1.7k views

Consider the grammar with the following translation rules and E as the start symbol

 \begin{align*}E \rightarrow & E_ 1\# \: T \\ &\mid T \end{align*} \begin{align*}T \rightarrow & T_1 \& \: F \\ &\mid F \end{align*} $F \rightarrow \text{num}$ $\left\{E.value = E_1.value * T.value\right\}$ $\{E.value = T.value\}$ $\{T.value = T_1.value + F.value\}$ $\{T.value = F.value\}$ $\{F.value=num.value\}$

Compute E.value for the root of the parse tree for the expression:$2$ # $3$ & $5$ # $6$ & $4$

1. $200$
2. $180$
3. $160$
4. $40$
edited | 1.7k views
+5
GATE 2004_45
original  question was :

Consider the grammar with the following translation rules and E as the start symbol

E→ E1 # T       {E.value=E1.value ∗ T.value}
| T             {E.value=T.value}
T→T1 & F        {T.value=T1.value + F.value}
| F               {T.value=F.value}
F→num            {F.value=num.value}
0

Here # is multiplication and & is addition by semantics rules given in the question.
By observation of productions,

1. here &(+) is higher precedence than #(*), because & is far from starting symbol
2. both &,# are left associative

So, we can solve the expression as $((2*(3+5))*(6+4)) =160$

edited by
0

Can you please explain how and both &,# are left associative ???

+7
if there is left recursion then operator will be left associative .. or if right recursion then operator will be right associate ..

eg : E---> E+T(here E derive E+T so it is left recursive

E---->T+E (here E derive T+E so it is right recursive
+3
Nice explanation.
Formal procedure of determining associativity and precedence in operator precedence grammar is using "Leading" and "Trailing". After computing leading and trailing of Nonterminals, we make operator precedence table that tells everything u want to know about associativity and precedence of operators in grammar.
+1
I am not able to prepare parse tree here. Can anyone help?
+2

parse tree

0
here is E and E1 is different
0

Sachin sir ,

So everytime ..to decide precedence and asscociativity operator relation table constructed using Lead and Trails is needed ??

Can't we answer it using this argument

"Operator which is at lower level in the grammar is termed to have higher precedence."

C   will   be ans.

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