LR parsing allows parsers to see the entire right-hand side of a rule and perform lookahead, allowing it to handle a wider range of grammars than LL parsing. The document provides an example of LR parsing a simple expression grammar. It demonstrates the steps of building the LR parsing items, closure, and goto functions to generate the LR parsing table from the grammar. LR parsing tables contain the states, symbols, and parsing actions (reduce, shift, accept).

1. Challenge the future
Delft
University of
Technology
Course IN4303
Compiler Construction
Eduardo Souza, Guido Wachsmuth, Eelco Visser
LR Parsing
Traditional Parsing Algorithms

2. lessons learned
LR Parsing
Recap: Traditional Parsing Algorithms
How can we parse context-free languages effectively?
• predictive parsing
Which grammar classes are supported by these algorithms?
• LL(k) grammars, LL(k) languages
How can we generate compiler tools from that?
• implement automaton
• generate parse tables
What are other techniques for implementing top-down parsers?
• Parser Combinators
• PEGs
• ALL(*)
2

3. today’s lecture
Lexical Analysis
Overview
3

4. today’s lecture
Lexical Analysis
Overview
efficient parsing algorithms
• LR parsing
• LR parse table generation
• SLR & LALR parse tables
• Generalized LR parsing
• Scannerless Generalized LR parsing
3

5. LR Parsing
LR Parsing
I
4

6. idea
LR Parsing
LR parsing
problems with LL parsing
• predicting right rule
• left recursion
LR parsing
• see whole right-hand side of a rule
• look ahead
• shift or reduce
5

7. example
LR Parsing
LR parsing
6
* 3 $
input
$
stack
7* 37 +
S → E $
E → E * E
E → E + E
E → Num
grammar

8. example
LR Parsing
LR parsing
6
* 3 $$ 7* 37 +
S → E $
E → E * E
E → E + E
E → Num

9. example
LR Parsing
LR parsing
6
* 3 $$ 7* 37 +
S → E $
E → E * E
E → E + E
E → Num

10. example
LR Parsing
LR parsing
6
* 3 $$ 7* 37 +
* 3 $7+$ E 3*
S → E $
E → E * E
E → E + E
E → Num

11. example
LR Parsing
LR parsing
6
* 3 $$ 7* 37 +
* 3 $7+$ E 3*
S → E $
E → E * E
E → E + E
E → Num

12. example
LR Parsing
LR parsing
6
* 3 $$ 7* 37 +
* 3 $7+$ E 3*
S → E $
E → E * E
E → E + E
E → Num

13. example
LR Parsing
LR parsing
6
* 3 $$ 7* 37 +
* 3 $7+$ E 3*
* 3 $7+$ E * E
S → E $
E → E * E
E → E + E
E → Num

14. example
LR Parsing
LR parsing
6
* 3 $$ 7* 37 +
* 3 $7+$ E 3*
* 3 $7+$ E * E
* 3 $7+$ E
S → E $
E → E * E
E → E + E
E → Num

15. example
LR Parsing
LR parsing
6
* 3 $$ 7* 37 +
* 3 $7+$ E 3*
* 3 $7+$ E * E
* 3 $7+$ E
S → E $
E → E * E
E → E + E
E → Num

16. example
LR Parsing
LR parsing
6
* 3 $$ 7* 37 +
* 3 $7+$ E 3*
* 3 $7+$ E * E
* 3 $7+$ E
S → E $
E → E * E
E → E + E
E → Num

17. example
LR Parsing
LR parsing
6
* 3 $$ 7* 37 +
* 3 $7+$ E 3*
* 3 $7+$ E * E
* 3 $7+$ E
$ E + E 3* $
S → E $
E → E * E
E → E + E
E → Num

18. example
LR Parsing
LR parsing
6
* 3 $$ 7* 37 +
* 3 $7+$ E 3*
* 3 $7+$ E * E
* 3 $7+$ E
$ E + E 3* $
S → E $
E → E * E
E → E + E
E → Num

19. example
LR Parsing
LR parsing
6
* 3 $$ 7* 37 +
* 3 $7+$ E 3*
* 3 $7+$ E * E
* 3 $7+$ E
$ E + E 3* $
S → E $
E → E * E
E → E + E
E → Num

20. example
LR Parsing
LR parsing
6
* 3 $$ 7* 37 +
* 3 $7+$ E 3*
* 3 $7+$ E * E
* 3 $7+$ E
$ E + E 3* $
$ E + E * E $
S → E $
E → E * E
E → E + E
E → Num

21. example
LR Parsing
LR parsing
6
* 3 $$ 7* 37 +
* 3 $7+$ E 3*
* 3 $7+$ E * E
* 3 $7+$ E
$ E + E 3* $
$ E + E
$ E + E * E $
$
S → E $
E → E * E
E → E + E
E → Num

22. example
LR Parsing
LR parsing
6
* 3 $$ 7* 37 +
* 3 $7+$ E 3*
* 3 $7+$ E * E
* 3 $7+$ E
$ E + E 3* $
$ E + E
$ E + E * E $
$
$ E $
S → E $
E → E * E
E → E + E
E → Num

23. example
LR Parsing
LR parsing
6
* 3 $$ 7* 37 +
* 3 $7+$ E 3*
* 3 $7+$ E * E
* 3 $7+$ E
$ E + E 3* $
$ E + E
$ E + E * E $
$
$ E $
S → E $
E → E * E
E → E + E
E → Num

24. example
LR Parsing
LR parsing
6
* 3 $$ 7* 37 +
* 3 $7+$ E 3*
* 3 $7+$ E * E
* 3 $7+$ E
$ E + E 3* $
$ E + E
$ E + E * E $
$
$ E $
$ S
S → E $
E → E * E
E → E + E
E → Num

25. LR Parsing
Grammar classes
7
context-free grammars
LL(k)
LL(1)
LL(0)

26. LR Parsing
Grammar classes
7
context-free grammars
LR(0)
LL(k)
LL(1)
LL(0)

27. LR Parsing
Grammar classes
7
context-free grammars
LR(1)
LR(0)
LL(k)
LL(1)
LL(0)

28. LR Parsing
Grammar classes
7
context-free grammars
LR(k)
LR(1)
LR(0)
LL(k)
LL(1)
LL(0)

29. LR Parsing
Grammar classes
7
context-free grammars
LR(k)
LR(1)
SLR
LR(0)
LL(k)
LL(1)
LL(0)

30. LR Parsing
Grammar classes
7
context-free grammars
LR(k)
LR(1)
LALR(1)
SLR
LR(0)
LL(k)
LL(1)
LL(0)

31. LR Parsing
LR Parse Tables
II
8

32. parse table
LR Parsing 9
rows
• states of a DFA
columns
• topmost stack symbol
• Σ, N
entries
• reduce, rule number
• shift, goto state
• goto state
• accept state
LR parsing
T1 ... N1 ...
1 s 3
2 g 5
3 r 1
4 r 2 a
5
6 g 1
7 s 1
8
...

33. items, closure & goto
LR Parsing
LR(0) parse tables
10
S → x
S → ( L )
L → S
L → L , S

34. S’ → . S $
items, closure & goto
LR Parsing
LR(0) parse tables
10
S → x
S → ( L )
L → S
L → L , S

35. S’ → . S $
items, closure & goto
LR Parsing
LR(0) parse tables
10
item
S → x
S → ( L )
L → S
L → L , S

36. closure
• for every item A → α . X β
• for every rule X → γ
• add item X → . γ
S’ → . S $
items, closure & goto
LR Parsing
LR(0) parse tables
10
item
S → x
S → ( L )
L → S
L → L , S

37. S’ → . S $
S → . x
S → . ( L )
closure
• for every item A → α . X β
• for every rule X → γ
• add item X → . γ
items, closure & goto
LR Parsing
LR(0) parse tables
10
S → x
S → ( L )
L → S
L → L , S

38. S’ → . S $
S → . x
S → . ( L )
items, closure & goto
LR Parsing
LR(0) parse tables
10
S → x
S → ( L )
L → S
L → L , S

39. S’ → . S $
S → . x
S → . ( L )
items, closure & goto
LR Parsing
LR(0) parse tables
10
S’ → S . $
S S → x
S → ( L )
L → S
L → L , S

40. S’ → . S $
S → . x
S → . ( L )
items, closure & goto
LR Parsing
LR(0) parse tables
10
S’ → S . $
S
x
S → x .
S → x
S → ( L )
L → S
L → L , S

41. S’ → . S $
S → . x
S → . ( L )
items, closure & goto
LR Parsing
LR(0) parse tables
10
S’ → S . $
S
x
S → x .
(
S → ( . L )
S → x
S → ( L )
L → S
L → L , S

42. S’ → . S $
S → . x
S → . ( L )
items, closure & goto
LR Parsing
LR(0) parse tables
10
S’ → S . $
S
x
S → x .
(
S → ( . L )
L → . S
L → . L , S
S → . x
S → . ( L )
S → x
S → ( L )
L → S
L → L , S

43. S’ → . S $
S → . x
S → . ( L )
items, closure & goto
LR Parsing
LR(0) parse tables
10
S’ → S . $
S
x
S → x .
(
S → ( . L )
L → . S
L → . L , S
S → . x
S → . ( L )
x
S → x
S → ( L )
L → S
L → L , S

44. S’ → . S $
S → . x
S → . ( L )
items, closure & goto
LR Parsing
LR(0) parse tables
10
S’ → S . $
S
x
S → x .
(
S → ( . L )
L → . S
L → . L , S
S → . x
S → . ( L )
x
(
S → x
S → ( L )
L → S
L → L , S

45. S’ → . S $
S → . x
S → . ( L )
items, closure & goto
LR Parsing
LR(0) parse tables
10
S’ → S . $
S
x
S → x .
(
S → ( . L )
L → . S
L → . L , S
S → . x
S → . ( L )
x
(
S
L → S .
S → x
S → ( L )
L → S
L → L , S

46. S’ → . S $
S → . x
S → . ( L )
items, closure & goto
LR Parsing
LR(0) parse tables
10
S’ → S . $
S
x
S → x .
(
S → ( . L )
L → . S
L → . L , S
S → . x
S → . ( L )
x
(
S
L → S .
L S → ( L . )
L → L . , S
S → x
S → ( L )
L → S
L → L , S

47. S’ → . S $
S → . x
S → . ( L )
items, closure & goto
LR Parsing
LR(0) parse tables
10
S’ → S . $
S
x
S → x .
(
S → ( . L )
L → . S
L → . L , S
S → . x
S → . ( L )
x
(
S
L → S .
L S → ( L . )
L → L . , S
)
S → ( L ) .
S → x
S → ( L )
L → S
L → L , S

48. S’ → . S $
S → . x
S → . ( L )
items, closure & goto
LR Parsing
LR(0) parse tables
10
S’ → S . $
S
x
S → x .
(
S → ( . L )
L → . S
L → . L , S
S → . x
S → . ( L )
x
(
S
L → S .
L S → ( L . )
L → L . , S
)
S → ( L ) .
,
L → L , . S
S → x
S → ( L )
L → S
L → L , S

49. S’ → . S $
S → . x
S → . ( L )
L → L , . S
S → . x
S → . ( L )
items, closure & goto
LR Parsing
LR(0) parse tables
10
S’ → S . $
S
x
S → x .
(
S → ( . L )
L → . S
L → . L , S
S → . x
S → . ( L )
x
(
S
L → S .
L S → ( L . )
L → L . , S
)
S → ( L ) .
,
S → x
S → ( L )
L → S
L → L , S

50. S’ → . S $
S → . x
S → . ( L )
L → L , . S
S → . x
S → . ( L )
items, closure & goto
LR Parsing
LR(0) parse tables
10
S’ → S . $
S
x
S → x .
(
S → ( . L )
L → . S
L → . L , S
S → . x
S → . ( L )
x
(
S
L → S .
L S → ( L . )
L → L . , S
)
S → ( L ) .
,
x
S → x
S → ( L )
L → S
L → L , S

51. S’ → . S $
S → . x
S → . ( L )
L → L , . S
S → . x
S → . ( L )
items, closure & goto
LR Parsing
LR(0) parse tables
10
S’ → S . $
S
x
S → x .
(
S → ( . L )
L → . S
L → . L , S
S → . x
S → . ( L )
x
(
S
L → S .
L S → ( L . )
L → L . , S
)
S → ( L ) .
,
x
(
S → x
S → ( L )
L → S
L → L , S

52. S’ → . S $
S → . x
S → . ( L )
L → L , . S
S → . x
S → . ( L )
items, closure & goto
LR Parsing
LR(0) parse tables
10
S’ → S . $
S
x
S → x .
(
S → ( . L )
L → . S
L → . L , S
S → . x
S → . ( L )
x
(
S
L → S .
L S → ( L . )
L → L . , S
)
S → ( L ) .
,
x
(
S
L → L , S .
S → x
S → ( L )
L → S
L → L , S

53. S’ → . S $
S → . x
S → . ( L )
L → L , . S
S → . x
S → . ( L )
items, closure & goto
LR Parsing
LR(0) parse tables
10
S’ → S . $
S
x
S → x .
(
S → ( . L )
L → . S
L → . L , S
S → . x
S → . ( L )
x
(
S
L → S .
L S → ( L . )
L → L . , S
)
S → ( L ) .
,
x
(
S
L → L , S .
S → x
S → ( L )
L → S
L → L , S
1
2
3
4 6 7
5
8
9

54. ( ) x , $ S L
1 s 3 s 2 g 4
2 r 1 r 1 r 1 r 1 r 1
3 s 3 s 2 g 6 g 5
4 a
5 s 7 s 8
6 r 3 r 3 r 3 r 3 r 3
7 r 2 r 2 r 2 r 2 r 2
8 s 3 s 2 g 9
9 r 4 r 4 r 4 r 4 r 4
result
LR Parsing 11
LR(0) parse tables
S → x
S → ( L )
L → S
L → L , S

55. ( ) x , $ S L
1 s 3 s 2 g 4
2 r 1 r 1 r 1 r 1 r 1
3 s 3 s 2 g 6 g 5
4 a
5 s 7 s 8
6 r 3 r 3 r 3 r 3 r 3
7 r 2 r 2 r 2 r 2 r 2
8 s 3 s 2 g 9
9 r 4 r 4 r 4 r 4 r 4
result
LR Parsing 11
LR(0) parse tables
S → x
S → ( L )
L → S
L → L , S
$)x,x(
1

56. ( ) x , $ S L
1 s 3 s 2 g 4
2 r 1 r 1 r 1 r 1 r 1
3 s 3 s 2 g 6 g 5
4 a
5 s 7 s 8
6 r 3 r 3 r 3 r 3 r 3
7 r 2 r 2 r 2 r 2 r 2
8 s 3 s 2 g 9
9 r 4 r 4 r 4 r 4 r 4
result
LR Parsing 11
LR(0) parse tables
S → x
S → ( L )
L → S
L → L , S
$)x,x
1
3

57. ( ) x , $ S L
1 s 3 s 2 g 4
2 r 1 r 1 r 1 r 1 r 1
3 s 3 s 2 g 6 g 5
4 a
5 s 7 s 8
6 r 3 r 3 r 3 r 3 r 3
7 r 2 r 2 r 2 r 2 r 2
8 s 3 s 2 g 9
9 r 4 r 4 r 4 r 4 r 4
result
LR Parsing 11
LR(0) parse tables
S → x
S → ( L )
L → S
L → L , S
$)x,
1
3
2

58. ( ) x , $ S L
1 s 3 s 2 g 4
2 r 1 r 1 r 1 r 1 r 1
3 s 3 s 2 g 6 g 5
4 a
5 s 7 s 8
6 r 3 r 3 r 3 r 3 r 3
7 r 2 r 2 r 2 r 2 r 2
8 s 3 s 2 g 9
9 r 4 r 4 r 4 r 4 r 4
result
LR Parsing 11
LR(0) parse tables
S → x
S → ( L )
L → S
L → L , S
$)x,
1
3

59. ( ) x , $ S L
1 s 3 s 2 g 4
2 r 1 r 1 r 1 r 1 r 1
3 s 3 s 2 g 6 g 5
4 a
5 s 7 s 8
6 r 3 r 3 r 3 r 3 r 3
7 r 2 r 2 r 2 r 2 r 2
8 s 3 s 2 g 9
9 r 4 r 4 r 4 r 4 r 4
result
LR Parsing 11
LR(0) parse tables
S → x
S → ( L )
L → S
L → L , S
$)x,
1
3
6

60. ( ) x , $ S L
1 s 3 s 2 g 4
2 r 1 r 1 r 1 r 1 r 1
3 s 3 s 2 g 6 g 5
4 a
5 s 7 s 8
6 r 3 r 3 r 3 r 3 r 3
7 r 2 r 2 r 2 r 2 r 2
8 s 3 s 2 g 9
9 r 4 r 4 r 4 r 4 r 4
result
LR Parsing 11
LR(0) parse tables
S → x
S → ( L )
L → S
L → L , S
$)x,
1
3

61. ( ) x , $ S L
1 s 3 s 2 g 4
2 r 1 r 1 r 1 r 1 r 1
3 s 3 s 2 g 6 g 5
4 a
5 s 7 s 8
6 r 3 r 3 r 3 r 3 r 3
7 r 2 r 2 r 2 r 2 r 2
8 s 3 s 2 g 9
9 r 4 r 4 r 4 r 4 r 4
result
LR Parsing 11
LR(0) parse tables
S → x
S → ( L )
L → S
L → L , S
$)x,
1
3
5

62. ( ) x , $ S L
1 s 3 s 2 g 4
2 r 1 r 1 r 1 r 1 r 1
3 s 3 s 2 g 6 g 5
4 a
5 s 7 s 8
6 r 3 r 3 r 3 r 3 r 3
7 r 2 r 2 r 2 r 2 r 2
8 s 3 s 2 g 9
9 r 4 r 4 r 4 r 4 r 4
result
LR Parsing 11
LR(0) parse tables
S → x
S → ( L )
L → S
L → L , S
$)x
1
3
5
8

63. ( ) x , $ S L
1 s 3 s 2 g 4
2 r 1 r 1 r 1 r 1 r 1
3 s 3 s 2 g 6 g 5
4 a
5 s 7 s 8
6 r 3 r 3 r 3 r 3 r 3
7 r 2 r 2 r 2 r 2 r 2
8 s 3 s 2 g 9
9 r 4 r 4 r 4 r 4 r 4
result
LR Parsing 11
LR(0) parse tables
S → x
S → ( L )
L → S
L → L , S
$)
1
3
5
8
2

64. ( ) x , $ S L
1 s 3 s 2 g 4
2 r 1 r 1 r 1 r 1 r 1
3 s 3 s 2 g 6 g 5
4 a
5 s 7 s 8
6 r 3 r 3 r 3 r 3 r 3
7 r 2 r 2 r 2 r 2 r 2
8 s 3 s 2 g 9
9 r 4 r 4 r 4 r 4 r 4
result
LR Parsing 11
LR(0) parse tables
S → x
S → ( L )
L → S
L → L , S
$)
1
3
5
8

65. ( ) x , $ S L
1 s 3 s 2 g 4
2 r 1 r 1 r 1 r 1 r 1
3 s 3 s 2 g 6 g 5
4 a
5 s 7 s 8
6 r 3 r 3 r 3 r 3 r 3
7 r 2 r 2 r 2 r 2 r 2
8 s 3 s 2 g 9
9 r 4 r 4 r 4 r 4 r 4
result
LR Parsing 11
LR(0) parse tables
S → x
S → ( L )
L → S
L → L , S
$)
1
3
5
8
9

66. ( ) x , $ S L
1 s 3 s 2 g 4
2 r 1 r 1 r 1 r 1 r 1
3 s 3 s 2 g 6 g 5
4 a
5 s 7 s 8
6 r 3 r 3 r 3 r 3 r 3
7 r 2 r 2 r 2 r 2 r 2
8 s 3 s 2 g 9
9 r 4 r 4 r 4 r 4 r 4
result
LR Parsing 11
LR(0) parse tables
S → x
S → ( L )
L → S
L → L , S
$)
1
3

67. ( ) x , $ S L
1 s 3 s 2 g 4
2 r 1 r 1 r 1 r 1 r 1
3 s 3 s 2 g 6 g 5
4 a
5 s 7 s 8
6 r 3 r 3 r 3 r 3 r 3
7 r 2 r 2 r 2 r 2 r 2
8 s 3 s 2 g 9
9 r 4 r 4 r 4 r 4 r 4
result
LR Parsing 11
LR(0) parse tables
S → x
S → ( L )
L → S
L → L , S
$)
1
3
5

68. ( ) x , $ S L
1 s 3 s 2 g 4
2 r 1 r 1 r 1 r 1 r 1
3 s 3 s 2 g 6 g 5
4 a
5 s 7 s 8
6 r 3 r 3 r 3 r 3 r 3
7 r 2 r 2 r 2 r 2 r 2
8 s 3 s 2 g 9
9 r 4 r 4 r 4 r 4 r 4
result
LR Parsing 11
LR(0) parse tables
S → x
S → ( L )
L → S
L → L , S
$
1
3
5
7

69. ( ) x , $ S L
1 s 3 s 2 g 4
2 r 1 r 1 r 1 r 1 r 1
3 s 3 s 2 g 6 g 5
4 a
5 s 7 s 8
6 r 3 r 3 r 3 r 3 r 3
7 r 2 r 2 r 2 r 2 r 2
8 s 3 s 2 g 9
9 r 4 r 4 r 4 r 4 r 4
result
LR Parsing 11
LR(0) parse tables
S → x
S → ( L )
L → S
L → L , S
$
1

70. ( ) x , $ S L
1 s 3 s 2 g 4
2 r 1 r 1 r 1 r 1 r 1
3 s 3 s 2 g 6 g 5
4 a
5 s 7 s 8
6 r 3 r 3 r 3 r 3 r 3
7 r 2 r 2 r 2 r 2 r 2
8 s 3 s 2 g 9
9 r 4 r 4 r 4 r 4 r 4
result
LR Parsing 11
LR(0) parse tables
S → x
S → ( L )
L → S
L → L , S
$
1
4

71. LR Parsing
Conflict Resolution
III
12

72. E → T + . E
E → . T + E
E → . T
T → . x
S → . E $
E → . T + E
E → . T
T → . x
shift-reduce conflicts
LR Parsing
SLR parse tables
13
T → x .
x
E
S → E . $
T
T +
E
E → T . + E
E → T .
E → T + E .
E → T + E
E → T
T → x
x

73. E → T + . E
E → . T + E
E → . T
T → . x
S → . E $
E → . T + E
E → . T
T → . x
shift-reduce conflicts
LR Parsing
SLR parse tables
13
T → x .
x
E
S → E . $
T
T +
E
E → T . + E
E → T .
E → T + E .
E → T + E
E → T
T → x
1
2
3
5 4 6x

74. E → T + . E
E → . T + E
E → . T
T → . x
S → . E $
E → . T + E
E → . T
T → . x
shift-reduce conflicts
LR Parsing
SLR parse tables
13
T → x .
x
E
S → E . $
T
T +
E
E → T . + E
E → T .
E → T + E .
E → T + E
E → T
T → x
1
2
3
5 4 6x
x + $ E T
1 s 5 g 2 g 3
2 a
3 r 2 ? r 2
4 s 5 g 6 g 3
5 r 3 r 3 r 3
6 r 1 r 1 r 1

75. E → T + . E
E → . T + E
E → . T
T → . x
S → . E $
E → . T + E
E → . T
T → . x
shift-reduce conflicts
LR Parsing
SLR parse tables
13
T → x .
x
E
S → E . $
T
T +
E
E → T . + E
E → T .
E → T + E .
E → T + E
E → T
T → x
1
2
3
5 4 6x
x + $ E T
1 s 5 g 2 g 3
2 a
3 s 4 r 2
4 s 5 g 6 g 3
5 r 3 r 3
6 r 1
Reduce a production S → …
on symbols k ∈ Σ, k ∈ Follow(S)

76. look-ahead
LR Parsing
LR(1) parse tables
14
E → T + E
E → T
T → x
S → . E $
E → . T + E
E → . T
T → . x
?
$
$
+ $
E
S → E . $ ?
T E → T . + E
E → T .
$
$
T → x .
x
+ $
T +
x
E → T + . E
E → . T + E
E → . T
T → . x
$
$
$
+ $ E E → T + E . $
closure
• for every item A → α . X β, z
• for every rule X → γ
• for every w ∈ First(βz)
• add item X → . γ, w

77. look-ahead
LR Parsing
LR(1) parse tables
14
E → T + E
E → T
T → x
S → . E $
E → . T + E
E → . T
T → . x
?
$
$
+ $
E
S → E . $ ?
T E → T . + E
E → T .
$
$
T → x .
x
+ $
T +
x
E → T + . E
E → . T + E
E → . T
T → . x
$
$
$
+ $ E E → T + E . $
x + $ E T
1 s 5 g 2 g 3
2 a
3 s 4 r 2
4 s 5 g 6 g 3
5 r 3 r 3
6 r 1
closure
• for every item A → α . X β, z
• for every rule X → γ
• for every w ∈ First(βz)
• add item X → . γ, w

78. state space reduction
LR Parsing
LALR(1) parse tables
unify states
• with same items
• and same outgoing transitions
• but different look-ahead sets
might introduce new conflicts
15

79. state space reduction
LR Parsing
LALR(1) parse tables
16
S’ → S $
S → a E c
S → a F d
S → b F c
S → b E d
E → e
F → e
S' → . S $
S → . a E c
S → . a F d
S → . b F c
S → . b E d
?
$
$
$
$

80. state space reduction
LR Parsing
LALR(1) parse tables
17
S’ → S $
S → a E c
S → a F d
S → b F c
S → b E d
E → e
F → e
S' → . S $
S → . a E c
S → . a F d
S → . b F c
S → . b E d
?
$
$
$
$
S → a . E c
S → a . F d
E → . e
F → . e
$
$
c
d
a

81. state space reduction
LR Parsing
LALR(1) parse tables
18
S’ → S $
S → a E c
S → a F d
S → b F c
S → b E d
E → e
F → e
S' → . S $
S → . a E c
S → . a F d
S → . b F c
S → . b E d
?
$
$
$
$
S → b . F c
S → b . E d
E → . e
F → . e
$
$
d
c
a
b
S → a . E c
S → a . F d
E → . e
F → . e
$
$
c
d

82. state space reduction
LR Parsing
LALR(1) parse tables
19
S’ → S $
S → a E c
S → a F d
S → b F c
S → b E d
E → e
F → e
S' → . S $
S → . a E c
S → . a F d
S → . b F c
S → . b E d
?
$
$
$
$
E → e .
F → e .
c
d
a
b e
S → b . F c
S → b . E d
E → . e
F → . e
$
$
d
c
S → a . E c
S → a . F d
E → . e
F → . e
$
$
c
d

83. state space reduction
LR Parsing
LALR(1) parse tables
20
S’ → S $
S → a E c
S → a F d
S → b F c
S → b E d
E → e
F → e
S' → . S $
S → . a E c
S → . a F d
S → . b F c
S → . b E d
?
$
$
$
$
E → e .
F → e .
c
d
a
b e
e
E → e .
F → e .
d
c
S → b . F c
S → b . E d
E → . e
F → . e
$
$
d
c
S → a . E c
S → a . F d
E → . e
F → . e
$
$
c
d

84. state space reduction
LR Parsing
LALR(1) parse tables
21
S’ → S $
S → a E c
S → a F d
S → b F c
S → b E d
E → e
F → e
S' → . S $
S → . a E c
S → . a F d
S → . b F c
S → . b E d
?
$
$
$
$
E → e .
F → e .
c
d
a
b e
e
E → e .
F → e .
d
c
S → b . F c
S → b . E d
E → . e
F → . e
$
$
d
c
S → a . E c
S → a . F d
E → . e
F → . e
$
$
c
d

85. state space reduction
LR Parsing
LALR(1) parse tables
22
S’ → S $
S → a E c
S → a F d
S → b F c
S → b E d
E → e
F → e
S' → . S $
S → . a E c
S → . a F d
S → . b F c
S → . b E d
?
$
$
$
$
S → a . E c
S → a . F d
E → . e
F → . e
$
$
c
d
S → b . F c
S → b . E d
E → . e
F → . e
$
$
d
c
E → e .
F → e .
{c, d}
{c, d}
a
b e
e

86. state space reduction
LR Parsing
LALR(1) parse tables
23
S’ → S $
S → a E c
S → a F d
S → b F c
S → b E d
E → e
F → e
S' → . S $
S → . a E c
S → . a F d
S → . b F c
S → . b E d
?
$
$
$
$
E → e .
F → e .
{c, d}
{c, d}
a
b e
e Reduce/Reduce
conflict!
S → a . E c
S → a . F d
E → . e
F → . e
$
$
c
d
S → b . F c
S → b . E d
E → . e
F → . e
$
$
d
c

87. LR Parsing
Generalized-LR Parsing
IV
24

88. Lexical Analysis
Generalized Parsing
• Parse all interpretations of the input, therefore it can handle
ambiguous grammars.
• Parsers split whenever finding an ambiguous interpretation and
act in (pseudo) parallel.
• Multiple parsers can join whenever they finish parsing an
ambiguous fragment of the input.
• Some parsers may "die", if the ambiguity was caused by a lack
of lookahead.
25

89. Lexical Analysis
Generalized LR
• Multiple parsers are synchronized on shift actions.
• Each parser has its own stack, and as they share states, the
overall structure becomes a graph (GSS).
• If two parsers have the same state on top of their stack, they
are joined into a single parser.
• Reduce actions affect all possible paths from the top of the
stack.
26

90. Lexical Analysis
Generalized LR
27
S → E $
E → E + E
E → E * E
E → a
SLR table

91. Lexical Analysis
Generalized LR
28
S → E $
E → E + E
E → E * E
E → a
S → . E $
E → . E + E
E → . E * E
E → . a
0
SLR table

92. Lexical Analysis
Generalized LR
29
S → E $
E → E + E
E → E * E
E → a
S → . E $
E → . E + E
E → . E * E
E → . a
S → E . $
E → E . + E
E → E . * E
E → a .
E
a
10
2
SLR table

93. Lexical Analysis
Generalized LR
30
S → E $
E → E + E
E → E * E
E → a
S → . E $
E → . E + E
E → . E * E
E → . a
S → E . $
E → E . + E
E → E . * E
E → a .
E → E + . E
E → . E + E
E → . E * E
E → . a
E → E * . E
E → . E + E
E → . E * E
E → . a
S → E $ .E
$
a
*
+
10 3
2
4
5
SLR table

94. Lexical Analysis
Generalized LR
31
S → E $
E → E + E
E → E * E
E → a
S → . E $
E → . E + E
E → . E * E
E → . a
S → E . $
E → E . + E
E → E . * E
E → a .
E → E + . E
E → . E + E
E → . E * E
E → . a
E → E * . E
E → . E + E
E → . E * E
E → . a
E → E * E .
E → E . + E
E → E . * E
S → E $ .E
$
a
*
+ E
a
10 3
2
4
5
6
SLR table

95. Lexical Analysis
Generalized LR
32
S → E $
E → E + E
E → E * E
E → a
S → . E $
E → . E + E
E → . E * E
E → . a
S → E . $
E → E . + E
E → E . * E
E → a .
E → E + . E
E → . E + E
E → . E * E
E → . a
E → E * . E
E → . E + E
E → . E * E
E → . a
E → E + E .
E → E . + E
E → E . * E
E → E * E .
E → E . + E
E → E . * E
S → E $ .E
$
a
*
+ E
E
a
a
10 3
2
4
5
7
6
SLR table

96. Lexical Analysis
Generalized LR
33
S → E $
E → E + E
E → E * E
E → a
S → . E $
E → . E + E
E → . E * E
E → . a
S → E . $
E → E . + E
E → E . * E
E → a .
E → E + . E
E → . E + E
E → . E * E
E → . a
E → E * . E
E → . E + E
E → . E * E
E → . a
E → E + E .
E → E . + E
E → E . * E
E → E * E .
E → E . + E
E → E . * E
S → E $ .E
$
a
*
+ E
*
E
+
a
a
10 3
2
4
5
7
6
SLR table

97. Lexical Analysis
Generalized LR
34
S → E $
E → E + E
E → E * E
E → a
S → . E $
E → . E + E
E → . E * E
E → . a
S → E . $
E → E . + E
E → E . * E
E → a .
E → E + . E
E → . E + E
E → . E * E
E → . a
E → E * . E
E → . E + E
E → . E * E
E → . a
E → E + E .
E → E . + E
E → E . * E
E → E * E .
E → E . + E
E → E . * E
S → E $ .E
$
a
*
+ E
*
*
+
E
+
a
a
10 3
2
4
5
7
6
SLR table

98. Lexical Analysis
Generalized LR
35
Nonter
minal
Nullable First Follow
S
E
State
Action Goto
a + * $ S E
0
1
2
3
4
5
6
7
(0) S → E $
(1) E → E + E
(2) E → E * E
(3) E → a
SLR table

99. Lexical Analysis
Generalized LR
36
Nonter
minal
Nullable First Follow
S no a -
E no a +, *, $
State
Action Goto
a + * $ S E
0
1
2
3
4
5
6
7
(0) S → E $
(1) E → E + E
(2) E → E * E
(3) E → a
SLR table

100. Lexical Analysis
Generalized LR
37
Nonter
minal
Nullable First Follow
S no a -
E no a +, *, $
State
Action Goto
a + * $ S E
0 s2 1
1 s4 s5 s3
2 r3 r3 r3
3 acc
4 s2 7
5 s2 6
6 s4/r2 s5/r2 r2
7 s4/r1 s5/r1 r1
(0) S → E $
(1) E → E + E
(2) E → E * E
(3) E → a
SLR table

101. Lexical Analysis
Generalized LR
38
Parsing
State
Action Goto
a + * $ S E
0 s2 1
1 s4 s5 s3
2 r3 r3 r3
3 acc
4 s2 7
5 s2 6
6 s4/r2 s5/r2 r2
7 s4/r1 s5/r1 r1
a + a * a
0
(0) S → E $
(1) E → E + E
(2) E → E * E
(3) E → a

102. Lexical Analysis
Generalized LR
39
Parsing
State
Action Goto
a + * $ S E
0 s2 1
1 s4 s5 s3
2 r3 r3 r3
3 acc
4 s2 7
5 s2 6
6 s4/r2 s5/r2 r2
7 s4/r1 s5/r1 r1
+ a * a
0
2a
(0) S → E $
(1) E → E + E
(2) E → E * E
(3) E → a
synchronize on shifts

103. 0
2a
Lexical Analysis
Generalized LR
40
Parsing
State
Action Goto
a + * $ S E
0 s2 1
1 s4 s5 s3
2 r3 r3 r3
3 acc
4 s2 7
5 s2 6
6 s4/r2 s5/r2 r2
7 s4/r1 s5/r1 r1
+ a * a
(0) S → E $
(1) E → E + E
(2) E → E * E
(3) E → a

104. Lexical Analysis
Generalized LR
41
Parsing
State
Action Goto
a + * $ S E
0 s2 1
1 s4 s5 s3
2 r3 r3 r3
3 acc
4 s2 7
5 s2 6
6 s4/r2 s5/r2 r2
7 s4/r1 s5/r1 r1
+ a * a
(0) S → E $
(1) E → E + E
(2) E → E * E
(3) E → a
0
2a
1a : E

105. 0
2a
1a : E 4
+
Lexical Analysis
Generalized LR
42
Parsing
State
Action Goto
a + * $ S E
0 s2 1
1 s4 s5 s3
2 r3 r3 r3
3 acc
4 s2 7
5 s2 6
6 s4/r2 s5/r2 r2
7 s4/r1 s5/r1 r1
a * a
(0) S → E $
(1) E → E + E
(2) E → E * E
(3) E → a
synchronize

106. Lexical Analysis
Generalized LR
43
Parsing
State
Action Goto
a + * $ S E
0 s2 1
1 s4 s5 s3
2 r3 r3 r3
3 acc
4 s2 7
5 s2 6
6 s4/r2 s5/r2 r2
7 s4/r1 s5/r1 r1
a * a
(0) S → E $
(1) E → E + E
(2) E → E * E
(3) E → a
0
1a : E 4
+

107. Lexical Analysis
Generalized LR
44
Parsing
State
Action Goto
a + * $ S E
0 s2 1
1 s4 s5 s3
2 r3 r3 r3
3 acc
4 s2 7
5 s2 6
6 s4/r2 s5/r2 r2
7 s4/r1 s5/r1 r1
* a
(0) S → E $
(1) E → E + E
(2) E → E * E
(3) E → a
0
1a : E 4
+
2
a
synchronize

108. 0
1a : E 4
+
2
a
Lexical Analysis
Generalized LR
45
Parsing
State
Action Goto
a + * $ S E
0 s2 1
1 s4 s5 s3
2 r3 r3 r3
3 acc
4 s2 7
5 s2 6
6 s4/r2 s5/r2 r2
7 s4/r1 s5/r1 r1
* a
(0) S → E $
(1) E → E + E
(2) E → E * E
(3) E → a

109. 0
1a : E 4
+
2
a
a : E
7
Lexical Analysis
Generalized LR
46
Parsing
State
Action Goto
a + * $ S E
0 s2 1
1 s4 s5 s3
2 r3 r3 r3
3 acc
4 s2 7
5 s2 6
6 s4/r2 s5/r2 r2
7 s4/r1 s5/r1 r1
* a
(0) S → E $
(1) E → E + E
(2) E → E * E
(3) E → a

110. Lexical Analysis
Generalized LR
47
Parsing
* a
(0) S → E $
(1) E → E + E
(2) E → E * E
(3) E → a
0
1a : E 4
+
2
a
a : E
7
1a + a : E
State
Action Goto
a + * $ S E
0 s2 1
1 s4 s5 s3
2 r3 r3 r3
3 acc
4 s2 7
5 s2 6
6 s4/r2 s5/r2 r2
7 s4/r1 s5/r1 r1

111. 0
1a : E 4
+
2
a
a : E
7
1a + a : E
5
**
Lexical Analysis
Generalized LR
48
Parsing
a
(0) S → E $
(1) E → E + E
(2) E → E * E
(3) E → a
synchronize
State
Action Goto
a + * $ S E
0 s2 1
1 s4 s5 s3
2 r3 r3 r3
3 acc
4 s2 7
5 s2 6
6 s4/r2 s5/r2 r2
7 s4/r1 s5/r1 r1

112. Lexical Analysis
Generalized LR
49
Parsing
State
Action Goto
a + * $ S E
0 s2 1
1 s4 s5 s3
2 r3 r3 r3
3 acc
4 s2 7
5 s2 6
6 s4/r2 s5/r2 r2
7 s4/r1 s5/r1 r1
(0) S → E $
(1) E → E + E
(2) E → E * E
(3) E → a
0
1a : E 4
+
a : E
7
1a + a : E
5
*
*
a

113. 0
1a : E 4
+
a : E
7
1a + a : E
5
*
*
2
a
Lexical Analysis
Generalized LR
50
Parsing
State
Action Goto
a + * $ S E
0 s2 1
1 s4 s5 s3
2 r3 r3 r3
3 acc
4 s2 7
5 s2 6
6 s4/r2 s5/r2 r2
7 s4/r1 s5/r1 r1
(0) S → E $
(1) E → E + E
(2) E → E * E
(3) E → a
synchronize

114. 0
1a : E 4
+
a : E
7
1a + a : E
5
*
*
2
a
Lexical Analysis
Generalized LR
51
Parsing
(0) S → E $
(1) E → E + E
(2) E → E * E
(3) E → a
State
Action Goto
a + * $ S E
0 s2 1
1 s4 s5 s3
2 r3 r3 r3
3 acc
4 s2 7
5 s2 6
6 s4/r2 s5/r2 r2
7 s4/r1 s5/r1 r1

115. 0
1a : E 4
+
a : E
7
1a + a : E
5
*
*
6
a : E
Lexical Analysis
Generalized LR
52
Parsing
(0) S → E $
(1) E → E + E
(2) E → E * E
(3) E → a
State
Action Goto
a + * $ S E
0 s2 1
1 s4 s5 s3
2 r3 r3 r3
3 acc
4 s2 7
5 s2 6
6 s4/r2 s5/r2 r2
7 s4/r1 s5/r1 r1

116. 0
1a : E 4
+
a : E
7
1a + a : E
5
*
*
6
a : E
Lexical Analysis
Generalized LR
53
Parsing
State
Action Goto
a + * $ S E
0 s2 1
1 s4 s5 s3
2 r3 r3 r3
3 acc
4 s2 7
5 s2 6
6 s4/r2 s5/r2 r2
7 s4/r1 s5/r1 r1
(0) S → E $
(1) E → E + E
(2) E → E * E
(3) E → a

117. 0
1a : E 4
+
a : E
7
1a + a : E
5
*
*
6
a : E
7
a * a : E
Lexical Analysis
Generalized LR
54
Parsing
State
Action Goto
a + * $ S E
0 s2 1
1 s4 s5 s3
2 r3 r3 r3
3 acc
4 s2 7
5 s2 6
6 s4/r2 s5/r2 r2
7 s4/r1 s5/r1 r1
(0) S → E $
(1) E → E + E
(2) E → E * E
(3) E → a

118. 0
1a : E 4
+
a : E
7
1a + a : E
5
*
*
6
a : E
7
a * a : E
Lexical Analysis
Generalized LR
55
Parsing
State
Action Goto
a + * $ S E
0 s2 1
1 s4 s5 s3
2 r3 r3 r3
3 acc
4 s2 7
5 s2 6
6 s4/r2 s5/r2 r2
7 s4/r1 s5/r1 r1
(0) S → E $
(1) E → E + E
(2) E → E * E
(3) E → a

119. 0
1a : E 4
+
a : E
7
1a + a : E
5
*
*
6
a : E
7
a * a : E
1
[a + a] * a : E
Lexical Analysis
Generalized LR
56
Parsing
State
Action Goto
a + * $ S E
0 s2 1
1 s4 s5 s3
2 r3 r3 r3
3 acc
4 s2 7
5 s2 6
6 s4/r2 s5/r2 r2
7 s4/r1 s5/r1 r1
(0) S → E $
(1) E → E + E
(2) E → E * E
(3) E → a

120. 0
1a : E 4
+
a : E
7
1a + a : E
5
*
*
6
a : E
7
a * a : E
1
[a + a] * a : E
Lexical Analysis
Generalized LR
57
Parsing
State
Action Goto
a + * $ S E
0 s2 1
1 s4 s5 s3
2 r3 r3 r3
3 acc
4 s2 7
5 s2 6
6 s4/r2 s5/r2 r2
7 s4/r1 s5/r1 r1
(0) S → E $
(1) E → E + E
(2) E → E * E
(3) E → a

121. [a + a] * a : E
or
a + [a * a] : E
0
1a : E 4
+
a : E
7
1a + a : E
5
*
*
6
a : E
7
a * a : E
1
Lexical Analysis
Generalized LR
58
Parsing
State
Action Goto
a + * $ S E
0 s2 1
1 s4 s5 s3
2 r3 r3 r3
3 acc
4 s2 7
5 s2 6
6 s4/r2 s5/r2 r2
7 s4/r1 s5/r1 r1
(0) S → E $
(1) E → E + E
(2) E → E * E
(3) E → a

122. [a + a] * a : E
or
a + [a * a] : E
0
1a : E 4
+
a : E
7
1a + a : E
5
*
*
6
a : E
7
a * a : E
1 3
$
Lexical Analysis
Generalized LR
59
Parsing
State
Action Goto
a + * $ S E
0 s2 1
1 s4 s5 s3
2 r3 r3 r3
3 acc
4 s2 7
5 s2 6
6 s4/r2 s5/r2 r2
7 s4/r1 s5/r1 r1
(0) S → E $
(1) E → E + E
(2) E → E * E
(3) E → a
synchronize
accept with trees on the link to initial state

123. LR Parsing
Scannerless Generalized-LR Parsing
V
60

124. Lexical Analysis
Scannerless Generalized LR
• Integrates scanning + parsing into a single GLR algorithm.
• Normalization separates lexical and context-free symbols.
• Crucial for avoiding conflicts when composing languages.
• Introduces lexical ambiguities. Solution:
‣Follow Restrictions (implement longest match).
‣Reject Rules (implement reserved keywords).
61

125. Lexical Analysis
Scannerless Generalized LR
62
Normalization
context-free syntax
Exp.Add = <<Exp> + <Exp>> {left}
Exp.Inc = <<Exp>++>
Exp.ID = ID
lexical syntax
ID = [a-zA-Z] IDRest*
IDRest = [a-zA-Z0-9]
LAYOUT = [ tnr]
ID = "let" {reject}

126. context-free syntax
Exp.Add = <<Exp> + <Exp>> {left}
Exp.Inc = <<Exp>++>
Exp.ID = ID
lexical syntax
ID = [a-zA-Z] IDRest*
IDRest = [a-zA-Z0-9]
LAYOUT = [ tnr]
ID = "let" {reject}
Lexical Analysis
Scannerless Generalized LR
63
Normalization
Exp-CF.Add = Exp-CF LAYOUT?-CF "+" LAYOUT?-CF Exp-CF {left}
Exp-CF.Inc = Exp-CF LAYOUT?-CF "++"
Exp-CF.ID = ID-CF
ID-LEX = [a-zA-Z] IDRest*-LEX
IDRest*-LEX = [a-zA-Z0-9]
ID-LEX = "let" {reject}
LAYOUT-CF = LAYOUT-LEX
Separate lexical from context-free symbols
and separate symbols in context-free syntax
by optional layout.

127. Lexical Analysis
Scannerless Generalized LR
64
Normalization
LAYOUT-CF = LAYOUT-LEX
IDRest-CF = IDRest-LEX
IDRest*-CF = IDRest*-LEX
ID-CF = ID-LEX
context-free syntax
Exp.Add = <<Exp> + <Exp>> {left}
Exp.Inc = <<Exp>++>
Exp.ID = ID
lexical syntax
ID = [a-zA-Z] IDRest*
IDRest = [a-zA-Z0-9]
LAYOUT = [ tnr]
ID = "let" {reject}
Create injections from lexical to
context-free symbols

128. Lexical Analysis
Scannerless Generalized LR
65
Normalization
"+" = [43]
"++" = [43] [43]
"let" = [108] [101] [116]
ID-LEX = [65-9097-122] IDRest*-LEX
IDRest*-LEX = [48-5765-9097-122]
LAYOUT-LEX = [9-101332]
context-free syntax
Exp.Add = <<Exp> + <Exp>> {left}
Exp.Inc = <<Exp>++>
Exp.ID = ID
lexical syntax
ID = [a-zA-Z] IDRest*
IDRest = [a-zA-Z0-9]
LAYOUT = [ tnr]
ID = "let" {reject}
Normalize literals symbols and
character classes.

129. Lexical Analysis
Scannerless Generalized LR
66
Normalization
LAYOUT?-CF = LAYOUT-CF
LAYOUT?-CF =
IDRest+-LEX = IDRest-LEX
IDRest+-LEX = IDRest+-LEX IDRest-LEX
IDRest*-LEX =
IDRest*-LEX = IDRest+-LEX
IDRest+-CF = IDRest+-LEX
context-free syntax
Exp.Add = <<Exp> + <Exp>> {left}
Exp.Inc = <<Exp>++>
Exp.ID = ID
lexical syntax
ID = [a-zA-Z] IDRest*
IDRest = [a-zA-Z0-9]
LAYOUT = [ tnr]
ID = "let" {reject}
Normalize regular expressions.

130. Lexical Analysis
Scannerless Generalized LR
67
Normalization
context-free start-symbols
Exp
<START> = LAYOUT?-CF Exp-CF LAYOUT?-CF
<Start> = <START> [256]
Define extra rules for the start symbols.

131. Lexical Analysis
Scannerless Generalized LR
68
Parse Table Generation
• Generation is based on SLR(1) item-sets.
• Uses character classes instead of tokens.
• Follow sets and goto actions are calculated for productions
instead of non-terminals.

132. Lexical Analysis
Scannerless Generalized LR
69
Lexical Disambiguation
• A reject rule is of the form:
ID = "let" {reject}
• When SGLR does a reduction with a reject rule, it marks the
link as rejected.
• Further action on a stack is forbidden whenever all links to it
are rejected.
• Follow restrictions are implemented as filters on the follow sets
of productions.

133. Lexical Analysis
Generalized LR
70
• Priority rules: applied at parse table generation.
E → E * . E
E → . E + E
E → . E * E
E → . a
multiplication has higher
priority than addition!
Context-free Disambiguation

134. Lexical Analysis
Generalized LR
71
• Priority rules: applied at parse table generation.
multiplication is left
associative!
E → E * . E
E → . E + E
E → . E * E
E → . a
Context-free Disambiguation

135. Lexical Analysis
Generalized LR
72
• Priority rules: applied at parse table generation.
• Disambiguation filters: applied after parsing (prefer and avoid).
multiplication is left
associative!
E → E * . E
E → . E + E
E → . E * E
E → . a
Context-free Disambiguation

136. LR Parsing
Summary
VI
73

137. lessons learned
LR Parsing
Summary
74

138. lessons learned
LR Parsing
Summary
How can we generate LR parse tables?
• items, closure, goto
74

139. lessons learned
LR Parsing
Summary
How can we generate LR parse tables?
• items, closure, goto
How can we improve LR(0) parse table generation?
• SLR: consider FOLLOW sets to avoid shift-reduce conflicts
• LR(1): consider look-ahead in states
• LALR(1): unify LR(1) states to reduce state space
74

140. lessons learned
LR Parsing
Summary
How can we generate LR parse tables?
• items, closure, goto
How can we improve LR(0) parse table generation?
• SLR: consider FOLLOW sets to avoid shift-reduce conflicts
• LR(1): consider look-ahead in states
• LALR(1): unify LR(1) states to reduce state space
How can we handle conflicts in the parse table?
• generalized parsing - supports all class of context free grammars
• scannerless generalized LR - allow for proper language composition.
74

141. learn more
LR Parsing
Literature
75

142. learn more
LR Parsing
Literature
LR parsing
Andrew W. Appel, Jens Palsberg: Modern Compiler Implementation in Java,
2nd edition. 2002
Alfred V. Aho, Ravi Sethi, Jeffrey D. Ullman, Monica S. Lam: Compilers:
Principles, Techniques, and Tools, 2nd edition. 2006
75

143. learn more
LR Parsing
Literature
LR parsing
Andrew W. Appel, Jens Palsberg: Modern Compiler Implementation in Java,
2nd edition. 2002
Alfred V. Aho, Ravi Sethi, Jeffrey D. Ullman, Monica S. Lam: Compilers:
Principles, Techniques, and Tools, 2nd edition. 2006
Generalised LR parsing
Eelco Visser: Syntax Definition for Language Prototyping. PhD thesis 1997
M.G.J. van den Brand, J. Scheerder, J.J. Vinju, and E. Visser: Disambiguation
Filters for Scannerless Generalized LR Parsers. CC 2002
75

144. LR Parsing
copyrights
76

145. LR Parsing 77

146. copyrights
LR Parsing
Pictures
Slide 1:
Book Scanner by Ben Woosley, some rights reserved
Slide 19:
Ostsee by Mario Thiel, some rights reserved
78