Chapter 4, Problem 11E

Explanation of Solution

Accumulating the value constant into value:

• The val is the root attribute in this grammar.
• At first instance the first 2 digits are passed and then computing the constant value for those elements.
• Next adding the other digits to list to find the constant value.
• It continues up to 9 digits.
• The following grammar represents s-attribute grammar for the given problem.

        $\begin{array}{l}\text{C }\to \text{ digits1 }\text{. digits2}\Rightarrow \text{C}\text{.val := digits1}\text{.val + digits2}\text{.val}\times {10}^{{\text{-digits}}_{\text{2}}\text{.len}}\\ \text{digits }\to \text{ digit more digits}\\ \Rightarrow \text{digits}\text{.val := digit}\text{.val}\times {10}^{\text{more\_digits}\text{.len}}+\text{more\_digits}\text{.val}\\ \Rightarrow \text{digits}\text{.len := more digits}\text{.len + 1}\\ \text{more digits }\to \text{ digits}\end{array}$        $\begin{array}{l}\Rightarrow \text{more digits}\text{.val := digits}\text{.val}\\ \Rightarrow \text{more digits}\text{.len := digits}\text{.len}\\ \text{more digits }\to \in \\ \Rightarrow \text{more digits}\text{.val := 0}\\ \Rightarrow \text{more digits}\end{array}$