GATE2002-22

Question

• A. Construct all the parse trees corresponding to $i + j * k$ for the grammar
     $E \rightarrow E+E$
     $E \rightarrow E*E$
     $E \rightarrow id$
• B. In this grammar, what is the precedence of the two operators $*$ and $+$?
• C. If only one parse tree is desired for any string in the same language, what changes are to be made so that the resulting LALR(1) grammar is unambiguous?

Comments

$E\ ->\ idE'\\E'\ ->\ +EE'|*EE'|\ \epsilon$

Although I know there is no need of removing left recursion in case LALR parser but can the above be also the answer to part c)?

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Same doubt.. Somebody please answer

Answer 1

1. two parse tree for i+j*k.
2. $+$ and $*$ having same precedence..
3. to make grammar LALR compatible give priority to $+$ over $*$ or vice versa.

following grammar is LALR(1)

$E \rightarrow  E + T$
$\qquad \mid T$
$T \rightarrow T * F$
$\qquad \mid F$
$F \rightarrow id$

Comments

could you please explain, how giving priority to + over * and vice versa makes it LALR(1) ?

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why hadn't you make the grammar non-left recursive? Since priority has to be given to someone, we can give it to + or *. Is this the reason?

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LALR parsers can parse left recursive grammar. no need to remove left recursion. Had it been LL(1) then you would have to remove..

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for given grammar how to  construct LALR(1) grammar which is unambiguous

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1.how giving priority to + over * and vice versa makes it LALR(1)

 for given grammar how to  construct LALR(1) grammar

 Here there is no point removing left recursion. It is asking 

If only one parse tree is desired for any string in the same language

In this particular grammar ambiguity arises because there is no precedence or associativity defined for any non terminal. Therefore changes we will have to make is

1. Decide the precedence of + and *.

2. Decide the associativity of + and *. 

These 2 points are taken care by @Digvijay Pandey sir's answer. 

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@tusharp i understood that for making grammar unambiguous..precedence and associativity are given but how to decide which operator should be left associative which is right and same the case of precedence??

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Doesn't matter but we always go with the normal conventions that we follow.

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normal conventions like?

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Like the conventions we use in C language.