Presentation slides for lecture 12 of course IN4303 on Compiler Construction at TU Delft.

1. Compiler Components & Generators
Traditional Parsing Algorithms
Guido Wachsmuth
Delft
Course IN4303
University of
Technology Compiler Construction
Challenge the future

2. Recap: Lexical Analysis
lessons learned
What are the formalisms to describe regular languages?
• regular grammars
• regular expressions
• finite state automata
Why are these formalisms equivalent?
• constructive proofs
How can we generate compiler tools from that?
• implement DFAs
• generate transition tables
Traditional Parsing Algorithms 2

3. Overview
today’s lecture
Lexical Analysis 3

4. Overview
today’s lecture
the exam
Lexical Analysis 3

5. Overview
today’s lecture
the exam
assignment 3
Lexical Analysis 3

6. Overview
today’s lecture
the exam
assignment 3
efficient parsing algorithms
• predictive parsing
• LR parsing
Lexical Analysis 3

7. Overview
today’s lecture
the exam
assignment 3
efficient parsing algorithms
• predictive parsing
• LR parsing
grammar classes
• LL(k) grammars
• LR(k) grammars
Lexical Analysis 3

8. I
the exam
Lexical Analysis 4

9. The exam
topics
• introduction
• declarative language definition (theory)
• compiling imperative & object-oriented languages
• compiler components & generators
style
• theory in praxis
• understanding over facts
• open questions
• closed book
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10. II
assignment
Lexical Analysis 6

11. MiniJava Compiler
schedule
Lab 1
explore Java Bytecode & Jasmin
first generator version
Lab 2 & 3
generator for statements & expressions
generator for classes, fields & methods
Lab 4
liveness analysis
submission due Jan 9, 23:59
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12. MiniJava Compiler
code generation
class Main {
public static void main(String[] args) {
System.out.println(42) ;
}
}
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13. Recap: Code Generation
to-jbc: Nil() -> [ ACONST_NULL() ]
to-jbc: NoVal() -> [ NOP() ]
to-jbc: Seq(es) -> <mapconcat(to-jbc)> es
to-jbc: Int(i) -> [ LDC(Int(i))
to-jbc: String(s) -> [ LDC(String(s))
to-jbc: Bop(op, e1, e2) -> <concat> [ <to-jbc> e1, <to-jbc> e2, <to-jbc> op ]
to-jbc: PLUS() -> [ IADD() ]
to-jbc: MINUS() -> [ ISUB() ]
to-jbc: MUL() -> [ IMUL() ]
to-jbc: DIV() -> [ IDIV() ]
to-jbc: Assign(lhs, e) -> <concat> [ <to-jbc> e, <lhs-to-jbc> lhs ]
to-jbc: Var(x) -> [ ILOAD(x) ] where <type-of> Var(x) => INT()
to-jbc: Var(x) -> [ ALOAD(x) ] where <type-of> Var(x) => STRING()
lhs-to-jbc: Var(x) -> [ ISTORE(x) ] where <type-of> Var(x) => INT()
lhs-to-jbc: Var(x) -> [ ASTORE(x) ] where <type-of> Var(x) => STRING()
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14. MiniJava Compiler
liveness analysis
.method public static main([Ljava/lang/String;)V
.limit locals 3
.limit stack 4
.var 1 is x I from startX to endX
.var 2 is y Z from startY to endY
...
.end method
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15. MiniJava Compiler
submission
procedure
ensure compiler works
add 5 positive test cases
include your Net ID in project name
export project as zip file
ensure editor works when imported
submit zip file via Blackboard
submission due Jan 9, 23:59
delay costs you 25 points
plus 1 point per hour or part thereof
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16. Assignment: MiniJava Editor
grades
code generation 60 points
classes 10 points
fields & methods 15 points
statements 15 points
expressions 20 points
liveness analysis 30+5 points
maximum stack size 5 bonus points
test cases 10 points
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17. III
predictive parsing
Lexical Analysis 13

18. Recap: A Theory of Language
formal languages
Traditional Parsing Algorithms 14

19. Recap: A Theory of Language
formal languages
vocabulary Σ
finite, nonempty set of elements (words, letters)
alphabet
Traditional Parsing Algorithms 14

20. Recap: A Theory of Language
formal languages
vocabulary Σ
finite, nonempty set of elements (words, letters)
alphabet
string over Σ
finite sequence of elements chosen from Σ
word, sentence, utterance
Traditional Parsing Algorithms 14

21. Recap: A Theory of Language
formal languages
vocabulary Σ
finite, nonempty set of elements (words, letters)
alphabet
string over Σ
finite sequence of elements chosen from Σ
word, sentence, utterance
formal language λ
set of strings over a vocabulary Σ
λ ⊆ Σ*
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22. Recap: A Theory of Language
formal grammars
Traditional Parsing Algorithms 15

23. Recap: A Theory of Language
formal grammars
formal grammar G = (N, Σ, P, S)
nonterminal symbols N
terminal symbols Σ
production rules P ⊆ (N∪Σ)* N (N∪Σ)* × (N∪Σ)*
start symbol S∈N
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24. Recap: A Theory of Language
formal grammars
formal grammar G = (N, Σ, P, S)
nonterminal symbols N nonterminal symbol
terminal symbols Σ
production rules P ⊆ (N∪Σ)* N (N∪Σ)* × (N∪Σ)*
start symbol S∈N
Traditional Parsing Algorithms 15

25. Recap: A Theory of Language
formal grammars
formal grammar G = (N, Σ, P, S)
nonterminal symbols N
terminal symbols Σ
production rules P ⊆ (N∪Σ)* N (N∪Σ)* × (N∪Σ)*
start symbol S∈N
context
Traditional Parsing Algorithms 15

26. Recap: A Theory of Language
formal grammars
formal grammar G = (N, Σ, P, S)
nonterminal symbols N
terminal symbols Σ
production rules P ⊆ (N∪Σ)* N (N∪Σ)* × (N∪Σ)*
start symbol S∈N
replacement
Traditional Parsing Algorithms 15

27. Recap: A Theory of Language
formal grammars
formal grammar G = (N, Σ, P, S)
nonterminal symbols N
terminal symbols Σ
production rules P ⊆ (N∪Σ)* N (N∪Σ)* × (N∪Σ)*
start symbol S∈N
grammar classes
type-0, unrestricted
type-1, context-sensitive: (a A c, a b c)
type-2, context-free: P ⊆ N × (N∪Σ)*
type-3, regular: (A, x) or (A, xB)
Traditional Parsing Algorithms 15

28. Recap: A Theory of Language
formal languages
Traditional Parsing Algorithms 16

29. Recap: A Theory of Language
formal languages
formal grammar G = (N, Σ, P, S)
Traditional Parsing Algorithms 16

30. Recap: A Theory of Language
formal languages
formal grammar G = (N, Σ, P, S)
derivation relation G ⊆ (N∪Σ)* × (N∪Σ)*
w G w’
∃(p, q)∈P: ∃u,v∈(N∪Σ)*:
w=u p v ∧ w’=u q v
Traditional Parsing Algorithms 16

31. Recap: A Theory of Language
formal languages
formal grammar G = (N, Σ, P, S)
derivation relation G ⊆ (N∪Σ)* × (N∪Σ)*
w G w’
∃(p, q)∈P: ∃u,v∈(N∪Σ)*:
w=u p v ∧ w’=u q v
formal language L(G) ⊆ Σ*
L(G) = {w∈Σ* | S G
*
w}
Traditional Parsing Algorithms 16

32. Recap: A Theory of Language
formal languages
formal grammar G = (N, Σ, P, S)
derivation relation G ⊆ (N∪Σ)* × (N∪Σ)*
w G w’
∃(p, q)∈P: ∃u,v∈(N∪Σ)*:
w=u p v ∧ w’=u q v
formal language L(G) ⊆ Σ*
L(G) = {w∈Σ* | S G
*
w}
classes of formal languages
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33. Predictive parsing
recursive descent
Exp → “while” Exp “do” Exp
public void parseExp() {
consume(WHILE);
parseExp();
consume(DO);
parseExp();
}
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34. Predictive parsing
look ahead
Exp → “while” Exp “do” Exp
Exp → “if” Exp “then” Exp “else” Exp
public void parseExp() {
switch current() {
case WHILE: consume(WHILE); parseExp(); ...; break;
case IF : consume(IF); parseExp(); ...; break;
default : error();
}
}
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35. Predictive parsing
parse table
rows T1 T2 T3 ...
• nonterminal symbols N N1 N1 →... N1 →...
• symbol to parse N2 N2 →...
columns N3 N3 →... N3 →...
N4 N4 →...
• terminal symbols Σ k
N5 N5 →...
• look ahead k
N6 N6 →... N6 →...
entries
N7 N7 →...
• production rules P
N8 N8 →... N8 →... N8 →...
• possible conflicts
...
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36. Predictive parsing
automaton
input
t1 … tn $
parse table
S
stack
$
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37. Predictive parsing
automaton
x … $
x
…
$
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38. Predictive parsing
automaton
… $
…
$
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39. Predictive parsing
automaton
x … $
x
Xi Xi
Xi → Y1... Yk
…
$
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40. Predictive parsing
automaton
x … $
Y1 x
…
Yk Xi
Xi → Y1... Yk
…
$
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41. Predictive parsing
filling the table
entry (X, w)∈P at row X and column T
T∈FIRST(w)
nullable(w) ∧ T∈FOLLOW(X)
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42. Predictive parsing
nullable
nullable(X)
(X, ε) ∈ P nullable(X)
(X0, X1 … Xk)∈P ∧ nullable(X1) ∧ … ∧ nullable(Xk) nullable(X0)
nullable(w)
nullable(ε)
nullable(X1 … Xk) = nullable(X1) ∧ … ∧ nullable(Xk)
Traditional Parsing Algorithms 24

43. Predictive parsing
first sets
FIRST(X)
X∈Σ : FIRST(X) = {X}
(X0, X1 … Xi … Xk)∈P ∧ nullable(X1 … Xi) FIRST(X0) ⊇ FIRST(Xi+1)
FIRST(w)
FIRST(ε) = {}
¬nullable(X) FIRST(Xw) = FIRST(X)
nullable(X) FIRST(Xw) = FIRST(X) ∪ FIRST(w)
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44. Predictive parsing
follow sets
FOLLOW(X)
(X0, X1 … Xi … Xk)∈P ∧ nullable(Xi+1 … Xk) FOLLOW(Xi) ⊇ FOLLOW(X0)
(X0, X1 … Xi … Xk)∈P FOLLOW(Xi) ⊇ FIRST(Xi+1 … Xk)
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45. Predictive parsing
encoding precedence
Exp → Num
Exp → “(” Exp “)”
Exp → Exp “*” Exp
Exp → Exp “+” Exp
Fact → Num
Fact → “(” Exp “)”
Term → Term “*” Fact
Term → Fact
Exp → Exp “+” Term
Exp → Term
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46. Predictive parsing
eliminating left recursion
Term → Term “*” Fact
Term → Fact
Exp → Exp “+” Term
Exp → Term
Term’ → “*” Fact Term’
Term’ →
Term → Fact Term’
Exp’ → “+” Term Exp’
Exp’ →
Exp → Term Exp’
Traditional Parsing Algorithms 28

47. Predictive parsing
left factoring
Exp → “if” Exp “then” Exp “else” Exp
Exp → “if” Exp “then” Exp
Exp → “if” Exp “then” Exp Else
Else → “else” Exp
Else →
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48. Grammar classes
context-free grammars
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49. Grammar classes
context-free grammars
LL(0)
Traditional Parsing Algorithms 30

50. Grammar classes
context-free grammars
LL(1)
LL(0)
Traditional Parsing Algorithms 30

51. Grammar classes
context-free grammars
LL(k)
LL(1)
LL(0)
Traditional Parsing Algorithms 30

52. coffee break
Traditional Parsing Algorithms 31

53. IV
LR parsing
Lexical Analysis 32

54. LR parsing
idea
problems with LL parsing
• predicting right rule
• left recursion
LR parsing
• see whole left-hand side of a rule
• look ahead
• shift or reduce
Traditional Parsing Algorithms 33

55. LR parsing
example
stack input
$ 7 * 3 + 7 * 3 $
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56. LR parsing
example
$ 7 * 3 + 7 * 3 $
Traditional Parsing Algorithms 34

57. LR parsing
example
$ 7 * 3 + 7 * 3 $
Traditional Parsing Algorithms 34

58. LR parsing
example
$ 7 * 3 + 7 * 3 $
$ E * 3 + 7 * 3 $
Traditional Parsing Algorithms 34

59. LR parsing
example
$ 7 * 3 + 7 * 3 $
$ E * 3 + 7 * 3 $
Traditional Parsing Algorithms 34

60. LR parsing
example
$ 7 * 3 + 7 * 3 $
$ E * 3 + 7 * 3 $
Traditional Parsing Algorithms 34

61. LR parsing
example
$ 7 * 3 + 7 * 3 $
$ E * 3 + 7 * 3 $
$ E * E + 7 * 3 $
Traditional Parsing Algorithms 34

62. LR parsing
example
$ 7 * 3 + 7 * 3 $
$ E * 3 + 7 * 3 $
$ E * E + 7 * 3 $
$ E + 7 * 3 $
Traditional Parsing Algorithms 34

63. LR parsing
example
$ 7 * 3 + 7 * 3 $
$ E * 3 + 7 * 3 $
$ E * E + 7 * 3 $
$ E + 7 * 3 $
Traditional Parsing Algorithms 34

64. LR parsing
example
$ 7 * 3 + 7 * 3 $
$ E * 3 + 7 * 3 $
$ E * E + 7 * 3 $
$ E + 7 * 3 $
Traditional Parsing Algorithms 34

65. LR parsing
example
$ 7 * 3 + 7 * 3 $
$ E * 3 + 7 * 3 $
$ E * E + 7 * 3 $
$ E + 7 * 3 $
$ E + E * 3 $
Traditional Parsing Algorithms 34

66. LR parsing
example
$ 7 * 3 + 7 * 3 $
$ E * 3 + 7 * 3 $
$ E * E + 7 * 3 $
$ E + 7 * 3 $
$ E + E * 3 $
Traditional Parsing Algorithms 34

67. LR parsing
example
$ 7 * 3 + 7 * 3 $
$ E * 3 + 7 * 3 $
$ E * E + 7 * 3 $
$ E + 7 * 3 $
$ E + E * 3 $
Traditional Parsing Algorithms 34

68. LR parsing
example
$ 7 * 3 + 7 * 3 $
$ E * 3 + 7 * 3 $
$ E * E + 7 * 3 $
$ E + 7 * 3 $
$ E + E * 3 $
$ E + E * E $
Traditional Parsing Algorithms 34

69. LR parsing
example
$ 7 * 3 + 7 * 3 $
$ E * 3 + 7 * 3 $
$ E * E + 7 * 3 $
$ E + 7 * 3 $
$ E + E * 3 $
$ E + E * E $
$ E + E $
Traditional Parsing Algorithms 34

70. LR parsing
example
$ 7 * 3 + 7 * 3 $
$ E * 3 + 7 * 3 $
$ E * E + 7 * 3 $
$ E + 7 * 3 $
$ E + E * 3 $
$ E + E * E $
$ E + E $
$ E $
Traditional Parsing Algorithms 34

71. LR parsing
example
$ 7 * 3 + 7 * 3 $
$ E * 3 + 7 * 3 $
$ E * E + 7 * 3 $
$ E + 7 * 3 $
$ E + E * 3 $
$ E + E * E $
$ E + E $
$ E $
Traditional Parsing Algorithms 34

72. LR parsing
example
$ 7 * 3 + 7 * 3 $
$ E * 3 + 7 * 3 $
$ E * E + 7 * 3 $
$ E + 7 * 3 $
$ E + E * 3 $
$ E + E * E $
$ E + E $
$ E $
$ S
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73. LR parsing
parse table
rows T1 ... N1 ...
• states of a DFA 1 s3
2 g5
columns
3 r1
• topmost stack symbol
4 r2
• Σ, N
5
entries
6 g1
• reduce, goto state 7 s1
• shift, goto state
8
• goto state
...
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74. Grammar classes
context-free grammars
LL(k)
LL(1)
LL(0)
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75. Grammar classes
context-free grammars
LL(k)
LL(1)
LL(0) LR(0)
Traditional Parsing Algorithms 36

76. Grammar classes
context-free grammars
LL(k)
LL(1) LR(1)
LL(0) LR(0)
Traditional Parsing Algorithms 36

77. Grammar classes
context-free grammars
LL(k) LR(k)
LL(1) LR(1)
LL(0) LR(0)
Traditional Parsing Algorithms 36

78. Grammar classes
context-free grammars
LL(k) LR(k)
LL(1) LR(1)
SLR
LL(0) LR(0)
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79. Grammar classes
context-free grammars
LL(k) LR(k)
LL(1) LR(1)
LALR(1)
SLR
LL(0) LR(0)
Traditional Parsing Algorithms 36

80. V
summary
Lexical Analysis 37

81. Summary
lessons learned
Traditional Parsing Algorithms 38

82. Summary
lessons learned
How can we parse context-free languages effectively?
• predictive parsing algorithms
• LR parsing algorithms
Traditional Parsing Algorithms 38

83. Summary
lessons learned
How can we parse context-free languages effectively?
• predictive parsing algorithms
• LR parsing algorithms
Which grammar classes are supported by these algorithms?
• LL(k) grammars, LL(k) languages
• LR(k) grammars, LR(k) languages
Traditional Parsing Algorithms 38

84. Summary
lessons learned
How can we parse context-free languages effectively?
• predictive parsing algorithms
• LR parsing algorithms
Which grammar classes are supported by these algorithms?
• LL(k) grammars, LL(k) languages
• LR(k) grammars, LR(k) languages
How can we generate compiler tools from that?
• implement automata
• generate parse tables
Traditional Parsing Algorithms 38

85. Summary
lessons learned
How can we parse context-free languages effectively?
• predictive parsing algorithms
• LR parsing algorithms
Which grammar classes are supported by these algorithms?
• LL(k) grammars, LL(k) languages
• LR(k) grammars, LR(k) languages
How can we generate compiler tools from that?
• implement automata
• generate parse tables
Traditional Parsing Algorithms 38

86. Literature
learn more
Traditional Parsing Algorithms 39

87. Literature
learn more
formal languages
Noam Chomsky: Three models for the description of language. 1956
J. E. Hopcroft, R. Motwani, J. D. Ullman: Introduction to Automata
Theory, Languages, and Computation. 2006
Traditional Parsing Algorithms 39

88. Literature
learn more
formal languages
Noam Chomsky: Three models for the description of language. 1956
J. E. Hopcroft, R. Motwani, J. D. Ullman: Introduction to Automata
Theory, Languages, and Computation. 2006
syntactical analysis
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
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89. Outlook
coming next
lectures
• Lecture 13: SDF inside
• Lecture 14: Static analysis
• Lecture 15: Beyond grammarware
Question & Answer Jan 5
• 10 questions, submit & vote
Lab Dec 3
• explore Java Bytecode
• explore Jasmin
• start generator
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90. questions
Lexical Analysis 41

91. credits
Lexical Analysis 42

92. Pictures
copyrights
Slide 1: Book Scanner by Ben Woosley, some rights reserved
Slide 5: Report card by Carosaurus, some rights reserved
Slides 7, 12: Students, TU Delft, Media Solutions, all rights reserved
Slides 8, 10: Italian Java book cover by unknown artist, some rights reserved
Slide 11: Envelopes by benchilada, some rights reserved
Slides 14-16: Noam Chomsky by Fellowsisters, some rights reserved
Slide 17, 18, 27-29: Tiger by Bernard Landgraf, some rights reserved
Slide 31: West Cornwall Pasty Co. by Dominica Williamson, some rights reserved
Slide 40: Ostsee by Mario Thiel, some rights reserved
Slide 41: Questions by Oberazzi, some rights reserved
Slide 42: Too Much Credit by Andres Rueda, some rights reserved
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