Chapter 2, Problem 26E

Explanation of Solution

Justification:

• The given grammar is not LL(1) grammar because of the production rule $\text{id}\in \text{PREDICT(expr}\to \text{id}\text{:=expr)}\cap \text{PREDICT(expr}\to \text{term}\text{term\_tail)}$.
• Its minor in the PREDICT set of the former productions.
• It is in PREDICT set of the latter production because the term belongs to factor which implies to id.
• To make it LL (1), one need to factor out the id. That is the simplest way to do this is to enlarge the language generated by the grammar.

$\begin{array}{l}\text{expr }\to \text{term expr\_tail}\\ \text{expr\_tail }\to \text{:= expr}\\ \to \text{term\_tail}\\ \text{term\_tail }\to \text{+ term term\_tail | }\in \end{array}$

      $\begin{array}{l}\text{term }\to \text{ factor factor\_tail }\\ \text{factor tail }\to \text{ * factor factor tail | }\in \\ \text{factor }\to \text{ ( expr ) | id}\end{array}$

• The semantic checks would be required to ensure that the fragments to the left of a sign := is in id