LL$(1)$ Grammar

$$ program $>$::$=$ def $$ funcname $>$ arguments $>\frac{\text{:}}{?}$

$$ block $>$ EOF

$$ funcname $>$::$=f|g$

$$ arguments variable $>$ morevars $>$

$$ morevars $>$::$=,$ variable $>$ morevars $>|lon$

$$ block $>$::$=$ stmtlist $>$

$$ stmtlist $>$::$\frac{?}{\frac{?}{?}}=t$ stmt $>$ morestmts $>$

$$ morestmts $>$::$\frac{?}{?}$

$=$ stmtlist $>|lon$

$$ stmt $>$::$=$ assign $>|$ ifstmt $>|$ returnstmt $>$

$$ assign $>$::$=$ variable $$ expr $>$

$$ condition $>$::$=$ variable $>$ expr $>$

$$ ifstmt $>$::$=$ if $$ condition $>$ : ::::::::::$=0|1|2>$

$$ returnstmt $>$::$=$ return $$ variable $>$

$$ expr $>$::$=$ term $>+$ term $>$

$$ term $>$::$=$ variable $>|$ digit $>$

$$ variable $>$::$=a|b|c$

$$ digit $>$::$=0|1|2$

represents the "new line" terminal. $\frac{?}{t}$ represents the "tab" terminal.

$(a)$ Show that the grammar above $isLL(1).$ Use a formal argument based

$on$ the definition $of$ the $LL(1)$ grammar.

$(b)$ Show the $LL(1)$ parse table.

$(c)$ Write a recursive descent parser $in$ pseudo$-$code. You may assume that

the $nex{t}_t$oken$()$ function $is$ already implemented for reading the next

token $in$ the remaining input string, and you can directly use $itin$ your

pseudocode.$\frac{?}{?}$

$>\frac{\frac{?}{?}}{t}$ else : $>$

$$ returnstmt $>$::$=$ return $$ variable $>$

$$ expr $>$::$=$ term $>+$ term $>$

$$ term $>$::$=$ variable $>|$ digit $>$

$$ variable $>$::$=a|b|c$

$$ digit $>$::$=0|1|2$

represents the "new line" terminal. $\frac{?}{t}$ represents the "tab" terminal.

$(a)$ Show that the grammar above $isLL(1).$ Use a formal argument based

$on$ the definition $of$ the $LL(1)$ grammar.

$(b)$ Show the $LL(1)$ parse table.

$(c)$ Write a recursive descent parser $in$ pseudo$-$code. You may assume that

the $nex{t}_t$oken$()$ function $is$ already implemented for reading the next

token $in$ the remaining input string, and you can directly use $itin$ your