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I'm trying to find out if the following grammar is ambiguous or unambiguous:

stmt -> IF expr THEN stmt | matchedStmt

matchedStmt -> IF expr THEN matchedStmt ELSE stmt | other

It implements the if-then-else struct.

expr and other are considered to be terminal symbols, as we don't care about them in this question.

I've been trying to find a string that has more than one parse trees, but I can't.

Can you please help me?

Trinimon
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Sofia
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1 Answers1

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That grammar is ambiguous, although it's heading in the right direction :)

Here's an ambiguity:

IF c1 THEN IF c2 THEN s2 ELSE IF c3 THEN s3 ELSE s4

Since IF c2 THEN s2 ELSE IF c3 THEN s3 can be reduced to:

IF c2 THEN matchedStmt ELSE stmt

which is a matchedStmt. So it's ambiguous whether ELSE s4 belongs to IF c3 or IF c1.

What you need is for matchedStmt to be completely matched on both sides of the ELSE, something like this:

stmt -> matchedStmt | unmatchedStmt

matchedStmt -> IF expr THEN matchedStmt ELSE matchedStmt
            |  other

unmatchedStmt -> IF expr THEN stmt
              |  IF expr THEN matchedStmt ELSE unmatchedStmt
rici
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  • Now it's clear! I was trying to find if it is ambiguous or not by finding a string that is produced by two parse trees, as I did for the first grammar, and I couldn't. I thought this was the only way of proving that is ambiguous, but, yes, we can say that about the "ELSE s4", that it's not obvious where it matches. Thank you very very much! :) – Sofia Nov 13 '13 at 20:04