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GO Classes DPP | COMPILER|SDT

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Consider the following S-attributed SDT scheme used to calculate the value of an expression. The grammar generates simple arithmetic additions and is suitable for an LR parser.

\[
\begin{array}{ll}
\text{Production} & \text{Semantic Rules} \\
E \rightarrow E_1 + T & E.\text{val} = E_1.\text{val} + T.\text{val} \\
E \rightarrow T & E.\text{val} = T.\text{val} \\
T \rightarrow \mathbf{id} & T.\text{val} = \mathbf{id}.\text{lexval}
\end{array}
\]

If the input string is $3+5+2$, what is the sequence of values stored on the semantic stack for the attribute val immediately after each reduction of the type $E \rightarrow E_1+T$ occurs?

  1. $8,10$
     
  2. $3, 5, 2$
     
  3. $3, 8, 10$
     
  4. $5,2$

1 Answer

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Initial Reductions:

  • id $(3)$ is reduced to $T$, then $T$ is reduced to $E$. Stack has $E . v a l=3$.
     
  • id $(5)$ is reduced to $T$. Stack now has $E(3)$ and $T(5)$.
     

First $E \rightarrow E_1+T$ Reduction:

  • The parser reduces $E(3)+T(5)$ to a new $E$.
     
  • E.val $=3+5=\mathbf{8}$.
     

Next Steps:

  • id $(2)$ is reduced to $T$. Stack now has $E$ $(8)$ and $T$ $(2)$.
     

Second $E \rightarrow E_1+T$ Reduction:

  • The parser reduces $E(8)+T(2)$ to the final $E$.
     
  • E.val $=8+2=\mathbf{1 0}$.

The sequence of values produced by the specific reduction $E \rightarrow E_1+T$ is $\mathbf{8 , 1 0}$.

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