GATE CS 2019 Q36 — Syntax-directed Translation

To determine the correct placeholders, let us analyze how type information flows in a variable declaration grammar using Syntax-Directed Translation (SDT).

1. Analysis of $D \rightarrow T L$

• The non-terminal $T$ synthesizes the type (either int or float) via the rules $T \rightarrow \text{int}$ and $T \rightarrow \text{float}$.
• This type information must be passed down (inherited) to the list of identifiers $L$.
• Therefore, the semantic action must assign the type of $T$ to $L$: $$L.\text{type} = T.\text{type}$$
• Comparing this with the given action $X_1.\text{type} = X_2.\text{type}$, we get: $$X_1 = L \quad \text{and} \quad X_2 = T$$

2. Analysis of $L \rightarrow L_1, id$

• The parent list $L$ has already inherited the type attribute in $L.\text{type}$.
• This type must be propagated down to the sublist $L_1$ so that the identifiers inside $L_1$ can also be declared with the same type.
• Therefore, the inherited type of $L_1$ is obtained from $L$: $$L_1.\text{type} = L.\text{type}$$
• Comparing this with the given action $X_3.\text{type} = X_4.\text{type}$, we get: $$X_3 = L_1 \quad \text{and} \quad X_4 = L$$

Conclusion

Matching our findings with the options:

• $X_1 = L$
• $X_2 = T$
• $X_3 = L_1$
• $X_4 = L$

This corresponds exactly to Option A.