Question

Consider the following expression grammar. The semantic rules for expression calculation are stated next to each grammar production.
$E\to \mathrm{number}E.\mathrm{val}=\mathrm{numbe}.\mathrm{val}$
$\begin{array}{c}|E\text{'}+\text{'}E{E}^{\left(1\right)}.\mathrm{val}=E^{\left(2\right)}.\mathrm{val}+E^{\left(3\right)}.\mathrm{val}\\ |E\text{'}\times \text{'}E{E}^{\left(1\right)}.\mathrm{val}=E^{\left(2\right)}.\mathrm{val}\times E^{\left(3\right)}.\mathrm{val};\end{array}$

Assume the conflicts in Part (a) of this question are resolved and an LALR(1) parser is generated for parsing arithmetic expressions as per the given grammar. Consider an expression 3 × 2 + 1. What precedence and associativity properties does the generated parser realize?

• A. Equal precedence and right associativity; expression is evaluated to 9
• B. Precedence of '×' is higher than that of '+', and both operators are left associative; expression is evaluated to 7
• C. Equal precedence and left associativity; expression is evaluated to 7
• D. Precedence of '+' is higher than that of '×', and both operators are left associative; expression is evaluated to 9

Answer 1

The correct option is A Equal precedence and right associativity; expression is evaluated to 9

SR conflict is resolved in favour of shift. All operators are shifted and evaluated from right end, because × and + have equal precedence.
Hence, × and + follows right associatively.

3 × 2 + 1 = 3 × 3 = 9