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+4 votes

$\begin{align*} &E\rightarrow E+E \qquad {\color{red}{\text{E.val} = \text{E}_1\text{.val} { \;\;\large + \;\; } \text{E}_2\text{.val}}} \\ &E\rightarrow E*E \; \qquad {\color{red}{\text{E.val} = \text{E}_1\text{.val} { \;\;\large - \;\; } \text{E}_2\text{.val}}} \\ &E\rightarrow E - E \qquad {\color{red}{\text{E.val} = \text{E}_1\text{.val} { \;\;\large * \;\; } \text{E}_2\text{.val}}} \\ &E\rightarrow \left ( E \right ) \;\;\; \; \qquad {\color{red}{\text{E.val} = \text{E}_1\text{.val}}} \\ &E\rightarrow \text{id} \;\;\; \; \;\;\; \qquad {\color{red}{\text{E.val} = \text{id}\text{.val}}} \\ \\ &\text{What is that value of the attribute comupted at the root when the expression} \\ &{\large\color{blue}{\left [ \left ( 3*3 \right )+\left ( 3*5 \right ) - 6 \right ]+7}} \quad \text{is evaluated using above SDT ?} \\ \end{align*}$

+3 votes

Best answer

$\begin{align*} &\text{Operator priority order } \\ &\rightarrow 1st \quad {\large \color{blue}{-}} \\ &\rightarrow 2nd \quad {\large \color{blue}{*}} \\ &\rightarrow 3rd \quad {\large \color{blue}{+}} \\ \\ \hline \\ &\text{While reducing to a production corresponding SDT is evaluated} \\ \\ &\Rightarrow \left ( {\color{red}{\left ( 3*3 \right )}}+{\color{red}{\left ( 3*5 \right )}} - 6 \right )+7 \\\\ &\Rightarrow \left ( 0 \;\;{\large \color{blue}{+}} \;\; {\color{red}{(- 2) \;\;{\large \color{red}{-}}\;\; 6}} \right ) + 7 \\\\ &\Rightarrow \left ( 0 \;\;{\large \color{blue}{+}} \;\; (-12) \right ) + 7 \\ \\ &\Rightarrow \left ( -12 \right ) + 7 \\ \\ &\Rightarrow -5 \\ \end{align*}$

+1

I have a doubt. Do the operators really have priority here?

The grammar seems to be E→E+E / E∗E / E−E / (E) / id

All the operators are at same level. So how is the priority decided? Shouldn't they all have equal priority?

The grammar seems to be E→E+E / E∗E / E−E / (E) / id

All the operators are at same level. So how is the priority decided? Shouldn't they all have equal priority?

+3

yes grammar is ambiguous so priority couldnt be decided(**in general case**)

but here they have **explicitly** mentioned that we have to **evaluate the expression** ..so we have **2 choices** either **give priority urself** or **use their gramamar** and decide(this is what we have to do..**see their levels** )....if they would have mentioned everything in one line like E→E+E / E∗E / E−E / (E) / id..then there was a confusion which was having higher priority...but again they have given **grammar in levels**..saying treat lowest with highest priority..

**NOTE**:for ambiguous grammars precednce is nt defined..we can play with it according our needs or according to their needs...this question is about satisfying their worries..!

+1 vote

0

who said - has more priority than +.both have same priority but precedence is from left to right(As far as i know)

[(3*3) + (3*3) -6]---in this expression,both - and + have same priority

but + before 7 has the lowest priority among all,thats why it is at the highest

[(3*3) + (3*3) -6]---in this expression,both - and + have same priority

but + before 7 has the lowest priority among all,thats why it is at the highest

0

Ya after that + ans - ,

In SDT that one is farthest from the start has high priority.

So - has more priority than +

In SDT that one is farthest from the start has high priority.

So - has more priority than +

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