I'd recommend to follow what toolic advised: close the file instead of manually nulifying $. The value of $. is reset automatically when the file is closed, so the following does what you need: 
while (<>) {
        print "$ARGV.$.:$_\n";
        close ARGV if eof;
}

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In reply to Re^5: How to reset a variable for each file inside a while( <> ) loop? by pjotrik
in thread How to reset a variable for each file inside a while( <> ) loop? by pat_mc

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