\[ \newcommand{\tr}{\Rightarrow} \newcommand{\trs}{\tr^{\!\ast}} \newcommand{\rlnm}[1]{\mathsf{(#1)}} \newcommand{\rred}[1]{\xrightarrow{#1}} \newcommand{\rreds}[1]{\mathrel{\xrightarrow{#1}\!\!^*}} \newcommand{\cl}{\mathsf{Cl}} \newcommand{\pow}{\mathcal{P}} \newcommand{\matches}{\mathrel{\mathsf{matches}}} \newcommand{\kw}[1]{\mathsf{#1}} \newcommand{\andop}{\mathrel{\&\!\&}} \newcommand{\orop}{\mathrel{\|}} \newcommand{\ff}{\mathsf{false}} \newcommand{\tt}{\mathsf{true}} \newcommand{\abra}[1]{\langle #1 \rangle} \newcommand{\bnfnt}[1]{\abra{\small \textsf{#1}}} \newcommand{\llbracket}{[\![} \newcommand{\rrbracket}{]\!]} \newcommand{\first}{\mathsf{First}} \newcommand{\nullable}{\mathsf{Nullable}} \newcommand{\follow}{\mathsf{Follow}} \newcommand{\tm}[1]{\mathsf{#1}} \]

The syntax of the While Programming Language is given by the CFG with:

• Terminal symbols: $0,1,\ldots{},9$, $’$, $a,b,\ldots,z,A,B,\ldots,Z$, $\andop$, $\orop$, $!$, $+$, $*$, $-$, $\leq$, $=$, $\leftarrow$, $;$.
• Nonterminal symbols: $S$, $B$, $A$, $D$, $E$, $L$, $U$, $M$, $V$, $N$

• Production rules:

  \[\begin{array}{rcl} S &\longrightarrow& \mathsf{skip} \mid V \leftarrow A \mid S ; S \mid \mathsf{if}\ B\ \mathsf{then}\ S\ \mathsf{else}\ S \mid \mathsf{while}\ B\ \mathsf{do}\ S \mid \{\ S\ \}\\ B &\longrightarrow& \tt \mid \ff \mid A \leq A \mid A = A \mid \mathop{!}B \mid B \andop B \mid B \orop B \mid (B)\\ A &\longrightarrow& V \mid N \mid A + A \mid A - A \mid A * A \mid (A)\\ D &\longrightarrow& 0 \mid 1 \mid \cdots{} \mid 9\\ E &\longrightarrow& D\ E \mid \epsilon\\ L &\longrightarrow& a \mid b \mid \cdots{} \mid z \\ U &\longrightarrow& A \mid B \mid \cdots{} \mid Z \mid '\\ M &\longrightarrow& L\ M \mid U\ M \mid \epsilon\\ V &\longrightarrow& L\ M\\ N &\longrightarrow& D\ E \end{array}\]
• Start symbol: $S$