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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

reopened | 377 views

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

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simple & good explanation..

the link which you gave is part-a and this particular question is part-b both are linked.

@Prajwal,

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

By this info. I think we may get result as 7 also.

(We know grammar is ambiguous here so same precedency )

But due to YACC tool(prefer shift over reduce) given as part of linked question here even if 3∗2 (E∗E) handle found on top of the stack at some point of time, it will shift on reading + instead of reducing with E→E∗E.

But as per ur given quotation it may compute 3*2 also.

Plz see Debashis's ans in given link there he have put the o/p with black screen.

Actually after writing this ans, Shobith had informed me about ambiguity in this grammar so i had hidden this answer but it was Arjun Sir who has reshown this answer which you can see in the status

He had removed all other ans in this particular question and just retained my answer.

It would be better if he only tell the reason for that!!

@Rajesh, question here assumes "yacc". I just corrected it.
@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?