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Consider the following expression grammar. The semantic rules for expression evaluation are stated next to each grammar production.

$\begin{align*}E \rightarrow & number \\ &| E \text{ '+' } E \\&| E \text{ '}\times\text{' } E \end{align*}$ $\begin {align*} &E.val = \text {number.val} \\ &E^{(1)}.val = E^{(2)}.val + E^{(3)}.val \\ &E^{(1)}.val = E^{(2)}.val \times E^{(3)}.val \end{align*}$

Assume the conflicts of this question are resolved using yacc tool and an LALR(1) parser is generated for parsing arithmetic expressions as per the given grammar. Consider an expression $3 \times 2 + 1$. What precedence and associativity properties does the generated parser realize?

  1. Equal precedence and left associativity; expression is evaluated to 7

  2. Equal precedence and right associativity; expression is evaluated to 9

  3. Precedence of ‘$\times$’ is higher than that of ‘+’, and both operators are left associative; expression is evaluated to 7

  4. Precedence of ‘$+$’ is higher than that of ‘$\times$’, and both operators are left associative; expression is evaluated to 9

asked in Compiler Design by Veteran (77.2k points)  
reopened by | 402 views

1 Answer

+7 votes
Best answer

LALR Parser is type of Bottom up Parser which uses Right most Derivation

For 3×2+1

E->E * E (Both shift and reduce possible but yacc prefers shift)

  ->E * E + E

  ->E * E + 1

  ->E * 2 + 1

  ->E * 3

  ->3 * 3

  ->9

All the productions are in same level therefore all have same precedence

Therefore Ans is B.Equal precedence and right associativity; expression is evaluated to 9

answered by Veteran (11.5k points)  
selected by
@Arjun sir

So the question says conflicts will be resolved by "yacc" does that mean ambiguity will be resolved?
yes.
Ok. @Arjun Sir.

@Prajwal Shift-Reduce Conflict (NOT AMBIGUITY)will solve by yacc by preferring Shift operation over reduce operation.

So, here though it will find 3∗2 (E∗E) handle on top of the stack initially, it will shift on reading + instead of reducing with E→E∗E.

so it work like right associativity(and we know priority is same due to ambiguous grammar.)

so 3*(2+1) =9
What makes it right associative?
(Both shift and reduce possible but yacc prefers shift)  why do we say this


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