Post on 23-Jul-2020
CSE401:LL(1) Parsing Example
Larry RuzzoSpring 2004
Slides by Chambers, Eggers, Notkin, Ruzzo, and others© W.L.Ruzzo & UW CSE 1994-2004
2
LL(1) Parsing TheoryGoal: Formal, rigorous description of those
grammars for which “I can figure out how todo 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)
3
Table-driven predictive parser Automatically compute PREDICT table
from grammar PREDICT(nonterminal,input-symbol)
action, e.g. which rhs or error
4
Example 1Stmt ::= 1 if expr then Stmt else Stmt | 2 while Expr do Stmt | 3 begin Stmts end
Stmts ::= 4 Stmt ; Stmts | 5 ε
Expr ::= 6 id
;
6Expr
5444Stmts
321Stmt
$idendbegindowhileelsethenif
empty = error
5
LL(1) Parsing Algorithmpush S$ /* 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 : abortrule X → α : push α
If not at end of input, Abort else Accept
6
Parser Example Following slides trace execution of the parser
(slide 5) on a token string according to thegrammar 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
7
S$
S
while id do begin begin end ; end $
X: a: Stack:
At top of loop
8
$
S
while id do begin begin end ; end $
X: Sa: whileStack:
Mid loopAction: 2 S ::= while E do S
9
whileEdoS$
S
E Swhile
id
do
begin begin end ; end $
X:a:Stack:
At top of loop
dowhile
10
EdoS$
S
E S
while id do begin begin end ; end $
X: whilea: whileStack:
Mid loop
while do
Action: Match
11
EdoS$
S
E S
whileid do begin begin end ; end $
X:a:Stack:
At top of loop
do
12
doS$
S
E S
whileid do begin begin end ; end $
X: Ea: idStack:
Mid loop
do
Action: 6 E ::= id
13
iddoS$
S
E S
id
do begin begin end ; end $
X:a:Stack:do
idwhile
At top of loop
14
doS$
S
E S
id do begin begin end ; end $
X: ida: idStack:
Mid loop
do
while
id
Action: Match
15
doS$
S
E S
iddo begin begin end ; end $
X:a:Stack:do
while
At top of loop
16
S$
S
E S
do begin begin end ; end $
X: doa: doStack:
Mid loop
do
while id
Action: Match
17
S$
S
E S
begin begin end ; end $
X: a: Stack:
dowhile id
At top of loop
18
$
S
E S
begin begin end ; end $
X: Sa: beginStack:
Mid loop
while doid
Action: 3 S ::= begin Ss end
19
beginSsend$
S
E S
Ss
begin begin end ; end $
X:a:Stack:
while doid
begin end
At top of loop
20
Ssend$
S
E S
Ss
begin begin end ; end $
X: begina: beginStack:
Mid loop
while doid
begin end
Action: Match
21
Ssend$
S
E S
Ss
begin end ; end $
X:a:Stack:
while doid begin
end
At top of loop
22
end$
S
E S
Ss
begin end ; end $
X: Ssa: beginStack:
Mid loop
while doid
end
begin
Action: 4 Ss ::= S ; Ss
23
S;Ssend$
S
E S
Ss
Ss
begin end
;
end $
S
X:a:Stack:
while doid
end
begin ;
At top of loop
24
;Ssend$
S
E S
Ss
Ss
begin end
;
end $
S
X: Sa: beginStack:
Mid loop
while doid
end
begin;
Action: 3 S ::= begin Ss end
25
beginSsend;Ssend$
S
E S
Ss
Ss
begin end
;
end $
S
X:a:Stack:
Top of loop
while doid
end
begin;
begin endSs
26
Ssend;Ssend$
S
E S
Ss
Ss
begin end
;
end $
S
X: begina: beginStack:
while doid
end
begin;
begin endSs
Mid loopAction: Match
27
Ssend;Ssend$
S
E S
Ss
Ss
end
;
end $
S
X:a:Stack:
while doid
end
begin;begin
endSs
Top of loop
28
end;Ssend$
S
E S
Ss
Ss
end
;
end $
S
X: Ssa: endStack:
while doid
end
begin;begin
endSs
Mid loopAction: 5 Ss ::= ε
29
end;Ssend$
S
E S
Ss
Ss
end
;
end $
S
X:a:Stack:
while doid
end
begin;begin
endSs
Top of loop
ε
30
;Ssend$
S
E S
Ss
Ss
end
;
end $
S
X: enda: endStack:
while doid
end
begin;begin
endSs
Mid loop
ε
Action: Match
31
;Ssend$
S
E S
Ss
Ss;
end $
S
X:a:Stack:
while doid
end
begin;begin end
Ss
Top of loop
ε
32
Ssend$
S
E S
Ss
Ss;
end $
S
X: ;a: ;Stack:
while doid
end
begin;begin end
Ss
Mid loop
ε
Action: Match
33
Ssend$
S
E S
Ss
Ss
;end $
S
X:a:Stack:
while doid
end
begin begin end
Ss
Top of loop
ε
34
end$
S
E S
Ss
Ss
;end $
S
X: Ssa: endStack:
while doid
end
begin begin end
Ss
Mid loop
ε
Action: 5 Ss ::= ε
35
end$
S
E S
Ss
Ss
;end $
S
X:a:Stack:
while doid
end
begin begin end
Ss
Top of loop
ε ε
36
$
S
E S
Ss
Ss
;end $
S
X: enda: endStack:
while doid
end
begin begin end
Ss
Mid loop
ε ε
Action: Match
37
$
S
E S
Ss
Ss
; end$
S
X:a:Stack:
while doid begin begin end
Ss
Top of loop
ε ε
38
S
E S
Ss
Ss
; end$
S
X: $a: $Stack:
while doid begin begin end
Ss
Mid loop
ε ε
Action: Match
39
S
E
ACCEPTS
Ss
Ss
; end $
S
X:a:Stack:
while doid begin begin end
Ss
Top of loop
ε ε