03b LL1 Example

8/12/2019 03b LL1 Example

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LL(1) Parsing TheoryGoal: Formal, rigorous description of those

grammars for which I can figure out how to

do a top-down parse by looking ahead justone token, plus corresponding algorithms.

Notation:

T = Set of Terminals(Tokens)N = Set of Nonterminals

$ = End-of-file character (T-like, but not in N !T)


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Table-driven predictive parser

! Automatically compute PREDICTtablefrom grammar

! PREDICT(nonterminal,input-symbol)

" action, e.g. which rhs or error


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Example 1Stmt ::= ifexpr thenStmt elseStmt |

2whileExpr doStmt | 3beginStmts end

Stmts ::= 4Stmt ;Stmts | 5"Expr ::= 6id

;

6Expr5Stmts

3Stmt$idendbegindowhileelsethenif

empty = error


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LL(1) Parsing Algorithmpush S$ /* S is start symbol */

while Stack not empty

X := pop(Stack)a := peek at next input token /* EOF => $ */

if X is terminal or $

If X==a, read token a else abort;

else look at PREDICT(X, a) /* X is nonterminal*/

Empty : abort

rule X #$: push $

If not at end of input, Abort else Accept


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Parser Example! Following slides trace execution of the parser

(slide 5) on a token string according to the

grammar from slide 4 and the correspondingparse tree

! Snapshots show parser state at the top of thewhile loop and just before the if statement ateach iteration, together with a summary ofthe action taken in the if

! Notice how the leaves on the right side of theparse tree correspond to the stack contents


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S$

S

while id do begin begin end ; end $

X:

a:

Stack:

At top of loop


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$

S


X: S

a: while

Stack:

Mid loop

Action: 2S ::= whileE doS


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while

EdoS$

S

E Swhile

id

do

begin begin end ; end $

X:

a:

Stack:

At top of loop

dowhile


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EdoS$

S

E S


X: while

a: while

Stack:

Mid loop

while do

Action: Match


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EdoS$

S

E S

whileid do begin begin end ; end $

X:

a:

Stack:

At top of loop

do


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doS$

S

E S

whileid do begin begin end ; end $

X: E

a: id

Stack:

Mid loop

do

Action: 6E ::= id


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iddoS$

S

E S

id

do begin begin end ; end $

X:

a:

Stack:do

idwhile

At top of loop


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doS$

S

E S

id do begin begin end ; end $

X: id

a: id

Stack:

Mid loop

do

while

id

Action: Match


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doS$

S

E S

iddo begin begin end ; end $

X:

a:

Stack:do

while

At top of loop


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S$

S

E S

do begin begin end ; end $

X: do

a: do

Stack:

Mid loop

do

while id

Action: Match


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S$

S

E S


X:

a:

Stack:

dowhile id

At top of loop


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$

S

E S


X: S

a: begin

Stack:

Mid loop

while doid

Action: 3S ::= beginSs end


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beginSsend$

S

E S

Ss


X:

a:

Stack:

while doid

begin end

At top of loop


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Ssend$

S

E S

Ss


X: begin

a: begin

Stack:

Mid loop

while doid

begin end

Action: Match


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Ssend$

S

E S

Ss

begin end ; end $

X:

a:

Stack:

while doid begin

end

At top of loop


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end$

S

E S

Ss

begin end ; end $

X: Ss

a: begin

Stack:

Mid loop

while doid

end

begin

Action: 4Ss ::= S ;Ss


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S

;Ssend$

S

E S

Ss

Ss

begin end

;

end $

S

X:

a:

Stack:

while doid

end

begin;

At top of loop


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;Ssend$

S

E S

Ss

Ss

begin end

;

end $

S

X: S

a: begin

Stack:

Mid loop

while doid

end

begin;

Action: 3S ::= beginSs end


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beginSsend

;Ssend$

S

E S

Ss

Ss

begin end

;

end $

S

X:

a:

Stack:

Top of loop

while doid

end

begin;

begin endSs


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Ssend

;Ssend$

S

E S

Ss

Ss

begin end

;

end $

S

X: begin

a: begin

Stack:

while doid

end

begin;

begin endSs

Mid loop

Action: Match


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Ssend

;Ssend$

S

E S

Ss

Ss

end

;

end $

S

X:

a:

Stack:

while doid

end

begin;

begin

endSs

Top of loop


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end

;Ssend$

S

E S

Ss

Ss

end

;

end $

S

X: Ss

a: end

Stack:

while doid

end

begin;

begin

endSs

Mid loop

Action: 5Ss ::= "


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end

;Ssend$

S

E S

Ss

Ss

end

;

end $

S

X:

a:

Stack:

while doid

end

begin;

begin

endSs

Top of loop

"


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;Ssend$

S

E S

Ss

Ss

end

;

end $

S

X: end

a: end

Stack:

while doid

end

begin;

begin

endSs

Mid loop

"

Action: Match


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;Ssend$

S

E S

Ss

Ss;

end $

S

X:

a:

Stack:

while doid

end

begin;

begin end

Ss

Top of loop

"


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Ssend$

S

E S

Ss

Ss;

end $

S

X: ;

a: ;

Stack:

while doid

end

begin;

begin end

Ss

Mid loop

"

Action: Match


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Ssend$

S

E S

Ss

Ss

;end $

S

X:

a:

Stack:

while doid

end

beginbegin end

Ss

Top of loop

"


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end$

S

E S

Ss

Ss

;end $

S

X: Ss

a: end

Stack:

while doid

end

beginbegin end

Ss

Mid loop

"

Action: 5Ss ::= "


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end$

S

E S

Ss

Ss

;end $

S

X:

a:

Stack:

while doid

end

beginbegin end

Ss

Top of loop

" "


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$

S

E S

Ss

Ss

;end $

S

X: end

a: end

Stack:

while doid

end

beginbegin end

Ss

Mid loop

" "

Action: Match


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$

S

E S

Ss

Ss

; end$

S

X:

a:

Stack:

while doid beginbegin end

Ss

Top of loop

" "


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S

E S

Ss

Ss

; end$

S

X: $

a: $

Stack:


Ss

Mid loop

" "

Action: Match


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S

E

ACCEP

TSSs

Ss

; end $

S

X:

a:

Stack:


Ss

Top of loop

" "

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03b LL1 Example