LL1 Parser What does LL signify The first
![LL(1) Parser LL(1) Parser](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-1.jpg)
![What does LL signify ? The first L means that the scanning takes place What does LL signify ? The first L means that the scanning takes place](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-2.jpg)
![n Input buffer contains the string to be parsed, followed by $ , a n Input buffer contains the string to be parsed, followed by $ , a](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-3.jpg)
![n How to control the parser? If X=a=$ , parser halts, string accepted. n n How to control the parser? If X=a=$ , parser halts, string accepted. n](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-4.jpg)
![Algo for Construction of predictive parsing table : 1. 2. 3. 4. For each Algo for Construction of predictive parsing table : 1. 2. 3. 4. For each](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-5.jpg)
![Example: Grammar E TE' E' +TE' | ë T FT' T' *FT' | ë Example: Grammar E TE' E' +TE' | ë T FT' T' *FT' | ë](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-6.jpg)
![First and Follow Symbol FIRST FOLLOW E (, id $, ) E’ +, ë First and Follow Symbol FIRST FOLLOW E (, id $, ) E’ +, ë](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-7.jpg)
![Building the table Id + * E E TE’ E’ F F id ) Building the table Id + * E E TE’ E’ F F id )](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-8.jpg)
![Input=id+id*id Stack $E $E'T'F $E'T'id $E'T' $E'T+ $E'T Input buffer id+id*id$ Id+id*id$ +id*id$ Input=id+id*id Stack $E $E'T'F $E'T'id $E'T' $E'T+ $E'T Input buffer id+id*id$ Id+id*id$ +id*id$](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-9.jpg)
![Stack $E'T'F $E'T'id $E'T'F* $E'T'F $E'T'id $E'T' $E' $ Input Buffer id*id$ id$ $ Stack $E'T'F $E'T'id $E'T'F* $E'T'F $E'T'id $E'T' $E' $ Input Buffer id*id$ id$ $](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-10.jpg)
![Thus, we can easily construct an LL parse with 1 lookahead. Since one look Thus, we can easily construct an LL parse with 1 lookahead. Since one look](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-11.jpg)
![Grammar: S i. Et. SS’ | a S’ Es | ë E b FIRST Grammar: S i. Et. SS’ | a S’ Es | ë E b FIRST](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-12.jpg)
![Parse Table a S b S a i t $ S i. Et. SS’ Parse Table a S b S a i t $ S i. Et. SS’](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-13.jpg)
![n The grammar is ambiguous and it is evident by the fact that we n The grammar is ambiguous and it is evident by the fact that we](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-14.jpg)
![Note that the ambiguity will be solved if we use LL(2) parser, i. e. Note that the ambiguity will be solved if we use LL(2) parser, i. e.](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-15.jpg)
![LL(1) grammars have distinct properties. No ambiguous grammar or left recursive grammar can be LL(1) grammars have distinct properties. No ambiguous grammar or left recursive grammar can be](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-16.jpg)
![1)For no terminal a both C and D derive strings beginning with a. Thus 1)For no terminal a both C and D derive strings beginning with a. Thus](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-17.jpg)
![Prepared by Mukesh Kumar B 04 CS 1013, CSE, IIT Kharagpur. Visit: http: //www. Prepared by Mukesh Kumar B 04 CS 1013, CSE, IIT Kharagpur. Visit: http: //www.](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-18.jpg)
- Slides: 18
![LL1 Parser LL(1) Parser](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-1.jpg)
LL(1) Parser
![What does LL signify The first L means that the scanning takes place What does LL signify ? The first L means that the scanning takes place](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-2.jpg)
What does LL signify ? The first L means that the scanning takes place from Left to right. The second L means that the Left derivation is produced first. The prime requirements are : n n Stack Parsing Table Input buffer Parsing program.
![n Input buffer contains the string to be parsed followed by a n Input buffer contains the string to be parsed, followed by $ , a](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-3.jpg)
n Input buffer contains the string to be parsed, followed by $ , a symbol used to indicate end of the input string. The stack indicates a sequence of grammar symbols with $ on the bottom, indicating bottom of the stack. Initially, the stack contains the start 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 a terminal or the symbol $.
![n How to control the parser If Xa parser halts string accepted n n How to control the parser? If X=a=$ , parser halts, string accepted. n](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-4.jpg)
n How to control the parser? If X=a=$ , parser halts, string accepted. n If X=a !=$ , parser pops X, and advances the input pointer to point to next input symbol. n If X is a non-terminal, the program consults entry M[X, a] of the parsing table M. Replace the top of stack(X) with production rule corresponding to entry in table. If entry = ERROR, call error recovery routine. n
![Algo for Construction of predictive parsing table 1 2 3 4 For each Algo for Construction of predictive parsing table : 1. 2. 3. 4. For each](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-5.jpg)
Algo for Construction of predictive parsing table : 1. 2. 3. 4. For each production A a of grammar G, do steps 2 and 3 For each terminal 'a' in FIRST(a) , add A a in M[A, a]. If e is in FIRST(a) , add A a to M[A, b] for each terminal b in FOLLOW(A). If ë is in FIRST(a ) , and $ is in FOLLOW(A), then add A a to M[A, $] Make each undefined entry as “ERROR”, i. e. An error entry.
![Example Grammar E TE E TE ë T FT T FT ë Example: Grammar E TE' E' +TE' | ë T FT' T' *FT' | ë](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-6.jpg)
Example: Grammar E TE' E' +TE' | ë T FT' T' *FT' | ë F (E) | id ( ë stands for epsilon)
![First and Follow Symbol FIRST FOLLOW E id E ë First and Follow Symbol FIRST FOLLOW E (, id $, ) E’ +, ë](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-7.jpg)
First and Follow Symbol FIRST FOLLOW E (, id $, ) E’ +, ë $, ) T (, id +, $, ) T’ *, ë +, $, ) F (, id *, +, $, )
![Building the table Id E E TE E F F id Building the table Id + * E E TE’ E’ F F id )](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-8.jpg)
Building the table Id + * E E TE’ E’ F F id ) $ E’ ë T’ ë E TE’ E’ +TE’ T T FT’ T’ ( T FT’ T’ ë T’ *FT’ F (E)
![Inputididid Stack E ETF ETid ET ET ET Input buffer ididid Ididid idid Input=id+id*id Stack $E $E'T'F $E'T'id $E'T' $E'T+ $E'T Input buffer id+id*id$ Id+id*id$ +id*id$](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-9.jpg)
Input=id+id*id Stack $E $E'T'F $E'T'id $E'T' $E'T+ $E'T Input buffer id+id*id$ Id+id*id$ +id*id$
![Stack ETF ETid ETF ETF ETid ET E Input Buffer idid id Stack $E'T'F $E'T'id $E'T'F* $E'T'F $E'T'id $E'T' $E' $ Input Buffer id*id$ id$ $](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-10.jpg)
Stack $E'T'F $E'T'id $E'T'F* $E'T'F $E'T'id $E'T' $E' $ Input Buffer id*id$ id$ $ $ Accepted
![Thus we can easily construct an LL parse with 1 lookahead Since one look Thus, we can easily construct an LL parse with 1 lookahead. Since one look](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-11.jpg)
Thus, we can easily construct an LL parse with 1 lookahead. Since one look ahead is involved, we also call it an LL(1) parser. There are grammars which may requite LL(k) parsing. For e. g. look at next example…. .
![Grammar S i Et SS a S Es ë E b FIRST Grammar: S i. Et. SS’ | a S’ Es | ë E b FIRST](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-12.jpg)
Grammar: S i. Et. SS’ | a S’ Es | ë E b FIRST FOLLOW S a, I $, ë S’ $, ë b t E Note that this is If then else statement
![Parse Table a S b S a i t S i Et SS Parse Table a S b S a i t $ S i. Et. SS’](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-13.jpg)
Parse Table a S b S a i t $ S i. Et. SS’ S ë S e. S S’ E e E b Ambiguity S ë
![n The grammar is ambiguous and it is evident by the fact that we n The grammar is ambiguous and it is evident by the fact that we](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-14.jpg)
n The grammar is ambiguous and it is evident by the fact that we have two entries corresponding to M[S’, e] containing S € and S’ e. S. This ambiguity can be resolved if we choose S’ e. S i. e associating the else’s with the closest previous “then”.
![Note that the ambiguity will be solved if we use LL2 parser i e Note that the ambiguity will be solved if we use LL(2) parser, i. e.](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-15.jpg)
Note that the ambiguity will be solved if we 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 we choose the appropriate rule.
![LL1 grammars have distinct properties No ambiguous grammar or left recursive grammar can be LL(1) grammars have distinct properties. No ambiguous grammar or left recursive grammar can be](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-16.jpg)
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 whenever a production A C | D the following conditions hold: …contd
![1For no terminal a both C and D derive strings beginning with a Thus 1)For no terminal a both C and D derive strings beginning with a. Thus](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-17.jpg)
1)For no terminal a both C and D derive strings 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 string beginning with terminal Follow(A).
![Prepared by Mukesh Kumar B 04 CS 1013 CSE IIT Kharagpur Visit http www Prepared by Mukesh Kumar B 04 CS 1013, CSE, IIT Kharagpur. Visit: http: //www.](https://slidetodoc.com/presentation_image/3d48b7ca4f077a71961fa3b4739de0af/image-18.jpg)
Prepared by Mukesh Kumar B 04 CS 1013, CSE, IIT Kharagpur. Visit: http: //www. facweb. iitkgp. ernet. in/~niloy/COURSE/ Autumn 2006/Compiler/main. html#Lecture
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