GATE CSE 1996 | Question: 2.10

Question

The grammar whose productions are

• $\langle\text{stmt}\rangle \to\text{ if id then } \langle\text{stmt}\rangle$
• $\langle\text{stmt}\rangle\to\text{ if id then } \langle\text{stmt}\rangle\text{ else } \langle\text{stmt}\rangle$
• $\langle\text{stmt}\rangle \to\text{ id }:=\text{ id}$

is ambiguous because

(a) the sentence

if a then if b then c:= d

has more than two parse trees

(b) the left most and right most derivations of the sentence

if a then if b then c:= d

give rise to different parse trees

(c) the sentence 

if a then if b then c:= d else c:= f

has more than two parse trees

(d) the sentence

if a then if b then c:= d else c:= f

has two parse trees

Comments

https://gateoverflow.in/86869/gate1990-16a

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The key word more than two parse trees plays a major rule

Answer 1

(d) the sentence

•  if a then if b then c: = d else c:= f  has two parse trees as follows:

1. if a then (if b then c:= d) else c:= f
2. and if a then (if b then c:=d else c:= f)

$$\begin{align*} \pmb{\text{Ambiguity - “dangling else"}} \end{align*}$$ 

stmt -> if expr then stmt |
        if expr then stmt else stmt | other stmts

$$\mathtt{\text{if $E_1$ then  if $E_2$  then  $S_1$  else  $S_2$ }}$$

       

Comments

option C is false because it can have only parse tree ryt?

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Option C is false as statement cannot have more than 2 parse tree.

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@Deepak Poonia sir is above comment correct? what if i explicitly mention “if a then if b then c:= d else c:= f” as new grammar rule.i will have more than 2 parse tree.