cs453 lr 1 lalr ambiguity
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CS453 LR(1), LALR, AMBIGUITY CS453 Shift-Reduce Cont' 1 LR(1), - PowerPoint PPT Presentation

CS453 LR(1), LALR, AMBIGUITY CS453 Shift-Reduce Cont' 1 LR(1), LALR, Ambiguity The plan: Shift reduce parsing LR(1) and LALR Ambiguous grammars - Precedence and associativity rules - Dangling else Java-cup precedence and associativity


  1. CS453 LR(1), LALR, AMBIGUITY CS453 Shift-Reduce Cont' 1

  2. LR(1), LALR, Ambiguity The plan: Shift reduce parsing LR(1) and LALR Ambiguous grammars - Precedence and associativity rules - Dangling else Java-cup precedence and associativity declarations Shift Reduce conflict in dangling else CS453 Shift-Reduce Cont' 2

  3. SLR still not good enough wrt reduce Grammar for C style assignment: 0: S’ à à S$ 1: S à à V = E 2: S à à E 3: E à à V 4:V à à x 5: V à à *E E is a simplified expression, in reality more complex (E+T …) Let’s build the SLR parse table: x * = $ S V E Is this grammar ambiguous? 1 s5 s6 g2 g3 g4 2 a NO 3 s7,r3 4 r2 But we still have a 5 r4 r4 shift reduce conflict. 6 s5 s6 g9 g8 7 s5 s6 g9 g10 8 r5 r5 We need to look ahead and 9 r3 r3 decide when to reduce. 10 r1 r1 CS453 Shift-Reduce Cont' 3

  4. LR(1) look ahead sets LR(1) items take a look ahead into account: (A à à α . β , z ) item is pair: (dotted rule, look-ahead symbol ) indicating α is on top of stack, and β z on input, but z is not part of A We will now reduce to A, not on follow(A), but if αβ is on top of stack and z on input, i.e. we have more precise information. Closure(I)= Reduce: Goto(I,X)= repeat R ={} J={} for all (A à α . X β , z ) in I for all (A à α .) in I for all (A à α . X β , z ) in I for any X à γ R+= (I, z, A à α ) J+=(A à α X . β , z ) for any w in First( β z) return Closure(J) I+= (X à . γ , w) (I, z, A à α ) means: until I does no change in State I, return I on symbol z reduce: A à α CS453 Shift-Reduce Cont' 4

  5. LR(1) state diagram: look-ahead sets 0: S’ à à S$ 1: S à à V = E 2: S à à E 3: E à à V 4:V à à x 5: V à à *E We will not shift the $, so the look ahead symbol for S’ does not matter This is indicated by a ? S’ à à . S$ ? when we have S’ à à . S$ ? S à à . V=E $ the same dotted S à à . V=E $ S à à . E $ rule with S à à . E $ E à à . V $ different E à à . V $ V à à . x $ look aheads V à à . x $, = V à à . *E $ we combine V à à . *E $, = V à à . x = them in V à à . *E = sets CS453 Shift-Reduce Cont' 5

  6. LR(1) state diagram (incomplete) 0: S’ à à S$ 1: S à à V = E 2: S à à E 3: E à à V 4:V à à x 5: V à à *E S’ à . S$ ? S S’ à S . $ ? S à . V=E $ 2 S à . E $ E à . V $ V S à V = . E $ = S à V . = E $ V à . x $, = E à . V $ E à V . $ V à . *E $,= V à .x $ 3 1 V à . *E $ In state 3: 4 we reduce E à à V on $, not on = ( even though = is in follow(E) ) we shift on = conflict resolved CS453 Shift-Reduce Cont' 6

  7. LALR(1) Look Ahead LR(1) : state diagram (incomplete) 0: S’ à à S$ 1: S à à V = E 2: S à à E 3: E à à V 4:V à à x 5: V à à *E S’ à . S$ ? S S’ à S . $ ? S à . V=E $ 2 S à . E $ V S à V = . E $ = E à . V $ S à V . = E $ E à . V $ V à . x $, = E à V . $ V à .x $ V à . *E $,= 3 V à . *E $ 1 x x 4 LALR combines states that are equal V à x . $,= V à x . $ except for the 5 6 look aheads CS453 Shift-Reduce Cont' 7

  8. LALR(1) Look ahead LR(1) : state diagram (incomplete) 0: S’ à à S$ 1: S à à V = E 2: S à à E 3: E à à V 4:V à à x 5: V à à *E S’ à . S$ ? S S’ à S . $ ? S à . V=E $ 2 S à . E $ V S à V = . E $ = E à . V $ S à V . = E $ E à . V $ V à . x $, = E à V . $ V à .x $ V à . *E $,= 3 V à . *E $ 1 x x 4 V à x . $,= 5 CS453 Shift-Reduce Cont' 8

  9. Shift reduce: ambiguous expression grammar (incomplete) 0: S ‘ à E$ 1: E à E+E 2: E à E*E 3: E à (E) 4: E à id E + E S’ à E.$ E à E+.E E à E +E. S’ à . E$ E à E . +E E à .E+E E à E.+E E à . E+E E à E . *E E à .E*E E à E.*E E à . E*E 2 3 4 … * 1 E E à E+.E E à E *E. State 4: two Shift/Reduce conflicts E à .E+E E à E.+E input +: R1 Why? E à .E*E E à E.*E input *: S Why? 5 6 NOTICE: State 6: two Shift/Reduce conflicts input +: R2 Why? + and * are left associative input *: R2 Why? CS453 Shift-Reduce Cont' 9

  10. Shift reduce: ambiguous expression grammar (incomplete) 0: S ‘ à E$ 1: E à E^E 2: E à id // ^ for exponent E ^ E S’ à E.$ E à E^ .E E à E ^ E. S’ à . E$ E à E . ^E E à .E^E E à E.^E E à . E^E 2 3 4 … 1 State 4: two Shift/Reduce conflicts input ^ : S Why? CS453 Shift-Reduce Cont' 10

  11. Shift reduce: ambiguous dangling else grammar 1: S à if c S else S 2: S à if c S 3: S à other abstracted to: 1: S à i S e S 2: i S 3: o i S S à i . S e S S à i S . e S S’ à . S$ S à i . S S à i S . S à . i S e S … S à . i S 4 5 S à .o State 5: Shift/Reduce conflict 1 o input e: S Why? S à o. 3 Is else left or right associative? CS453 Shift-Reduce Cont' 11

  12. Shift reduce: ambiguous cast grammar 1: E à E+E 2: E à ( byte ) E 3: E à ( E ) 4: E à id E à E . + E E à . E+E … E à ( byte ) E . E à . ( byte ) E E à . ( E ) E à . id Shift/Reduce conflict input +: R2 Why? ( type ) is a right associative cast operator, but consists of three tokens. This is a place where the strict nesting of ( ) does not hold. The conflict can be resolved by declaring ( ) a right associative unary operator with higher precedence than the other operators. CS453 Shift-Reduce Cont' 12

  13. Ambiguity in JavaCUP There is no conflict free LR parser for ambiguous grammars - So we have to fix the problem in other ways Expressions: operators and productions are given precedence – Tokens explicitly in precedence declarations – Productions implicitly based on last operator in the stack When in shift-reduce conflict – Shift if look ahead token has higher precedence than production on stack – Reduce if operator in the stack has higher precedence than look ahead Within same precedence level – Left associativity results in a reduce – Right associativity results in a shift Dangling else - Shifting the else will bind else to last unbound if (Java semantics) - Not shifting can cause a valid program to be rejected CS453 Shift-Reduce Cont' 13

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