Discussion
Consider the following syntax-directed definition (SDD).
| \(S \to DHTU\) | { \(S.val = D.val + H.val + T.val + U.val;\) } |
| \(D \to\) "M"\(D_{1}\) | { \(D.val = 5 + D_{1}.val;\) } |
| \(D \to \epsilon\) | { \(D.val = -5;\) } |
| \(H \to\) "L"\(H_{1}\) | { \(H.val = 5 * 10 + H_{1}.val;\) } |
| \(H \to \epsilon\) | { \(H.val = -10;\) } |
| \(T \to\) "C"\(T_{1}\) | { \(T.val = 5 * 100 + T_{1}.val;\) } |
| \(T \to \epsilon\) | { \(T.val = -5;\) } |
| \(U \to\) "K" | { \(U.val = 5;\) } |
Given "MMLK" as the input, which one of the following options is the CORRECT value computed by the SDD (in the attribute \(S.val\))?
Answer: A
The value computed is 45.
Parse 'MMLK' as \(S \to DHTU\) with D = MM, H = L, T = \(\epsilon\) and U = K, then evaluate bottom-up:
\[ \begin{aligned} D &= 5 + (5 + (-5)) = 5 \\ H &= 5 \times 10 + (-10) = 40 \\ T &= -5,\quad U = 5 \\ S &= 5 + 40 - 5 + 5 = 45 \end{aligned} \]
The \(\epsilon\) productions contribute negative values that are easy to forget: dropping the −5 for the empty T gives 50, and dropping the −5 at the end of D's chain as well gives 55.
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