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Bottom-Up Syntax Analysis

Bottom-Up Syntax Analysis. Mooly Sagiv http://www.cs.tau.ac.il/~msagiv/courses/wcc13.html Textbook:Modern Compiler Design Chapter 2.2.5 (modified). Pushdown automata Deterministic Report an error as soon as the input is not a prefix of a valid program

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Bottom-Up Syntax Analysis

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  1. Bottom-Up Syntax Analysis Mooly Sagiv http://www.cs.tau.ac.il/~msagiv/courses/wcc13.html Textbook:Modern Compiler Design Chapter 2.2.5 (modified)

  2. Pushdown automata Deterministic Report an error as soon as the input is not a prefix of a valid program Not usable for all context free grammars context free grammar tokens parser Efficient Parsers cup “Ambiguity errors” parse tree

  3. Top-Down (Predictive Parsing) LL Construct parse tree in a top-down matter Find the leftmost derivation For every non-terminal and token predict the next production Bottom-Up LR Construct parse tree in a bottom-up manner Find the rightmost derivation in a reverse order For every potential right hand side and token decide when a production is found Kinds of Parsers

  4. Input A context free grammar A stream of tokens Output A syntax tree or error Method Construct parse tree in a bottom-up manner Find the rightmost derivation in (reversed order) For every potential right hand side and token decide when a production is found Report an error as soon as the input is not a prefix of valid program Bottom-Up Syntax Analysis

  5. Pushdown automata Bottom-up parsing (informal) Non-deterministic bottom-up parsing Deterministic bottom-up parsing Interesting non LR grammars Plan

  6. Pushdown Automaton input u t w $ V control parser-table $ stack

  7. stack tree input $ i + i $ stack tree input + i $ i$ i Informal Example(1) S  E$E  T | E + TT i|(E) shift

  8. stack tree input T$ T + i $ i i Informal Example(2) S  E$E  T | E+TT i|( E) stack tree input i$ + i $ reduceT i

  9. T stack tree input E E$ + i $ T i i Informal Example(3) S  E$E  T | E+TT i | ( E) stack tree input T$ + i $ reduce E  T

  10. E stack tree input +E$ E i $ T T i i + Informal Example(4) S  E$E  T| E+TT i|(E) stack tree input E$ + i $ shift

  11. E stack tree input E i+E$ $ T T + i i i + Informal Example(5) S  E$E  T| E+TT i|(E) stack tree input +E$ i $ shift

  12. stack tree input E T+E$ $ T T T i i + + i i Informal Example(6) S  E$E  T| E+TT i|(E) stack tree input E i+E$ $ reduce T i

  13. stack tree input E $ E$ E T T T i i i + + Informal Example(7) S  E$E  T| E+TT i|(E) stack tree input E $ T T+E$ reduce E E+T i

  14. stack tree input E $E $ E T T T i i i + + Informal Example(8) S  E$E  T| E+TT i|(E) stack tree input E $ E$ E T shift i

  15. T i + Informal Example(9) S  E$E  T| E+TT i|(E) stack tree input E $ $E $ E T i reduce S  E$

  16. Informal Example reduce S  E$ reduce E  E+T reduce T i reduce E  T reduce T  i

  17. The Problem • Deciding between shift and reduce

  18. stack tree input E $ E$ E T T T i i i + + Informal Example(7) S  E$ E  T | E+T T i| (E) stack tree input E $ T T+E$ reduce E E + T i

  19. E E T T E i i i + + Informal Example(7’) S  E$ E  T | E+T T i|( E) stack tree input E $ T T+E$ reduce E  T stack tree input $ E+E$ 

  20. still need to be matched already matched regularexpression input input T· expecting to match  already matched  Bottom-UP LR(0) Items

  21. S  E$ E  T E  E+ T T i T (E)

  22. stack input 6: E E+T 1: S E$ i + i $ Formal Example(1) S  E$ E  T | E+TT i| (E) stack input 1: S E$ i + i $ -move 6

  23. stack stack input input 4: E T 6: E E+T 1: S E$ 6: E E+T 1: S E$ i + i $ i + i $ Formal Example(2) S  E$ E  T | E+T T i|(E) -move 4

  24. stack stack input input 10: T  i 4: E T 6: E E+T 1: S E$ 4: ET 6: E E+T 1: S E$ i + i $ i + i $ Formal Example(3) S  E$ E  T | E+TT i |(E) -move 10

  25. stack input 11: T i 10: T  i 4: E T 6: E E+T 1: S E$ + i $ Formal Example(4) S  E$ E  T | E+T T i|(E) stack input 10: T  i 4: E T 6: E E+T 1: S E$ i + i $ shift 11

  26. stack input 5: E  T 4: E T 6: E E+T 1: S E$ + i $ Formal Example(5) S  E$ E T | E+ TT i|(E) stack input 11: T i 10: T  i 4: E T 6: E E+T 1: S E$ + i $ reduce T i

  27. stack stack input input 7: E  E+T 6: E E+T 1: S E$ 5: E  T 4: E T 6: E E+T 1: S E$ + i $ + i $ Formal Example(6) S  E$ E  T | E+ T T i|(E) reduce E  T

  28. stack stack input input 8: E  E+T 7: E  E+T 6: E E+T 1: S E$ 7: E  E+T 6: E E+T 1: S E$ i $ + i $ Formal Example(7) S  E$ E  T| E+TT i| (E) shift 8

  29. stack input 10: T i 8: E  E+T 7: E  E+T 6: E E+T 1: S E$ i $ stack input 8: E  E+T 7: E  E+T 6: E E+T 1: S E$ i $ Formal Example(8) S  E$ E  T | E+T T i| (E) -move 10

  30. stack input 11: T i  10: T i 8: E  E+T 7: E  E+T 6: E E+T 1: S E$ stack input $ 10: T i 8: E  E+T 7: E  E+T 6: E E+T 1: S E$ i $ Formal Example(9) S  E$ E  T | E+T T i| (E) shift 11

  31. stack input 9: E  E+T  8: E  E+T 7: E  E+T 6: E E+T 1: S E$ $ Formal Example(10) S  E$ E  T| E+ T T i|( E) stack input 11: T i  10: T i 8: E  E+T 7: E  E+T 6: E E+T 1: S E$ $ reduce T i

  32. stack input 2: S E $ 1: S E$ $ Formal Example(11) S  E$ E  T | E+T T i|(E) stack input 9: E  E+T  8: E  E+T 7: E  E+T 6: E E+T 1: S E$ $ reduce E  E+T

  33. stack input 3: S E $  2: S E $ 1: S E$ Formal Example(12) S  E$ E  T |E+TT i| (E) stack input 2: S E $ 1: S E$ $ shift 3

  34. Formal Example(13) S  E$ E  T | E+T T i|(E) stack input 3: S E $  2: S E $ 1: S E$ reduce S  E$

  35. But how can this be done efficiently? Deterministic Pushdown Automaton

  36. 3 2 1 Handles • Identify the leftmost node (nonterminal) that has not been constructed but all whose children have been constructed input t1 t2 t4 t5 t6 t7 t8

  37. Identifying Handles • Create a deteteministic finite state automaton over grammar symbols • Sets of LR(0) items • Accepting states identify handles • Use automaton to build parser tables • reduce For items A on every token • shift For itemsA  t on token t • When conflicts occur the grammar is not LR(0) • When no conflicts occur use a DPDA which pushes states on the stack

  38. A Trivial Example • S  A B $ • A  a • B  a

  39. S  E$ E  T E  E+ T T i T (E)

  40. 1 1: S E$ 4: E T 6: E E +T 10: T i 12: T  (E) 2: S E $ 7: E E +T 0 T 6 E 5: E T $ i 2 5 3: S E $  11: T i + ( i 7 13: T (E) 4: E T 6: E E +T 10: T i 12: T  (E) 3 8: E E +T 10: T i 12: T  (E) ( i ( E T 8 + 14: T (E ) 7: E E +T 9: E E +T  ) 4 15: T (E)  9

  41. Example Control Table

  42. input stack shift 5 0($) i + i $

  43. stack input 5 (i) 0 ($) reduceT i + i $

  44. stack input 6 (T) 0 ($) + i $ reduce E  T

  45. stack input shift 3 1(E) 0 ($) + i $

  46. stack input shift 5 3 (+) 1(E) 0 ($) i $

  47. stack input 5 (i) 3 (+) 1(E) 0($) reduce T i $

  48. input stack reduce E  E+T 4 (T) 3 (+) 1(E) 0($) $

  49. stack input 1 (E) 0 ($) $ shift 2

  50. stack input 2 ($) 1 (E) 0 ($) accept

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