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Lecture 4: LL Parsing

Lecture 4: LL Parsing. CS 540 George Mason University. Parsing. Syntatic/semantic structure. Syntatic structure. tokens. Scanner (lexical analysis). Parser (syntax analysis). Semantic Analysis (IC generator). Code Generator. Source language. Target language. Code

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Lecture 4: LL Parsing

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  1. Lecture 4: LL Parsing CS 540 George Mason University

  2. Parsing Syntatic/semantic structure Syntatic structure tokens Scanner (lexical analysis) Parser (syntax analysis) Semantic Analysis (IC generator) Code Generator Source language Target language Code Optimizer • Syntax described formally • Tokens organized into syntax tree that describes structure • Error checking Symbol Table CS 540 Spring 2010 GMU

  3. Top Down (LL) Parsing P P begin SS end SS  S ; SS SS  e S  simplestmt S  begin SS end begin simplestmt ; simplestmt ; end CS 540 Spring 2010 GMU

  4. Top Down (LL) Parsing P P begin SS end SS  S ; SS SS  e S  simplestmt S  begin SS end SS begin simplestmt ; simplestmt ; end CS 540 Spring 2010 GMU

  5. Top Down (LL) Parsing P P begin SS end SS  S ; SS SS  e S  simplestmt S  begin SS end SS SS S begin simplestmt ; simplestmt ; end CS 540 Spring 2010 GMU

  6. Top Down (LL) Parsing P P begin SS end SS  S ; SS SS  e S  simplestmt S  begin SS end SS SS S begin simplestmt ; simplestmt ; end CS 540 Spring 2010 GMU

  7. Top Down (LL) Parsing P P begin SS end SS  S ; SS SS  e S  simplestmt S  begin SS end SS SS SS S S begin simplestmt ; simplestmt ; end CS 540 Spring 2010 GMU

  8. Top Down (LL) Parsing P P begin SS end SS  S ; SS SS  e S  simplestmt S  begin SS end SS SS SS S S begin simplestmt ; simplestmt ; end CS 540 Spring 2010 GMU

  9. Top Down (LL) Parsing P beginSSend  beginS; SS end  beginsimplestmt;SSend  beginsimplestmt; S ; SS end  beginsimplestmt; simplestmt ; SSend  beginsimplestmt; simplestmt ; end P begin SS end SS  S ; SS SS  e S  simplestmt S  begin SS end 1 P 2 SS 4 SS 3 SS 6 S 5 S e begin simplestmt ; simplestmt ; end CS 540 Spring 2010 GMU

  10. Grammar S S S  a B | b C B  b b C C  c c Two strings in the language: abbcc and bcc Can choose between them based on the first character of the input. b C a B c c b b C c c CS 540 Spring 2010 GMU

  11. LL(k) parsing also known as the lookahead • Process input k symbols at a time. • Initially, ‘current’ non-terminal is start symbol. • Algorithm • Loop until no more input • Given next k input tokens and ‘current’ non-terminal T, choose a rule R (T  …) • For each element X in rule R from left to right, if X is a non-terminal, we will need to ‘expand’ X else if symbol X is a terminal, see if next input symbol matches X; if so, update from the input • Typically, we consider LL(1) CS 540 Spring 2010 GMU

  12. Two Approaches • Recursive Descent parsing • Code tailored to the grammar • Table Driven – predictive parsing • Table tailored to the grammar • General Algorithm Both algorithms driven by the tokens coming from the lexer. CS 540 Spring 2010 GMU

  13. Writing a Recursive Descent Parser • Generate a procedure for each non-terminal. Use next token from yylex() (lookahead) to choose (PREDICT) which production to ‘mimic’. • for non-terminal X, call procedure X() • for terminals X, call ‘match(X)’ Ex: B  b C D B() { if (lookahead == ‘b’) { match(‘b’); C(); D(); } else … } CS 540 Spring 2010 GMU

  14. Writing a Recursive Descent Parser Also need the following: match(symbol) { if (symbol == lookahead) lookahead = yylex() else error() } main() { lookahead = yylex(); S(); /* S is the start symbol */ if (lookahead == EOF) then accept else reject } error() { … } CS 540 Spring 2010 GMU

  15. S() { if (lookahead == a ) { match(a);B(); } S  a B else if (lookahead == b) { match(b); C(); } S  b C else error(“expecting a or b”); } B() { if (lookahead == b) {match(b); match(b); C();} B  b b C else error(); } C() { if (lookahead == c) { match(c) ; match(c) ;} C  c c else error(); } Back to grammar CS 540 Spring 2010 GMU

  16. Parsing abbcc S abbcc Remaining input: Call S() from main() S() { if (lookahead == a ) { match(a);B(); } S  a B else if (lookahead == b) { match(b); C(); } S  b C else error(“expecting a or b”); } CS 540 Spring 2010 GMU

  17. Parsing abbcc S bbcc Remaining input: a B Call B() from A(): B() { if (lookahead == b) {match(b); match(b); C();} B  b b C else error(); } CS 540 Spring 2010 GMU

  18. Parsing abbcc S cc Remaining input: a B Call C() from B(): C() { if (lookahead == c) { match(c) ; match(c) ;} C  c c else error(); } b b C CS 540 Spring 2010 GMU

  19. Parsing abbcc S Remaining input: a B b b C c c CS 540 Spring 2010 GMU

  20. How do we find the lookaheads? • Can compute PREDICT sets from FIRST and FOLLOW for LL(1) parsing: • PREDICT(A  a) = (FIRST(a) – {e}) FOLLOW(A) if e in FIRST(a) = FIRST(a) if e not in FIRST(a) NOTE: e never in PREDICT sets For LL(k) grammars, the PREDICT sets for the productions associated with a given non-terminal must be disjoint. CS 540 Spring 2010 GMU

  21. Example FIRST(F) = {(,id} FIRST(T) = {(,id} FIRST(E) = {(,id} FIRST(T’) = {*,e} FIRST(E’) = {+,e} FOLLOW(E) = {$,)} FOLLOW(E’) = {$,)} FOLLOW(T) = {+$,)} FOLLOW(T’) = {+,$,)} FOLLOW(F) = {*,+,$,)} Assume E is the start symbol CS 540 Spring 2010 GMU

  22. E() { if (lookahead in {(,id } ) { T(); E_prime(); } E  T E’ else error(“E expecting ( or identifier”); } E_prime() { if (lookahead in {+}) {match(+); T(); E_prime();} E’  + T E’ else if (lookahead in {),end_of_file}) return; E’  e else error(“E_prime expecting +, ) or end of file”); } T() { if (lookahead in {(,id}) { F(); T_prime(); } T  F T’ else error(“T expecting ( or identifier”); } CS 540 Spring 2010 GMU

  23. T_prime() { if (lookahead in {*}) {match(*); F(); T_prime();} T’  * F T’ else if (lookahead in {+,),end_of_file}) return; T’  e else error(“T_prime expecting *, ) or end of file”); } F() { if (lookahead in {id}) match(id); F  id else if (lookahead in {(} ) { match( ( ); E(); match ( ) ); } F  ( E ) else error(“F expecting ( or identifier”);} CS 540 Spring 2010 GMU

  24. Parsing a + b * c E Remaining input: a+b*c CS 540 Spring 2010 GMU

  25. Parsing a + b * c E Remaining input: a+b*c T E’ E() { if (lookahead in {(,id } ) { T(); E_prime(); } else error(“E expecting ( or identifier”); } CS 540 Spring 2010 GMU

  26. Parsing a + b * c E Remaining input: a+b*c TE’ F T’ T() { if (lookahead in {(,id } ) { F(); T_prime(); } else error(“T expecting ( or identifier”); } CS 540 Spring 2010 GMU

  27. Parsing a + b * c E Remaining input: +b*c TE’ FT’ F() { if (lookahead in {id } ) match(id) else if (lookahead in { ( } { match( ( ); E(); match( ) ); } else error(“F expecting ( or identifier”); } id a CS 540 Spring 2010 GMU

  28. Parsing a + b * c E Remaining input: +b*c TE’ F T’ T_prime() { if (lookahead in {*}) {match(*); F(); T_prime();}’ else if (lookahead in {+,),end_of_file}) return; else error(“T_prime expecting *, ) or end of file”); } } id a e CS 540 Spring 2010 GMU

  29. Parsing a + b * c E Remaining input: b*c T E’ F T’ +T E’ E_prime() { if (lookahead in {+}) {match(+); T(); E_prime();}’ else if (lookahead in {),end_of_file}) return; else error(“E_prime expecting *, ) or end of file”); } } id a e CS 540 Spring 2010 GMU

  30. Parsing a + b * c E Remaining input: b*c T E’ F T’ +TE’ T() { if (lookahead in {(,id } ) { F(); T_prime(); } else error(“T expecting ( or identifier”); } id a F T’ e CS 540 Spring 2010 GMU

  31. Parsing a + b * c E Remaining input: *c T E’ F T’ +TE’ F() { if (lookahead in {id } ) match(id) else if (lookahead in { ( } { match( ( ); E(); match( ) ); } else error(“F expecting ( or identifier”); } id a F T’ e id b CS 540 Spring 2010 GMU

  32. Parsing a + b * c E Remaining input: c T E’ F T’ +T E’ T_prime() { if (lookahead in {*}) {match(*); F(); T_prime();}’ else if (lookahead in {+,),end_of_file}) return; else error(“T_prime expecting *, ) or end of file”); } } id a F T’ e id b *F T’ CS 540 Spring 2010 GMU

  33. Parsing a + b * c E Remaining input: T E’ F T’ +TE’ F() { if (lookahead in {id } ) match(id) else if (lookahead in { ( } { match( ( ); E(); match( ) ); } else error(“F expecting ( or identifier”); } id a F T’ e id b *F T’ id c CS 540 Spring 2010 GMU

  34. Parsing a + b * c E Remaining input: T E’ F T’ +TE’ T_prime() { if (lookahead in {*}) {match(*); F(); T_prime();}’ else if (lookahead in {+,),end_of_file}) return; else error(“T_prime expecting *, ) or end of file”); } } id a F T’ e id b * F T’ e id c CS 540 Spring 2010 GMU

  35. Parsing a + b * c E Remaining input: T E’ F T’ + T E’ E_prime() { if (lookahead in {+}) {match(+); T(); E_prime();}’ else if (lookahead in {),end_of_file}) return; else error(“E_prime expecting *, ) or end of file”); } } id a F T’ e e id b * F T’ e id c CS 540 Spring 2010 GMU

  36. Stacks in Recursive Descent Parsing E • Runtime stack • Procedure activations correspond to a path in parse tree from root to some interior node E’ T F id b CS 540 Spring 2010 GMU

  37. Two Approaches • Recursive Descent parsing • Code tailored to the grammar • Table Driven – predictive parsing • Table tailored to the grammar • General Algorithm Both algorithms driven by the tokens coming from the lexer. CS 540 Spring 2010 GMU

  38. LL(1) Predictive Parse Tables An LL(1) Parse table is a mapping T: Vn x Vt production P or error • For all productions A  a do For each terminal t in Predict(A a), T[A][t] = A  a • Every undefined table entry is an error. CS 540 Spring 2010 GMU

  39. Using LL(1) Parse Tables ALGORITHM INPUT: token sequence to be parsed, followed by ‘$’ (end of file) DATA STRUCTURES: • Parse stack: Initialized by pushing ‘$’ and then pushing the start symbol • Parse table T CS 540 Spring 2010 GMU

  40. Algorithm: Predictive Parsing similar to ‘match’ push($); push(start_symbol); lookahead = yylex() repeat X = pop(stack) if X is a terminal symbol or $ then if X = lookahead then lookahead = yylex() else error() else /* X is non-terminal */ if T[X][lookahead] = X  Y1 Y2 …Ym push(Ym) … push (Y1) else error() until X = $ token similar to ‘mimic’ CS 540 Spring 2010 GMU

  41. Example CS 540 Spring 2010 GMU

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  43. Assume E is the start symbol CS 540 Spring 2010 GMU

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