Parsing - Introduction to Compiler Construction in a Java World - page 109

The row of entries for state 0 is derived from item set s 0 .
{ By step 2a of Algorithm 3.11, the transition goto(s 0 , ( ) = s 4 implies Action[0,
( ] = s4, and goto(s 0 , id ) = s 5 implies Action[0, id ] = s5. The s4 means \shift
the next input symbol ( onto the stack and go into state 4"; the s5 means \shift
the next input symbol id onto the stack and go into state 5."
The row of entries for state 1 is derived from item set s 1 :
{ By step 2a, the transition goto(s 1 , + ) = s 6 implies Action[1, + ] = s6. Remember,
the s6 means \shift the next input symbol + onto the stack and go into state 6".
{ By step 2b, because item set s 1 contains [E 0 ::= E, # ], Action[1, # ] = accept. This
says, that if the parser is in state 1 and the next input symbol is the terminator
# , the parser accepts the input string as being in the language.
The row of entries for state 2 is derived from item set s 2 :
{ By step 2a, the transition goto(s 2 , * ) = s 7 implies Action[2, * ] = s7.
{ By step 2c, the items 7 [E ::= T, +/# ] imply two entries: Action[2, # ] = r2 and
Action[2, + ] = r2. These entries say that if the parser is in state 2 and the next
incoming symbol is either a # or a + , reduce the T on the stack to a E using
production rule 2: E ::= T.
The row of entries for state 3 is derived from item set s 3 :
{ By step 2c, the items [T ::= F, +/*/# ] imply three entries: Action[3, # ]= r4,
Action[3, + ] = r4, and Action[3, * ] = r4. These entries say that if the parser is
in state 3 and the next incoming symbol is either a # , a + , or a * reduce the F
on the stack to a T using production rule 4: T ::= F.
All other entries in rows 0, 1, 2, and 3 are left blank to indicate an error. If, for example,
the parser is in state 0 and the next incoming symbol is a + , the parser raises an error. The
derivations of the entries in rows 4 to 21 in the Action table (see Figure 3.7) are left as an
exercise.
Now let us consider the first four states of the Goto table:
The row of entries for state 0 is derived from item set s 0 :
{ By step 3a of Algorithm 3.11, the goto(s 0 , E) = 1 implies Goto[0, E] = 1, goto(s 0 ,
T) = 2 implies Goto[0, E] = 4, and goto(s 0 , F) = 3 implies Goto[0, E] = 3. The
entry Goto[0, E] = 1 says that in state 0, once the parser scans and parses an
E, the parser goes into state 1.
The row of entries for state 1 is derived from item set s 1 . Because there are no
transitions on a non-terminal from item set s 1 , no entries are indicated for state 1 in
the Goto table.
The row of entries for state 2 is derived from item set s 2 . Because there are no
transitions on a non-terminal from item set s 2 , no entries are indicated for state 2 in
the Goto table.
7 Recall that the [E::=T, +/# ] denotes two items: [E::=T, + ] and [E::=T, # ].