The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
x
+16 votes
638 views
  1. Construct all the parse trees corresponding to $i + j * k$ for the grammar
       $E \rightarrow E+E$
       $E \rightarrow E*E$
       $E \rightarrow id$
  2. In this grammar, what is the precedence of the two operators $*$ and $+$?
  3. 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?
asked in Compiler Design by Veteran (59.7k points)
edited by | 638 views
0
$E\ ->\ idE'\\E'\ ->\ +EE'|*EE'|\ \epsilon$

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)?

1 Answer

+20 votes
Best answer
  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)

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

answered by Veteran (55.6k points)
edited by
+2
could you please explain, how giving priority to + over * and vice versa makes it LALR(1) ?
+1
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?
+7
LALR parsers can parse left recursive grammar. no need to remove left recursion. Had it been LL(1) then you would have to remove..
0
for given grammar how to  construct LALR(1) grammar which is unambiguous
+1

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. 

Related questions



Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true

44,305 questions
49,797 answers
164,419 comments
65,857 users