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LL(1) Parser
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What does LL signify ?The first L means that the scanning takes
placefrom Left to right.The second L means that the Left derivation
is
produced first.
The prime requirements are : - Stack
Parsing Table Input buffer Parsing program .
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Input buffer contains the string to be
parsed, followed by $ ,a symbol used toindicate end of the input
string. The stackindicates a sequence of grammar symbols
with $ on the bottom,indicating bottom ofthe stack. Initially,
the stack contains thestart symbol of the grammar on the top of$.
The parsing table is a 2-D array M[A,a]where A is a nonterminal,
and a is aterminal or the symbol $.
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How to control the parser?
If X=a=$ , parser halts, string accepted.
If X=a !=$ , parser pops X, and advances theinput pointer to
point to next input symbol.
If X is a non-terminal, the program consultsentry M[X,a] of the
parsing table M. Replacethe top of stack(X) with production
rulecorresponding to entry in table. If entry =
ERROR, call error recovery routine.
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Algo for Construction of predictive
parsing table :
1. For each production Aa of grammar G, dosteps 2 and 3
2. For each terminal 'a' in FIRST(a) , add Aa inM[A,a].
3. If e is in FIRST(a) , add Aa to M[A,b] foreach terminal b in
FOLLOW(A). If is inFIRST(a ) , and $ is in FOLLOW(A), then add
Aa to M[A,$]4. Make each undefined entry as ERROR, i.e.
An error entry.
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Example:
Grammar
ETE'
E'+TE' |
T FT'
T'
*FT' | F(E) | id
( stands for epsilon)
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First and Follow
Symbol FIRST FOLLOW
E (,id $,)
E +, $,)
T (,id +,$,)
T *, +,$,)
F (,id *,+,$,)
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Building the table
Id + * ( ) $
E ETE ETE
E
E+TE E E
T TFT TFT
T
T T*FT T T
F Fid F(E)
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Input=id+id*id
Stack Input buffer
$E id+id*id$
$E'T' Id+id*id$
$E'T'F Id+id*id$
$E'T'id Id+id*id$
$E'T' +id*id$$E' +id*id$
$E'T+ +id*id$
$E'T id*id$
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Stack Input Buffer
$E'T'F id*id$$E'T'id id*id$
$E'T' *id$
$E'T'F* *id$$E'T'F id$
$E'T'id id$
$E'T' $$E' $
$ Accepted
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Thus, we can easily construct an LL parsewith 1 lookahead. Since
one look ahead is
involved, we also call it an LL(1) parser.There are grammars
which may requiteLL(k) parsing.
For e.g. look at next example..
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Parse Table
a b e i t $
S Sa SiEtSS
S S
SeS
S
E EbAmbiguity
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The grammar is ambiguous and it isevident by the fact that we
have two
entries corresponding to M[S,e]containing S and SeS.
Thisambiguity can be resolved if we choose
SeS i.e associating the elses with theclosest previous then.
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Note that the ambiguity will be solved ifwe use LL(2) parser,
i.e. always see for
the two input symbols. How?
When input is e then it looks at next
input. Depending on the next input wechoose the appropriate
rule.
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LL(1) grammars have distinct properties. -No ambiguous grammar
or left recursive
grammar can be LL(1).A grammar is LL(1) if and only if whenevera
production A C | D the following
conditions hold:contd
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1)For no terminal a both C and D derivestrings beginning with
a.
Thus First(C) != First(D)
2)At most one of C or D can derive
3) If C* then D does not derive any stringbeginning with
terminal Follow(A).
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Prepared byMukesh Kumar B
04CS1013,CSE,IIT Kharagpur.
Visit:http://www.facweb.iitkgp.ernet.in/~niloy/COURSE/Autumn2006/Compiler/main.html#Lecture
http://www.facweb.iitkgp.ernet.in/~niloy/COURSE/Autumn2006/Compiler/main.htmlhttp://www.facweb.iitkgp.ernet.in/~niloy/COURSE/Autumn2006/Compiler/main.htmlhttp://www.facweb.iitkgp.ernet.in/~niloy/COURSE/Autumn2006/Compiler/main.htmlhttp://www.facweb.iitkgp.ernet.in/~niloy/COURSE/Autumn2006/Compiler/main.html
