After almost two years of moderate usage I encountered lack of one of useful feature of the standard grep: prepending line numbers and file names to the output. This night I decided to close this issue and implemented the absent functionality. By the way I turned on auto flushing as well. Please meet the updated version and use/test it if you want :)

# print line numbers
paragrep -n PATTERN FILENAME

# print file names
paragrep -H PATTERN FILENAME

# suppress printing file names
paragrep -h PATTERN FILENAME...
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Later, if none of us discover any bugs, I update the initial post with the recent version of the script. The script lives on github by the link https://github.com/ildar-shaimordanov/perl-utils/blob/master/perl/paragrep.