21 T T * P,)+* P id ,)+* P (E) ,)+*,*,,,,,(,,,id,,P,state 22 T T * P ,)+*,LR(1) Parsing (22),30,LR(1) Parsing (23),LR(1) The go_to table u

41、sed to drive an LR(1) is extracted directly from the LR(1) machine The algorithm to generate “go_to” table is same that we discuss in LR(0),,31,LR(1) Parsing (24),LR(1) Action table is extracted directly from the configur-ation sets of the LR(1) machine A projection function, P P : S1Vt2Q S1 be the

42、set of LR(1) machine states P(s,a)=Reducei | B ,a s and production i is B (if A a,b s Then Shift Else ),,32,LR(1) Parsing (25),LR(1) G is LR(1) if and only if s S1 a Vt |P(s,a)|1 If G is LR(1), the action table is trivially extracted from P P(s,$)=Shift actions$=Accept P(s,a)=Shift, a$ actionsa=Shi

43、ft P(s,a)=Reducei, actionsa=Reducei P(s,a)= actionsa=Error,,33,LR(1) Parsing (26),,Example: state 7,,Reduce when look-ahead $+ Shift when look-ahead *,P(s,a)= Reducei | B ,a s and production i is B (if A a,b s Then Shift Else ),34,Complete Table Merge Action table & Go-To table,35,Combare G3 action

44、 in LR(0) and LR(1),for grammar G3 : 1.S E $ 2.E E + T 3.E T 4.T T * P 5.T P 6.P id 7.P ( E ),LR(0),LR(1),ambiguous,state 7 E T T T *P,state 7 E T ,$+ T T *P,$+*,LR(0),LR(1),,,36,,Initial :(id+id)$,step1:0 (id+id)$ shift (,Tree:,,,,,(,37,,Initial :(id+id)$,step2:0 6 id+id)$ shift id,Tre

45、e:,(,,,,,id,38,,Initial :(id+id)$,step3:0 6 10 +id)$ Reduce 6,Tree:,(,,,,,id,,,P,,,,39,,Initial :(id+id)$,step4:0 6 14 +id)$ Reduce 5,Tree:,(,,,,,id,,,P,,,,,T,,40,,Initial :(id+id)$,step5:0 6 19 +id)$ Reduce 3,Tree:,(,,,,,id,,,P,,,,,T,E,,41,,Initial :(id+id)$,step6:0 6 12 +id)$ shift

46、 +,Tree:,(,,,,,id,,P,,T,E,,+,42,,Initial :(id+id)$,step7:0 6 12 17 id)$ shift id,Tree:,(,,,,,id,,P,,,T,E,,+,id,43,,Initial :(id+id)$,step8:0 6 12 17 10 )$ Reduce 6,Tree:,(,,,,,id,,P,,T,E,,+,id,,,,,,P,44,,Initial :(id+id)$,step9:0 6 12 17 14 )$ Reduce 5,Tree:,(,,,,,id,,P,,T,E,,+,id,,,,,,P,,

47、T,45,,Initial :(id+id)$,step10:0 6 12 17 20 )$ Reduce 2,Tree:,(,,,,,id,,P,T,+,id,,,,,P,,,,,E,,T,,E,,,,46,,Initial :(id+id)$,step11:0 6 12 )$ Shift 13,Tree:,(,,,,,id,,P,T,+,id,P,T,,,E,,,E,,,,),47,,Initial :(id+id)$,step12:0 6 12 13 $ Reduce 7,Tree:,(,,,,,id,,P,T,+,id,P,T,,,E,,,E,,,,),,,,,

48、,,P,,,,48,,Initial :(id+id)$,step13:0 4 $ Reduce 7,Tree:,(,,,,id,,P,T,+,id,P,T,E,,E,,,),,,,,,P,,,,,,,,T,,49,,Initial :(id+id)$,step14:0 7 $ Reduce 3,Tree:,(,,,,id,,P,T,+,id,P,T,E,,E,,,),,,,,,P,,,,,,,,T,,,E,50,,Initial :(id+id)$,step15:0 1 $ Accept,Tree:,(,,,,id,,P,T,+,id,P,T,E,,E,,,),P,,,,,,,,T,,,E,

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