GATE CS 2003 Q59 — Syntax-directed Translation

To find the 3-address code generated for the statement $X := Y + Z$, we construct the parse tree and evaluate the semantic actions bottom-up.

1. Parse Tree Construction

The parse tree for the expression $X := Y + Z$ is:

• $S \rightarrow \mathbf{id} := E$ (where $\mathbf{id}$ is $X$)
  • $E \rightarrow E_1 + E_2$
    • $E_1 \rightarrow \mathbf{id}$ (where $\mathbf{id}$ is $Y$)
    • $E_2 \rightarrow \mathbf{id}$ (where $\mathbf{id}$ is $Z$)

2. Bottom-Up Evaluation of Semantic Actions

1. For the leaf nodes:
   • $E_1 \rightarrow \mathbf{id}$ (with $\mathbf{id} = Y$):
     $E_1.place = Y$
   • $E_2 \rightarrow \mathbf{id}$ (with $\mathbf{id} = Z$):
     $E_2.place = Z$
2. For the production $E \rightarrow E_1 + E_2$:
   • A new temporary variable is created: $t_1 = newtemp()$
   • The code generation function is called:
     $gen(t_1 = E_1.place + E_2.place;) \implies \mathbf{t_1 = Y + Z;}$
   • The place attribute is synthesized:
     $E.place = t_1$
3. For the production $S \rightarrow \mathbf{id} := E$ (with $\mathbf{id} = X$):
   • The code generation function is called:
     $gen(X = E.place;) \implies \mathbf{X = t_1;}$

3. Final Generated Code

Combining the generated statements in order of their execution, we get:

$$t_1 = Y + Z; \quad X = t_1;$$

This matches Option B.