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CS412/413

CS412/413. Introduction to Compilers and Translators Spring ’99 Lecture 5: Bottom-up parsing. Outline. Creating LL(1) grammars Limitations of LL(1) grammars Bottom-up parsing LR(0) parser construction. Administration. Should have received mail about group assignments by now

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CS412/413

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  1. CS412/413 Introduction to Compilers and Translators Spring ’99 Lecture 5: Bottom-up parsing

  2. Outline • Creating LL(1) grammars • Limitations of LL(1) grammars • Bottom-up parsing • LR(0) parser construction CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  3. Administration • Should have received mail about group assignments by now • Homework 1 due next class (Friday) • Monday considered 2 days late (-20%), Tuesday 3 days (-40%) • No class next Monday (Feb 8) CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  4. Programming Assignment • Due Monday, Feb 15 • Implement a lexer for Iota language • Do not need to implement DFA construction • Opportunity to work as group • We expect high quality CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  5. Review • Can construct recursive descent parsers for LL(1) grammars Language grammar How to perform this step? LL(1) grammar predictive parse table recursive-descent parser recursive-descent parser w/ AST generation CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  6. Grammars • Have been using grammar for language of “sums with parentheses” • Original grammar: S S + E| E E number | ( S ) • LL(1) grammar for same language: S  ES’ S’   | + S E number | ( S ) (1+(3+4))+5 CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  7. (1 + 2 + (3 + 4)) + 5 Left-recursive vs Right-recursive • Original grammar was left-recursive SS+ E S E • LL(1) grammar is right-recursive : parsed top-down S  E S’ S’   | + S • Left-recursive grammars don’t work with top-down parsing -- need an arbitrary amount of look-ahead S  E + S S  E S S + E (...) + (...) + (...) + (...) ... S + E S + E CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  8. How to create an LL(1) grammar • Write a right-recursive grammar S  E + S S  E • Left-factor common prefixes, place suffix in new non-terminal S  E S’ S’   S’  + S CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  9. (1 + 2 + (3 + 4)) + 5 Right Recursion S • Right recursion : right-associative E S’ + ( S ) + S + 5 E S’ 5 1 + 1 + S 2 + E S’ 3 4 2 + S E S’ • Left recursion : left-associative +  ( S ) + 5 E S’ + + + S 3 E 1 2 3 4 4 CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  10. Associativity • We can provide left-associativity by massaging the recursive-descent code void parse_S() { switch (token) { case ‘(’: case number: parse_E(); parse_S’(); return; default: throw new ParseError(); } } void parse_S’() { switch (token) { case ‘+’: token = input.read(); parse_S(); return; case ‘)‘: return; case EOF: return; default: throw new ParseError(); } } CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  11. Associativity void parse_S() {// parses a sequence of E + E + E ... switch (token) { case ‘(’: case number: parse_E(); switch (token) { case ‘+’: token = input.read(); parse_S(); return; case ‘)‘: return; case EOF: return; default: throw new ParseError(); } return; default: throw new ParseError(); } } tail recursion CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  12. + 3 4 Flattening Associative Operators void parse_S () { // parses an arbitrary sequence of E + E + E ... while (true) { switch (token) { case ‘(’: case number: parse_E (); switch (token) { case ‘+’: token = input.read(); break; case ‘)‘: case EOF: return; default: throw new ParseError(); } break; default: throw new ParseError(); } } } (1 + 2 + (3+4)) + 5 + + 5 1 2 CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  13. Summary • Now have complete recipe for building a parser Language grammar LL(1) grammar predictive parse table recursive-descent parser recursive-descent parser w/ AST generation CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  14. Bottom-up parsing • A more powerful parsing technology • LR grammars -- more power than LL • can handle left-recursive grammars, virtually all programming languages • More natural expression of programming language syntax • Shift-reduce parsers • automatic parser generators (e.g. yacc) • detect errors as soon as possible • allows better error recovery CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  15. S S + E| E E number | ( S ) Top-down parsing (1+2+(3+4))+5 S S+E E+E  (S)+E  (S+E)+E (S+E+E)+E (E+E+E)+E (1+E+E)+E(1+2+E)+E ... • In left-most derivation, entire tree above a token (2) has been expanded when encountered • Must be able to predict! S S + E E 5 ( S ) S + E ( S ) S + E E S + E 2 4 1 E 3 CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  16. S S + E| E E number | ( S ) Bottom-up parsing • Right-most derivation-- backward • Start with the tokens • End with the start symbol (1+2+(3+4))+5 (E+2+(3+4))+5  (S+2+(3+4))+5 (S+E+(3+4))+5  (S+(3+4))+5  (S+(E+4))+5 (S+(S+4))+5 (S+(S+E))+5  (S+(S))+5 (S+E)+5  (S)+5  E+5  S+E S CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  17. S S + E| E E number | ( S ) Bottom-up parsing (1+2+(3+4))+5 (1+2+(3+4))+5 (E+2+(3+4))+5  (1 +2+(3+4))+5 (S+2+(3+4))+5  (1 +2+(3+4))+5 (S+E+(3+4))+5  (1+2 +(3+4))+5 (S+(3+4))+5  (1+2+(3 +4))+5 (S+(E+4))+5  (1+2+(3 +4))+5 (S+(S+4))+5  (1+2+(3 +4))+5 (S+(S+E))+5  (1+2+(3+4 ))+5 (S+(S))+5  (1+2+(3+4 ))+5 (S+E)+5  (1+2+(3+4) )+5 (S)+5  (1+2+(3+4) )+5 E+5  (1+2+(3+4)) +5 S+E(1+2+(3+4))+5 S(1+2+(3+4))+5 right-most derivation CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  18. S S + E| E E number | ( S ) Bottom-up parsing • (1+2+(3+4))+5 (E+2+(3+4))+5  (S+2+(3+4))+5 (S+E+(3+4))+5 … • Advantage of bottom-up parsing: can select productions based on more information S S + E E 5 ( S ) S + E ( S ) S+E E S + E 2 4 1 E 3 CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  19. Top-down vs. Bottom-up Bottom-up: Don’t need to figure out as much of the parse tree for a given amount of input scanned unscanned scanned unscanned Top-down Bottom-up CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  20. Shift-reduce parsing • Parsing is a sequence of shift and reduce operations • Parser state is a stack of terminals and non-terminals (grows to the right) • Unconsumed input is a string of terminals • Current derivation step is always stack+input • Shift -- push head of input onto stack stack input ( 1+2+(3+4))+5 (1 +2+(3+4))+5 CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  21. Reduce • Replace symbols  in top of stack with non-terminal symbol X, corresponding to production X   (pop , push X) stack input (S+E +(3+4))+5 reduce S S+E (S +(3+4))+5 • What effect does this have on derivation? CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  22. S S + E| E E number | ( S ) Shift-reduce parsing derivation input stream action stack (1+2+(3+4))+5 (1+2+(3+4))+5 shift (1+2+(3+4))+5  ( 1+2+(3+4))+5 shift (1+2+(3+4))+5  (1 +2+(3+4))+5 reduceEnum (E+2+(3+4))+5  (E +2+(3+4))+5 reduceS  E (S+2+(3+4))+5  (S +2+(3+4))+5 shift (S+2+(3+4))+5  (S+ 2+(3+4))+5 shift (S+2+(3+4))+5  (S+2 +(3+4))+5 reduceEnum (S+E+(3+4))+5  (S+E +(3+4))+5 reduce S S+E (S+(3+4))+5  (S +(3+4))+5 shift (S+(3+4))+5  (S+ (3+4))+5 shift (S+(3+4))+5  (S+( 3+4))+5 shift (S+(3+4))+5  (S+(3 +4))+5 reduce Enum CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  23. Problem • How do we know which action to take -- whether to shift or reduce, and which production? • Sometimes can reduce but shouldn’t • e.g., X   can always be reduced • Sometimes can reduce in different ways CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  24. Action Selection Problem • Given stack  and input symbol b, should we • shift b onto the stack (making it b) • reduce some production X   assuming that stack has the form   (making it X) • Should apply reduction X   depending on what stack prefix  is -- but  is different for different possible reductions, since ’s have different length. How to keep track? CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  25. Parser States • Idea: summarize all possible stack prefixes  as a parser state • A state transition function updates the parser state as shifts and reductions are performed: DFA • Summarizing discards information • affects what grammars parser handles • affects size of DFA (number of states) CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  26. LR(0) parser • Left-to-right scanning, Right-most derivation, zero look-ahead characters • Too weak to handle most language grammars (including this one) • But will help us understand how to build better parsers CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  27. LR(0) states • A state is a set of items • An LR(0) item is a production from the language with a separator “.” somewhere in the RHS of the production • Stuff before “.” already on stack (beginnings of possible ’s) • Stuff after “.” : what we might see next • The prefixes  represented by state E number . E  ( .S ) state item CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  28. An LR(0) grammar: non-empty lists S  ( L ) S  id L  S L  L , S x (x,y) (x, (y,z), w) ((((x)))) (x, (y, (z, w))) CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  29. S  ( L ) | id L  S | L, S Closure S ’  . S $ S  . ( L ) S  . id start state Closure S ’  .S $ • Closure of a state adds items for all productions whose LHS occurs in an item in the state, just after “.” • Added items have the “.”located at the beginning • Like NFA  DFA conversion CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  30. Applying shift actions S  ( .L ) L  .S L  .L , S S  . ( L ) S  . id S  ( L ) | id L  S | L , S S ’  . S $ S  . ( L ) S  . id ( ( id id S  id . In new state, include all items that have appropriate input symbol just after dot, and advance dot in those items. (and take closure) CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  31. Applying reduce actions S  ( .L ) L  .S L  .L , S S  . ( L ) S  . id S  ( L.) L  L . , S • Need to set state after reducing • On reduction, pop back to old state and take DFA transition on non-terminal reduced L S ’  . S $ S  . ( L ) S  . id ( S ( L  S. id id S  id . states causing reductions CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  32. Full DFA (Appel p. 63) 8 9 2 L  L , . S S  . ( L ) S  . id 1 id S id S ’  . S $ S  . ( L ) S  . id S  id . L  L , S . id 3 S  ( .L ) L  .S L  .L , S S  . ( L ) S  . id ( 5 L S  ( L.) L  L . , S S ) ( S 6 S  ( L ). 4 7 L  S. S ’  S . $ $ final state CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

  33. Idea: stack is labeled w/state Let’s try parsing ((x),y) derivation stack input action ((x),y)  1 ((x),y) shift, goto 3 ((x),y)  1 (3 (x),y)shift, goto 3 ((x),y)  1 (3 (3 x),y)shift, goto 2 ((x),y)  1 (3 (3 x2 ),y)reduce Sid ((S),y)  1 (3 (3 S7 ),y)reduce LS ((L),y)  1 (3 (3 L5 ),y)shift, goto 6 ((L),y)  1 (3 (3 L5)6 ,y)reduce S(L) (S,y)  1 (3 S7 ,y)reduce LS (L,y)  1 (3 L5 ,y)shift, goto 8 (L,y)  1 (3 L5 , 8 y)shift, goto 9 (L,y)  1 (3 L5 , 8 y2 )reduce Sid (L,S)  1 (3 L5 , 8 S9 )reduce LL , S (L)  1 (3 L5 )shift, goto 6 (L)  1 (3 L5 )6 reduce S(L) S 1S4$ done S  ( L ) | id L  S | L, S

  34. Summary • Grammars can be parsed bottom-up using a DFA + stack • State construction converts grammar into states that capture information needed to know what action to take • Stack entries labeled by state index • Next time: SLR, LR(1) parsers, automatic parser generators CS 412/413 Introduction to Compilers and Translators -- Spring '99 Andrew Myers

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