Chapter 4, Problem 6E

Explanation of Solution

Expanding the grammar to accumulate to find count of the maximum depth:

• In Exercise 2.13, they used sub calls to refer the production parts.
• They split the production based on the parentheses.
• The following grammar represents the expanded grammar which is used to find the count of maximum depth in a production.

  $\begin{array}{l}\text{stmt }\to \text{ assignment }\Rightarrow \text{stmt}\text{.depth := assignment}\text{.depth}\\ \text{stmt }\to \text{ subr\_call }\Rightarrow \text{stmt}\text{.depth := subr\_call}\text{.depth}\\ \text{assignment }\to \text{id := expr }\Rightarrow \text{assignment}\text{.depth := expr}\text{.depth}\\ \text{subr\_call }\to \text{ id ( arg list ) }\Rightarrow \text{ubr\_call}\text{.depth := arg\_list}\text{.depth}\end{array}$

               $\begin{array}{l}\text{expr }\to \text{primary expr\_tail }\Rightarrow \text{expr}\text{.depth := max(primary}\text{.depth, expr\_tail}\text{.depth)}\\ \text{expr\_tail }\to \text{ op expr }\Rightarrow \text{expr\_tail}\text{.depth := expr}\text{.depth}\\ \text{expr\_tail }\to \text{ expr }\Rightarrow \text{tail}\end{array}$