温故知新

1. sm 温故知新 $ action goto … ai … an a1 输入 Xm sm-1 LR分析程序 输出 栈 Xm-1 … s0 LR分析器的模型 1。句柄与某个产生式的右部符号串相同 2。句柄是句型的一个子串 3。把句柄归约成非终结符代表了最右推导逆过程的一步 上下文无关文法 ！ 最左推导 最右推导 自上而下 自下而上 句柄 归约 移进-归约冲突 移进-归约分析 递归下降预测分析 归约-归约冲突 LL(1)文法 LR文法 非递归的预测分析 2个函数 活前缀 右句型的前缀，该前缀不超过最右句柄的右端 • 简单的LR方法（SLR） • 规范的LR方法 • 向前看的LR方法(LALR） 1/41

2. 3.5LR Parser 3.5.3 Constructing SLR Parse Table LR(0)item(item for short) a production of G with a dot at some position of the body Ex：AXYZ has four items A  ·XYZ A  X·YZ A  XY·Z A  XYZ· Ex：Ahas only one item A  · Intuitively , an item indicates ho w much of a production we have seen at a given point in the parsing process.

3. S  aABe A  Abc | b B  d a b b c d e $ $ S0 S ·aABe

4. S  aABe A  Abc | b B  d Two possibilities b b c d e $ $ a S0 S1 A ·Abc S  a ·ABe A ·b S  a ·ABe A ·Abc A ·b action(1,b)=S2

5. S  aABe A  Abc | b B  d b c d e $ $ a b S0 S1 S2 S2 achieved by shifting b from S1 S1 S  a ·ABe A ·Abc A ·b A  · bbecomes A  b · S2 A  b · Next, reduce

6. S  aABe A  Abc | b B  d b c d e $ $ a A S0 S1 S3 Check: from S1, after seeing A, where to go? S  a A·Be Two possibilities S1 S  a ·ABe A ·Abc A ·b A  A·bc S3 S  a A ·Be A  A·bc B ·d

7. S  aABe A  Abc | b B  d c d e $ $ a A b S0 S1 S3 S4 After shifting b becomes S3 S  a A ·Be A  A·bc B ·d S4 A  Ab ·c

8. S  aABe A  Abc | b B  d d e $ $ a A b c S0 S1 S3 S4 S5 becomes S4 A  Ab ·c Next, reduce S5 A  Ab c ·

9. S  aABe A  Abc | b B  d d e $ $ a A S0 S1 S3 becomes Next? S3 S  a A ·Be A  A·bc B ·d

10. S  aABe A  Abc | b B  d e $ $ a A d S0 S1 S3 S6 S2 S  a A·Be A  A·bc B · d becomes S6 B  d · Next, reduce

11. S  aABe A  Abc | b B  d e $ $ a A B S0 S1 S3 S7 S3 S  a A·Be A  A·bc B · d becomes S7 S  a AB ·e

12. S  aABe A  Abc | b B  d $ $ a A B e S0 S1 S3 S7 S7 S  a AB ·e becomes Next, reduce S8 S  a AB e ·

13. S  aABe A  Abc | b B  d $ $ S S0 OK Accept

14. 3.5LRParser Two steps of constructing SLR Parse table 1. Construct a DFA to recognize the viable prefixes 2. Construct the parse table with respect to the DFA

15. 3.5LRParser Constructing the DFA 1. Augmented Grammar E   E E  E + T | T T T * F | F F ( E ) | id acceptance occurs when and only when the parser is about to reduce b y E   E id + id F + id T+id E+id E+F E+T E E rmE+T rmE+F rm E+id rm T+id rm F+id rm id+id

16. 3.5LRParser Constructing the DFA 2. Construct the canonical LR(0) collection I0: E  ·E E   E E  E + T | T T T * F | F F ( E ) | id closure(I) 1、 add every item in I to closure(I) 2、If Aα·Bβis inclosure(I), and Bγ is a production, then add B ·γ to closure(I)if it’s not there E  ·E + T E  ·T T  ·T * F T  ·F F  ·(E) F  ·id 5/41

17. 3.5LRParser Constructing the DFA 2. Construct the canonical LR(0) collection I0: E  ·E (Kernel items) E  ·E + T E  ·T (Nonkernel items， T  ·T *F could be obtained by T  ·F computing the closure F  ·(E) function of kernel items) F  ·id E   E E  E + T | T T T * F | F F ( E ) | id E’·E and those items in which dot not at the left end

18. 3.5LRParser Constructing the DFA 2. Construct the canonical LR(0) collection I0: I1: E  ·E E   E· E  ·E + T E  E· + T E  ·T T  ·T *F T  ·F F  ·(E) F  ·id E   E E  E + T | T T T * F | F F ( E ) | id

19. 3.5LRParser Constructing the DFA 2. Construct the canonical LR(0) collection I0: I1: E  ·E E   E· E  ·E + T E  E· + T E  ·T T  ·T *F I1 := goto ( I0, E ) T  ·F F  ·(E) F  ·id E   E E  E + T | T T T * F | F F ( E ) | id

20. 3.5LRParser Constructing the DFA 2. Construct the canonical LR(0) collection I0: I1: E  ·E E   E· E  ·E + T E  E· + T E  ·T T  ·T *F I2: T  ·F E T· F  ·(E) T T· *F F  ·id E   E E  E + T | T T T * F | F F ( E ) | id

21. 3.5LRParser Constructing the DFA 2. Construct the canonical LR(0) collection I0: I1: E  ·E E   E· E  ·E + T E  E· + T E  ·T T  ·T *F I2: T  ·F E T· F  ·(E) T T· *F F  ·id I3: T  F· E   E E  E + T | T T T * F | F F ( E ) | id 10/41

22. 3.5LRParser I0: I4: E  ·E F  (·E ) E  ·E + T E  ·E + T E  ·T E  ·T T  ·T *F T  ·T *F T  ·F T  ·F F  ·(E) F  ·(E) F  ·id F  ·id E   E E  E + T | T T T * F | F F ( E ) | id

23. 3.5LRParser I0: I4: E  ·E F  (·E ) E  ·E + T E  ·E + T E  ·T E  ·T T  ·T *F T  ·T *F T  ·F T  ·F F  ·(E) F  ·(E) F  ·id F  ·id I5: F id· E   E E  E + T | T T T * F | F F ( E ) | id

24. 3.5LRParser E I1 I0 T I2 F I3 ( I4 id I5

25. 3.5LRParser E I1 I0 T I2 F I3 ( I4 id I5 E   E E  E + T | T T T * F | F F ( E ) | id I1: E   E· E  E·+ T

26. 3.5LRParser E I1 I0 T I2 F I3 ( I4 id I5 E   E E  E + T | T T T * F | F F ( E ) | id I1: E   E· E  E·+ T I6: EE + ·T T ·T * F T ·F F ·(E) F ·id 15/41

27. 3.5LRParser E I1 I0 T I2 F I3 ( I4 id I5 E   E E  E + T | T T T * F | F F ( E ) | id I2: E T· TT·*F I7: TT*·F F ·(E) F ·id

28. 3.5LRParser E I1 I0 T I2 F I3 ( I4 id I5 E   E E  E + T | T T T * F | F F ( E ) | id I3: T F·

29. 3.5LRParser E I1 I0 T I2 F I3 ( I4 id I5 E   E E  E + T | T T T * F | F F ( E ) | id I4: F (·E ) E  ·E + T E  ·T T  ·T *F T ·F F  ·( E ) F  ·id

30. 3.5LRParser E I1 I0 T I2 F I3 ( I4 id I5 I4: I8: F (·E ) F (E·) E  ·E + T E  E·+ T E  ·T T  ·T *F T ·F F  ·( E ) F  ·id E   E E  E + T | T T T * F | F F ( E ) | id

31. 3.5LRParser E I1 I0 T I2 F I3 ( I4 id I5 I4: I8: F (·E ) F (E·) E  ·E + T E  E·+ T E  ·T T  ·T *F I2: T ·F E T· F  ·( E ) TT·*F F  ·id E   E E  E + T | T T T * F | F F ( E ) | id 20/41

32. 3.5LRParser E I1 I0 T I2 F I3 ( I4 id I5 I4: I8: F (·E ) F (E·) E  ·E + T E  E·+ T E  ·T T  ·T *F I2: T ·F E T· F  ·( E ) TT·*F F  ·id I3: TF· E   E E  E + T | T T T * F | F F ( E ) | id

33. 3.5LRParser E I1 I0 T I2 F I3 ( I4 id I5 I4: I8: F (·E ) F (E·) E  ·E + T E  E·+ T E  ·T T  ·T *F I2: T ·F E T· F  ·( E ) TT·*F F  ·id I3: TF· I4: F (·E ) . . . E   E E  E + T | T T T * F | F F ( E ) | id

34. 3.5LRParser E E   E E  E + T | T T T * F | F F ( E ) | id I1 I0 T I2 F I3 ( I4 id I5 I4: I8: F (·E ) F (E·) E  ·E + T E  E·+ T E  ·T T  ·T *F I2: T ·F E T· F  ·( E ) TT·*F F  ·id I3: TF· I4:I5: F (·E )Fid· . . .

35. 3.5LRParser E I1 I0 T I2 F I3 ( I4 id I5 E   E E  E + T | T T T * F | F F ( E ) | id I5: Fid·

36. 3.5LRParser E + E   E E  E + T | T T T * F | F F ( E ) | id I1 I0 I6 T * I7 I2 F I3 ( E I4 I8 T ( 指向I2 F 指向I3 id id 25/47 I5

37. 3.5LRParser E + T * I1 I0 I9 To I7 I6 F To I3 ( To I4 id To I5 T * F I10 I7 I2 ( F To I4 I3 id To I5 ( E ) I11 I4 I8 + To I6 T ( To I2 F To I3 id id I5

38. 3.5LRParser Properties of the constructed DFA Definition：valid item If S*rm Aw rm12w，we say item A1·2is valid for a viable prefix 1 In general, an item will b e v alid for man y viable prefixes S*rm AAw rmA12w rm 1212w For any viable prefix 1, suppose A1·2is valid If 2 , should shift If 2 = , should reduce by A1

39. 3.5LRParser Properties of the constructed DFA Definition：valid item If S*rm Aw rm12w，we say item A1·2is valid for a viable prefix 1 In general, an item will b e v alid for man y viable prefixes A viable prefix may have multiple valid items The valid items of a viable prefix  is the item set (state) reached by the path 

40. 3.5LRParser ExE + T* is a viable prefix. After reading it, DFAreaches I7 I7: TT *·F, F ·(E ), F ·id E E E EE E  E+T E+T E+T  E+T* F E+T* F  E+T* F  E+T*id E+T*(E ) E+T*id E+T* F *id Definition：Valid item If S*rmAw rm12w，we say item A1·2is valid for viable prefix 1

41. 3.5LRParser Two steps of constructing SLR Parse table 1. Construct a DFA to recognize the viable prefixes 2. Construct the parse table with respect to the DFA 30/41

42. 3.5LRParser Construct SLR Parse table from DFA For state i from Ii，its actionfunction defined as： If [A·a]in Ii，and goto(Ii, a ) = Ij，then action[i, a]is sj。 If [A·]in Ii，then for all a in FOLLOW(A)，place action[i, a]with rj, where jis the id of A If [SS·]in Ii，action[ i, $ ]is acc。 If conflict occurs, the grammar is not SLR(1)

43. 3.5LRParser Construct SLRParse table State Iconstructed from Ii, its action function defined as follows . . . Construct gotofunction as follows： For all nonterminalA, ifgoto(Ii, A) = Ij, then goto[i, A] = j。

44. 3.5LRParser Construct SLRParse table State Iconstructed from Ii, its action function defined as follows . . . Construct gotofunction as follows： Set other entries as error

45. 3.5LRParser Construct SLRParse table State Iconstructed from Ii, its action function defined as follows . . . Construct gotofunction as follows： Set other entries as error The state that contains [S·S]is the initial state

46. 3.5LRParser 例 I2: E  T· T  T· *F 因为FOLLOW(E) = {$, +, )},所以 action[2, $]=action[2, +]=action[2, )]=r2 action[2, *] = s7 E   E E  E + T | T T T * F | F F ( E ) | id 35/41

47. 3.5LRParser ExLimitation of SLR(1) S  V = E S  E V *E V  id E  V I0: S  · S S  ·V = E S  · E V  · *E V  · id E  · V I2: S  V ·= E E  V· V

48. 3.5LRParser ExLimitation of SLR(1) S  V = E S  E V *E V  id E  V I0: S  · S S  ·V = E S  · E V  · *E V  · id E  · V I2: S  V ·= E E  V· V I2the first item: action[2, = ] = s6

49. 3.5LRParser ExLimitation of SLR(1) S  V = E S  E V *E V  id E  V I0: S  · S S  ·V = E S  · E V  · *E V  · id E  · V I2: S  V ·= E E  V· V I2the first item: action[2, = ] = s6 I2the second item: action[2, = ] = r5 Reduce by EV In that = belongs to FOLLW(E)

50. 3.5LRParser ExLimitation of SLR(1) S  V = E S  E V *E V  id E  V I0: S  · S S  ·V = E S  · E V  · *E V  · id E  · V I2: S  V ·= E E  V· V I2the first item: action[2, = ] = s6 I2the second item: action[2, = ] = r5 Reduce by EV In that = belongs to FOLLW(E)