4.4 LL(1) Parsers

• The selection of production rules for LL(1) grammars can be represented in a table referred to as a LL(1) parsing tables
• Pushdown-oriented parsers driven by LL(1) tables are said to be LL(1) parsers.
  1. Place the start symbol at the top of the stack
  2. Scan the first lookahead token $a$
  3. Repeatedly determine the symbol $X$ at the top of the stack and act according to the case.

     $X$ is nonterminal and the parse table provides the production rule $X\to \alpha$ at entry ($X$,$a$) replace $X$ on top of the stack with the reverse of $\alpha$ $X=a$ and $a\ne \text{ \$}$ pop $X$ and scan a new lookahead token $a$ $X=\text{ \$}$ and $a=\text{ \$}$ declare success and halt otherwise declare error

1. $E$ $\to$ $T{E}^{\prime }$ $\left\{\text{ (},a\right\}$ 2. $E^{\prime }$ $\to$ $+T{E}^{\prime }$ $\left\{+\right\}$ 3. $$ $\to$ $ϵ$ $\left\{\text{ )},\text{ \$}\right\}$ 4. $T$ $\to$ $F{T}^{\prime }$ $\left\{\text{ (},a\right\}$ 5. $T^{\prime }$ $\to$ $\ast F{T}^{\prime }$ $\left\{\ast \right\}$ 6. $$ $\to$ $ϵ$ $\left\{+,\text{ )},\text{ \$}\right\}$ 7. $F$ $\to$ $\left(E\right)$ $\left\{\text{ (}\right\}$ 8. $$ $\to$ $a$ $\left\{a\right\}$

a + * ( ) $ E 1     1     E’   2     3 3 T 4     4     T’   6 5   6 6 F 8     7

$\stackrel{\text{ table}\left(E,a\right)=1}{\Rightarrow }$

$\stackrel{\text{ table}\left(T,a\right)=4}{\Rightarrow }$

$\stackrel{\text{ table}\left(F,a\right)=8}{\Rightarrow }$

$\Rightarrow$

$\stackrel{\text{ table}\left(T^{\prime },+\right)=6}{\Rightarrow }$

$\stackrel{\text{ table}\left(E\prime ,+\right)=2}{\Rightarrow }$

$\Rightarrow$

$\stackrel{\text{ table}\left(T,a\right)=4}{\Rightarrow }$

$\stackrel{\text{ table}\left(F,a\right)=8}{\Rightarrow }$

$\Rightarrow$

$\stackrel{\text{ table}\left(T^{\prime },\ast \right)=5}{\Rightarrow }$

$\Rightarrow$

$\stackrel{\text{ table}\left(F,a\right)=8}{\Rightarrow }$

$\Rightarrow$

$\stackrel{\text{ table}\left(T^{\prime },\$\right)=6}{\Rightarrow }$

$\stackrel{\text{ table}\left(E\prime ,\$\right)=3}{\Rightarrow }$