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Understanding Lemon generated Parser

Lemon uses LALR (1) parsers means Look Ahead exactly one token from Left to Right. When the parser receive the input Token, it also reads previous State number from the Parser stack. Using this Token and State number Parser process with the pre calculated Tables like yy_action, yy_shift_ofst, yy_reduce_ofst , Depends upon the values the corresponding action shift or Reduce is performed .
Current Token with Previous State Number => Action

Parser Action :
Shift : The Current Token with value is pushed at the top of the stack
Reduce : The corresponding rule is applied & Parser Stack is poped. Depends upon the rule number of The number symbols is poped from stack.

Parser Stack:
it is associated with 4 elements :
Parser Stack Index(Index): It is the parser index value.
State Number(State No) : it holds state number ,which is used for the calculating with next State.
Symbol Index(Symbol): Symbol Index, The integer unique Symbol id.
Token Value(Value): Token Value.
Initially Parser Stack is initializes by $ symbol

Parser Tables:
• yy_action: A single table containing all the possible state number
• yy_shift_ofst: For each state, the offset into yy_action for shifting terminals into the parser stack
• yy_reduce_ofst: For each state, the offset into yy_action holds for the reducing the parse Stack
• yyRuleInfo : From the Rule Index value , we can map this array index value
a. LHS Symbol Index : Symbol of the LHS of the given Rule Index
b. NRHS: Number of RHS in that Rule

Algorthim:
Get current token ,token value till end of token
Do {
get action value
if(value > totalstate){
reduce rule of (value –totalstate)
tokenpushedtostack=true
}
else{
push current token with value on stack
do the Rule Action
}
While(tokenpushedtostack);
If(ActionValue== Totalstate+totalrule+1) {
Success =>program accept
}
If(ActionValue== Totalstate+totalrule) {
Syntax error=> The input is not subset of given grammar
}

The Lemon Grammar specification
We will take a simple example of Context free Grammar(CFG) arithmetic calculator
Example1.y

program ::=  expr(A) . { printf ("Result=%d\n", A); }
expr(A) ::= INTEGER(B) PLUS INTEGER(C).	{  A = B + C ; }
expr(A) ::= INTEGER(B) TIMES INTEGER(C).{  A = B * C ; }
expr(A) ::= INTEGER(B) .

Lemon .output file (.out) File Description
TotalState = YYNState = 7 (more info can be seen in .out file )
TotalRules = YYNRulee= 4
This CFG rules and symbol index vales as follows

The Expression are evaluates as follows :
=3+4*5+6
=3 +20+6
=23+6
=29;

This Lemon parser for the above expression as follows

Parse(p,INTEGER,3);
Parse(p,PLUS,0);
Parse(p,INTEGER,4);
Parse(p,TIMES,0);
Parse(p,INTEGER,5);
Parse(p,PLUS,0);
Parse(p,INTEGER,6);
Parse(p,0,0);

The Parser Table generated by lemon parser as follows
static const YYACTIONTYPE yy_action[] = {
 /*     0 */     7,    5,    2,    1,   10,   13,   10,   10,    8,   13,
 /*    10 */     8,    1,    9,   13,    9,    9,    6,   12,    4,   13,
 /*    20 */     3,
};
static const signed char yy_shift_ofst[] = {
 /*     0 */    17,   17,   17,   12,    4,    8,    0,
};
 
static const signed char yy_reduce_ofst[] = {
 /*     0 */    11,   15,   -4,    1,    1,    1,    1,
};
 
} 

yyRuleInfo[] = {
{ 6, 1 }, => program = INTEGER (Total RHS =1)
{ 5, 3 }, => expr = expr +expr (Total RHS =3)
{ 5, 3 },=> expr =expr *expr (Total RHS =3)
{ 5, 1 }, expr = INTEGER(Total RHS =1)
};

1.Parse(p,INTEGER,3);
Calculate Action :
Current Token = INTEGER = 1, Previous State = 0

Action = yy_action[ yy_shift_ofst[Previous State]+Current Token ]
= yy_action[yy_shift_ofst[0]+1]
= yy_action[17+1] => 4

4 < 7 then shift Shift this token in Parser stack

2.Parse(p,PLUS,0);
1.Calculate Action
Current Token = PLUS = 2, Previous State = 4
Action = yy_action[ yy_shift_ofst[4]+2 ]
= yy_action[4+2] =>10
Action value > YYNState then Reduce
10 > 7

1.Reduce Action:
Reduce Rule Index =action value – TotalState => 10-7= 3 => expr ::= INTEGER
ReduceToken = yyRuleinfo[3].lhs => 5 (expr : integer)
TotalRHSSymbol = yyRuleinfo[3].nrhs => 1
Stateno :
get Previous Stack Index = Current Stack Index – TotalRHSSymbol
= 1-1 => 0
PreviousStateno = stack[Previous Stack Index].stateno => 0
=yy_action[yy_reduce_ofst[PreviousStateno] +Token]
=yy_action[yy_reduce_ofst[0] +Token]
= yy_action[11+5] => 6

2.Calculate Action
Current Token = PLUS = 2, Previous State = 6
Action = yy_action[ yy_shift_ofst[6]+2 ]
= yy_action[0+2] =>2
Action value< yyNState then push to stack push(2,PLUS,0)

3.Parse(p,INTEGER,4);
Calculate Action:
Current Token = INTEGER =1, Previous State = 2
=yy_action[ yy_shift_ofst[2]+1 ]
= yy_action[17+1] =>4
Action value< yyNState then push to stack push(4,INTEGER,4)

4.Parse(p,TIMES,0);
Calculate Action
Current Token = TIMES =3, Previous State = 4
Action = yy_action[ yy_shift_ofst[4]+3 ]
= yy_action[4+3] =>10
1.Reduce Action :
Reduce Rule Index =action value – TotalState => 10-7= 3 => expr ::= INTEGER
ReduceToken = yyRuleinfo[3].lhs => 5(expr : integer)
TotalRHSSymbol = yyRuleinfo[3].nrhs => 1
Stateno :
get Previous Stack Index: Current Stack Index – TotalRHSSymbol
=3-1 => 2
PreviousStateno= stack[2].stateno => 2
=yy_action[yy_reduce_ofst[PreviousStateno] +Token]
=yy_action[yy_reduce_ofst[2] +5]
= yy_action[-4+5] => 5
Reduce stack index 3 & apply rule 3


Calculate Action
Current Token = TIMES =3, Previous State = 5
=yy_action[ yy_shift_ofst[5]+3 ]
= yy_action[8+3] =>1
Push stack (1,Times,0);

5.Parse(p,INTEGER,5);
Calculate Action
Current Token = INTEGER =1, Previous State = 1
=yy_action[ yy_shift_ofst[1]+1 ]
= yy_action[17+1] =>4
Action value< yyNState then push to stack push(4,INTEGER,5)

6.Parse(p,PLUS,0);
1.Calculate Action
Current Token = PLUS =2, Previous State = 4
=yy_action[ yy_shift_ofst[4]+2 ]
= yy_action[4+1] =>10
10 > 7 then reduce
1.Reduce Action :
Reduce Rule Index =action value – TotalState => 10-7= 3 => expr ::= INTEGER
ReduceToken = yyRuleinfo[3].lhs => 5
TotalRHSSymbol = yyRuleinfo[3].nrhs => 1
Stateno :
get Previous Stack Index: Current Stack Index – TotalRHSSymbol
=5-1 => 4
PreviousStateno= stack[4].stateno => 1
=yy_action[yy_reduce_ofst[PreviousStateno] +Token]
=yy_action[yy_reduce_ofst[1] +5]
= yy_action[15+5] => 3
apply rule 3 at stack index 5

2. Calculate Action
Current Token = PLUS =2, Previous State = 3
=yy_action[ yy_shift_ofst[3]+2 ]
= yy_action[12+2] =>9
9> 7 then
2.Reduce Action :
Reduce Rule Index =action value – TotalState => 9-7= 2 => expr ::= expr TIMES expr
ReduceToken = yyRuleinfo[2].lhs => 5
TotalRHSSymbol = yyRuleinfo[2].nrhs => 3
Stateno :
get Previous Stack Index: Current Stack Index – TotalRHSSymbol
=5-3 => 2
PreviousStateno= stack[2].stateno => 2
=yy_action[yy_reduce_ofst[PreviousStateno] +Token]
=yy_action[yy_reduce_ofst[2] +5]
= yy_action[-4+5] => 5


3.Calculate Action

Current Token = PLUS =2,Previous State = 5
=yy_action[ yy_shift_ofst[5]+2 ]
= yy_action[8+2] =>8
8> 7 then

3.Reduce Action :
Reduce Rule Index =action value – TotalState => 8-7= 1=> expr ::= exprPLUS expr
ReduceToken = yyRuleinfo[2].lhs => 5
TotalRHSSymbol = yyRuleinfo[2].nrhs => 3
Stateno :
get Previous Stack Index: Current Stack Index – TotalRHSSymbol
=3-3 => 0
PreviousStateno= stack[2].stateno => 2
=yy_action[yy_reduce_ofst[PreviousStateno] +Token]
=yy_action[yy_reduce_ofst[0] +5]
= yy_action[11+5] => 6

3.Calculate Action
Current Token = PLUS =2
Previous State = 6
=yy_action[ yy_shift_ofst[6]+2 ]
= yy_action[0+2] =>2
2> 7 then push stack (2,PLUS,0)

7.Parse(p,INTEGER,6);
Calculate Action :
Current Token = INTEGER =1, Previous State =2
=yy_action[ yy_shift_ofst[2]+1 ]
= yy_action[17+1] =>4
Push stack(4,INTEGER,6);

8.Parse(p,0,0);
Calculate Action :
Current Token = $ =0,Previous State =4
=yy_action[ yy_shift_ofst[4]+0 ]
= yy_action[4+0] =>10

1.Reduce Action :
Reduce Rule Index =action value – TotalState => 10-7= 3=> expr ::= INTEGER
ReduceToken = yyRuleinfo[3].lhs => 5
TotalRHSSymbol = yyRuleinfo[3].nrhs => 1
Stateno :
get Previous Stack Index: Current Stack Index – TotalRHSSymbol
=3-1 => 2
PreviousStateno= stack[2].stateno => 2
=yy_action[yy_reduce_ofst[PreviousStateno] +Token]
=yy_action[yy_reduce_ofst[2] +5]
= yy_action[-4+5] => 5

1.Calculate Action :
Current Token = $ =0 , Previous State =5
=yy_action[ yy_shift_ofst[5]+0 ]
= yy_action[8+0] =>8
8-7 => rule 1
Reduce Rule Index =action value – TotalState =>8-7= 1=> expr ::= expr PLUS expr
ReduceToken = yyRuleinfo[1].lhs => 5
TotalRHSSymbol = yyRuleinfo[1].nrhs => 3
Stateno :
get Previous Stack Index: Current Stack Index – TotalRHSSymbol
=3-3 => 0
PreviousStateno= stack[0].stateno => 0
=yy_action[yy_reduce_ofst[PreviousStateno] +Token]
=yy_action[yy_reduce_ofst[0] +5]
= yy_action[11+5] => 6
Reduce Rule 1

2. Calculate Action :
Current Token = $ =0 , Previous State =6
=yy_action[ yy_shift_ofst[6]+0 ]
= yy_action[0+0] =>7
7>7 =>

1.Reduce Action :
Reduce Rule Index =action value – TotalState => 7-7= 0=> program ::= INTEGER
ReduceToken = yyRuleinfo[0].lhs => 6
TotalRHSSymbol = yyRuleinfo[0].nrhs => 1
Stateno :
get Previous Stack Index: Current Stack Index – TotalRHSSymbol
=1-1 => 0
PreviousStateno= stack[0].stateno => 0
=yy_action[yy_reduce_ofst[PreviousStateno] +Token]
=yy_action[yy_reduce_ofst[0] +6]
= yy_action[11+6] =>12

program accept = Totalstate+totalrule+1
=7 + 4 +1 =>12
Hence program accept

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