Compiler Components and their Generators - Traditional Parsing Algorithms
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This document discusses parsing algorithms for compilers. It begins with an overview of topics to be covered, including lexical analysis, parsing algorithms like predictive and LR parsing, grammar classes, and an assignment on implementing a MiniJava compiler. It then covers predictive parsing in more detail, including how to generate parsing tables from grammars and how to use these tables in a predictive parsing automaton. Finally, it discusses LR parsing and how it can handle issues like left recursion that predictive parsing cannot. It provides an example of an LR parsing step involving expression evaluation.
![MiniJava Compiler
code generation
class Main {
public static void main(String[] args) {
System.out.println(42) ;
}
}
Traditional Parsing Algorithms 8](https://image.slidesharecdn.com/cc-parsing-101202183301-phpapp01/85/Compiler-Components-and-their-Generators-Traditional-Parsing-Algorithms-12-320.jpg)
![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()
Traditional Parsing Algorithms 9](https://image.slidesharecdn.com/cc-parsing-101202183301-phpapp01/85/Compiler-Components-and-their-Generators-Traditional-Parsing-Algorithms-13-320.jpg)
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Compiler Components and their Generators - Traditional Parsing Algorithms
- 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 Traditional Parsing Algorithms 5
- 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 Traditional Parsing Algorithms 7
- 12. MiniJava Compiler code generation class Main { public static void main(String[] args) { System.out.println(42) ; } } Traditional Parsing Algorithms 8
- 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() Traditional Parsing Algorithms 9
- 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 Traditional Parsing Algorithms 10
- 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 Traditional Parsing Algorithms 11
- 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 Traditional Parsing Algorithms 12
- 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* Traditional Parsing Algorithms 14
- 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 Traditional Parsing Algorithms 15
- 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 Traditional Parsing Algorithms 16
- 33. Predictive parsing recursive descent Exp → “while” Exp “do” Exp public void parseExp() { consume(WHILE); parseExp(); consume(DO); parseExp(); } Traditional Parsing Algorithms 17
- 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(); } } Traditional Parsing Algorithms 18
- 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 ... Traditional Parsing Algorithms 19
- 36. Predictive parsing automaton input t1 … tn $ parse table S stack $ Traditional Parsing Algorithms 20
- 37. Predictive parsing automaton x … $ x … $ Traditional Parsing Algorithms 21
- 38. Predictive parsing automaton … $ … $ Traditional Parsing Algorithms 21
- 39. Predictive parsing automaton x … $ x Xi Xi Xi → Y1... Yk … $ Traditional Parsing Algorithms 22
- 40. Predictive parsing automaton x … $ Y1 x … Yk Xi Xi → Y1... Yk … $ Traditional Parsing Algorithms 22
- 41. Predictive parsing filling the table entry (X, w)∈P at row X and column T T∈FIRST(w) nullable(w) ∧ T∈FOLLOW(X) Traditional Parsing Algorithms 23
- 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) Traditional Parsing Algorithms 25
- 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) Traditional Parsing Algorithms 26
- 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 Traditional Parsing Algorithms 27
- 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 → Traditional Parsing Algorithms 29
- 48. Grammar classes context-free grammars Traditional Parsing Algorithms 30
- 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 $ Traditional Parsing Algorithms 34
- 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 Traditional Parsing Algorithms 34
- 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 ... Traditional Parsing Algorithms 35
- 74. Grammar classes context-free grammars LL(k) LL(1) LL(0) Traditional Parsing Algorithms 36
- 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) Traditional Parsing Algorithms 36
- 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 Traditional Parsing Algorithms 39
- 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 Traditional Parsing Algorithms 40
- 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 Traditional Parsing Algorithms 43
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