That is like asking to draw a red line using green ink :)

The way to do it is to use the green ink to define a universe containing hardcoded red lines:

#untested, and quite silly
eval "print $_ if $i .. $j;";
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You could use the constant pragma but it is not really saving you anything.

$ seq 1 6 > lines
$ cat lines
1
2
3
4
5
6
$ perl -ne '
> use constant { I => 3, J => 5 };
> print if I .. J;' lines
3
4
5
$
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I hope this is of interest.

And can't I say to Perl to use my $i and $j as constants?

You can say anything you want :) but scalar literals are not scalar variables