1. Compiler Construction
Sohail Aslam
Lecture 27
compiler: Bottom-up Parsing

2. else if [A → a, a]  Ii and A  S' then Action[i,a] ← “reduce A → a”
for each item Ii  CC
if [A → aab, b]  Ii and goto(Ii, a) == Ij then Action[i,a] ← “shift j”
else if [A → a, a]  Ii and A  S' then Action[i,a] ← “reduce A → a”
end of lec 26
compiler: Bottom-up Parsing

3. else if [S' → S, $]  Ii then Action[i,a] ← “accept” end for
// the goto table
for each non-terminal A  G if goto(Ii, A) = Ij then Goto[i, A]  j

4. LR Table Construction
The initial state is the one that contains the item [S' → S, $]
All remaining entries are marked “error”

5. LR Table Construction
The initial state is the one that contains the item [S' → S, $]
All remaining entries are marked “error”

6. Table Construction Example
1. S' → E 2. E → T – E
3. E → T 4. T → F  T 5. T → F 6. F → id

7. Symbol FIRST
S' { id } E { id } T { id } F { id } id { id }  {  } – { – }

8. I0 = {closure([S' → E, $])}
{ [S' → E, $], [E → T – E, $], [E → T, $], [T → FT, $], [T → F, $] [T → FT, –], [T → F, –], [F → id, $], [F → id, –], [F → id, ] }

9. I0 = {closure([S' → E, $])}
{ [S' → E, $], [E → T – E, $], [E → T, $], [T → FT, $], [T → F, $] [T → FT, –], [T → F, –], [F → id, $], [F → id, –], [F → id, ] }

10. I0 = {closure([S' → E, $])}
{ [S' → E, $], [E → T – E, $], [E → T, $], [T → FT, $], [T → F, $] [T → FT, –], [T → F, –], [F → id, $], [F → id, –], [F → id, ] }

11. I0 = {closure([S' → E, $])}
{ [S' → E, $], [E → T – E, $], [E → T, $], [T → FT, $], [T → F, $] [T → FT, –], [T → F, –], [F → id, $], [F → id, –], [F → id, ] }

12. I0 = {closure([S' → E, $])}
{ [S' → E, $], [E → T – E, $], [E → T, $], [T → FT, $], [T → F, $] [T → FT, –], [T → F, –], [F → id, $], [F → id, –], [F → id, ] }

13. I1 = {goto(I0, E)}
{[S' → E, $] }
I2 = {goto(I0, T)}
{[E → T – E,$], [E →T,$]}

14. I0 = {closure([S' → E, $])}
{ [S' → E, $], [E → T – E, $], [E → T, $], [T → FT, $], [T → F, $] [T → FT, –], [T → F, –], [F → id, $], [F → id, –], [F → id, ] }

15. I1 = {goto(I0, E)}
{[S' → E, $] }
I2 = {goto(I0, T)}
{[E → T – E,$], [E →T,$]}

16. I1 = {goto(I0, E)}
{[S' → E, $] }
I2 = {goto(I0, T)}
{[E → T – E,$], [E →T,$]}

17. I0 = {closure([S' → E, $])}
{ [S' → E, $], [E → T – E, $], [E → T, $], [T → FT, $], [T → F, $] [T → FT, –], [T → F, –], [F → id, $], [F → id, –], [F → id, ] }

18. I1 = {goto(I0, E)}
{[S' → E, $] }
I2 = {goto(I0, T)}
{[E → T – E,$], [E →T,$]}

19. I3 = {goto(I0, F)}
{ [T → F T, $], [T → F, $],
[T → F T, –], [T → F, –] }

20. I0 = {closure([S' → E, $])}
{ [S' → E, $], [E → T – E, $], [E → T, $], [T → FT, $], [T → F, $] [T → FT, –], [T → F, –], [F → id, $], [F → id, –], [F → id, ] }

21. I3 = {goto(I0, F)}
{ [T → F T, $], [T → F, $],
[T → F T, –], [T → F, –] }

22. I4 = {goto(I0, id)}
{ [F → id , $],
[F → id , –],
[F → id , ] }

23. I0 = {closure([S' → E, $])}
{ [S' → E, $], [E → T – E, $], [E → T, $], [T → FT, $], [T → F, $] [T → FT, –], [T → F, –], [F → id, $], [F → id, –], [F → id, ] }

24. I4 = {goto(I0, id)}
{ [F → id , $],
[F → id , –],
[F → id , ] }

25. I5 = {goto(I2, –)}
{[E →T–  E, $], [E → T–E, $],
[E → T, $], [T → FT, $],
[T → FT, –], [T → F, $],
[T → F, –], [F → id, $],
[F → id, –], [F → id, ] }

26. I5 = {goto(I2, –)}
{[E →T–  E, $], [E → T–E, $],
[E → T, $], [T → FT, $],
[T → FT, –], [T → F, $],
[T → F, –], [F → id, $],
[F → id, –], [F → id, ] }

27. I5 = {goto(I2, –)}
{[E →T–  E, $], [E → T–E, $],
[E → T, $], [T → FT, $],
[T → FT, –], [T → F, $],
[T → F, –], [F → id, $],
[F → id, –], [F → id, ] }

28. I5 = {goto(I2, –)}
{[E →T–  E, $], [E → T–E, $],
[E → T, $], [T → FT, $],
[T → FT, –], [T → F, $],
[T → F, –], [F → id, $],
[F → id, –], [F → id, ] }

29. I6 = {goto(I3, )}
{[T → F T, $], [T → F T, –],
[T → FT, $], [T → FT, –], [T → F, $], [T → F, –],
[F → id, $], [F → id, –],
[F → id, ] }

30. I6 = {goto(I3, )}
{[T → F T, $], [T → F T, –],
[T → FT, $], [T → FT, –], [T → F, $], [T → F, –],
[F → id, $], [F → id, –],
[F → id, ] }

31. I6 = {goto(I3, )}
{[T → F T, $], [T → F T, –],
[T → FT, $], [T → FT, –], [T → F, $], [T → F, –],
[F → id, $], [F → id, –],
[F → id, ] }

32. I7 = {goto(I5, E)}
{[E → T – E , $] }
I2 = {goto(I5, T)}
I3 = {goto(I5, F)}
I4 = {goto(I5, id)}

33. I7 = {goto(I5, E)}
{[E → T – E , $] }
I2 = {goto(I5, T)}
I3 = {goto(I5, F)}
I4 = {goto(I5, id)}

34. I7 = {goto(I5, E)}
{[E → T – E , $] }
I2 = {goto(I5, T)}
I3 = {goto(I5, F)}
I4 = {goto(I5, id)}

35. I7 = {goto(I5, E)}
{[E → T – E , $] }
I2 = {goto(I5, T)}
I3 = {goto(I5, F)}
I4 = {goto(I5, id)}

36. I7 = {goto(I5, E)}
{[E → T – E , $] }
I2 = {goto(I5, T)}
I3 = {goto(I5, F)}
I4 = {goto(I5, id)}

37. I8 = {goto(I6, T)}
{ [T → FT , $],
[T → FT , –] }
I3 = {goto(I6, F)}
I4 = {goto(I6, id)}

38. I8 = {goto(I6, T)}
{ [T → FT , $],
[T → FT , –] }
I3 = {goto(I6, F)}
I4 = {goto(I6, id)}

39. I8 = {goto(I6, T)}
{ [T → FT , $],
[T → FT , –] }
I3 = {goto(I6, F)}
I4 = {goto(I6, id)}

40. Filling the LR(1) Table
Action
Goto id –  $ E T F 1 2 3 4 5 6 7 8

41. Apply
1. if [A → aab, b]  Ii and goto(Ii, a) = Ij then set Action[i,a]  “shift j”. Here, a is a terminal.

42. goto(I0, id) = I4  Action[0, id]  shift 4
I0={[S' → E,$],[E →T– E, $], [E → T, $], [T → FT, $], [T → FT, –], [T → F, $], [T → F, –], [F → id, $], [F → id, –], [F → id, ] }
goto(I0, id) = I4
 Action[0, id]  shift 4

43. goto(I0, id) = I4  Action[0, id]  shift 4
I0={[S' → E,$],[E →T– E, $], [E → T, $], [T → FT, $], [T → FT, –], [T → F, $], [T → F, –], [F → id, $], [F → id, –], [F → id, ] }
goto(I0, id) = I4
 Action[0, id]  shift 4

44. goto(I0, id) = I4  Action[0, id]  shift 4
I0={[S' → E,$],[E →T– E, $], [E → T, $], [T → FT, $], [T → FT, –], [T → F, $], [T → F, –], [F → id, $], [F → id, –], [F → id, ] }
goto(I0, id) = I4
 Action[0, id]  shift 4

45. goto(I0, id) = I4  Action[0, id]  shift 4
I0={[S' → E,$],[E →T– E, $], [E → T, $], [T → FT, $], [T → FT, –], [T → F, $], [T → F, –], [F → id, $], [F → id, –], [F → id, ] }
goto(I0, id) = I4
 Action[0, id]  shift 4

46. Action
Goto id –  $ E T F s4 1 2 3 4 5 6 7 8

47. goto(I2, –) = I5  Action[2, –]  shift 5
I2= {[E → T – E, $], [E →T,$]}
goto(I2, –) = I5
 Action[2, –]  shift 5

48. goto(I2, –) = I5  Action[2, –]  shift 5
I2= {[E → T – E, $], [E →T,$]}
goto(I2, –) = I5
 Action[2, –]  shift 5

49. goto(I2, –) = I5  Action[2, –]  shift 5
I2= {[E → T – E, $], [E →T,$]}
goto(I2, –) = I5
 Action[2, –]  shift 5

50. Action
Goto id –  $ E T F s4 1 2 s5 3 4 5 6 7 8

51. goto(I3, ) = I6  Action[3, ]  shift 6
I3={ [T → F T, $], [T → F, $],
[T → F T, –], [T → F, –]}
goto(I3, ) = I6
 Action[3, ]  shift 6

52. goto(I3, ) = I6  Action[3, ]  shift 6
I3={ [T → F T, $], [T → F, $],
[T → F T, –], [T → F, –]}
goto(I3, ) = I6
 Action[3, ]  shift 6

53. goto(I3, ) = I6  Action[3, ]  shift 6
I3={ [T → F T, $], [T → F, $],
[T → F T, –], [T → F, –]}
goto(I3, ) = I6
 Action[3, ]  shift 6

54. Action
Goto id –  $ E T F s4 1 2 s5 3 s6 4 5 6 7 8

55. goto(I5, id) = I4
 Action[5, id]  shift 4
goto(I6, id) = I4
 Action[6, id]  shift 4

56. goto(I5, id) = I4
 Action[5, id]  shift 4
goto(I6, id) = I4
 Action[6, id]  shift 4

57. Action
Goto id –  $ E T F s4 1 2 s5 3 s6 4 5 6 7 8

58. Apply
2. if [A → a, a]  Ii and A  S' then set action[i,a] to “reduce A → a”

59. I2 = { [E → T – E, $], [E →T,$] }
 Action[2, $]  reduce 3

60. I2 = { [E → T – E, $], [E →T,$] }
 Action[2, $]  reduce 3

61. Action
Goto id –  $ E T F s4 1 2 s5 r3 3 s6 4 5 6 7 8

62. I3 = { [T → F T, $], [T → F, $],
[T → F T, –], [T → F, –] }
 Action[3, $]  reduce 5
 Action[3, –]  reduce 5

63. I3 = { [T → F T, $], [T → F, $],
[T → F T, –], [T → F, –] }
 Action[3, $]  reduce 5
 Action[3, –]  reduce 5

64. Action
Goto id –  $ E T F s4 1 2 s5 r3 3 r5 s6 4 5 6 7 8

65. I4 = { [F → id, $], [F → id, –],
[F → id, ] }
 Action[4, $]  reduce 6
 Action[4, –]  reduce 6
 Action[4, ]  reduce 6

66. I4 = { [F → id, $], [F → id, –],
[F → id, ] }
 Action[4, $]  reduce 6
Action[4, –]  reduce 6
 Action[4, ]  reduce 6

67. Action
Goto id –  $ E T F s4 1 2 s5 r3 3 r5 s6 4 r6 5 6 7 8

68. I7 = {[E → T – E, $] }
Action[7, $]  reduce 2
I8 = { [T → FT, $],
[T → FT, –] }
 Action[8, $]  reduce 4
 Action[8, –]  reduce 4

69. I7 = {[E → T – E, $] }
Action[7, $]  reduce 2
I8 = { [T → FT, $],
[T → FT, –] }
 Action[8, $]  reduce 4
 Action[8, –]  reduce 4

70. I7 = {[E → T – E, $] }
Action[7, $]  reduce 2
I8 = { [T → FT, $],
[T → FT, –] }
 Action[8, $]  reduce 4
 Action[8, –]  reduce 4

71. Action
Goto id –  $ E T F s4 1 2 s5 r3 3 r5 s6 4 r6 5 6 7 r2 8 r4

72. Apply
3. if [S' → S, $]  Ii then set action[i,$] to “accept”

73. I1 = {[S' → E, $] }
 Action[1, $]  accept

74. Action Goto id –  $ E T F s4 1 2 s5 r3 3 r5 s6 4 r6 5 6 7 r2 8 r4s4 1
accept 2 s5 r3 3 r5 s6 4 r6 5 6 7 r2 8 r4

75. Apply
for each non-terminal A  G
- if goto(Ii, A) = Ij then goto[i, A]  j.

76. goto(I0, E) = I1  goto[0,E]  1
goto(I0, T) = I2  goto[0,T]  2
goto(I0, F) = I3  goto[0,F]  3
goto(I5, E) = I7  goto[5,E]  7
goto(I5, T) = I2  goto[5,T]  2
goto(I5, F) = I3  goto[5,F]  3
goto(I6, T) = I8  goto[6,T]  8
goto(I6, F) = I3  goto[6,F]  3

77. Action
Goto id –  $ E T F s4 1 2 3
acc s5 r3 r5 s6 4 r6 5 7 6 8 r2 r4

78. Example Parse
Let us parse the expression x – y  z using the LR(1) table
The scanner will encode the input string as id – id  id $ where $ is the EOF marker

79. Example Parse
Let us parse the expression x – y  z using the LR(1) table
The scanner will encode the input string as id – id  id $ where $ is the EOF marker
end of lec 27
compiler: Bottom-up Parsing