Yes, you can.

package MyPackage;
$is_require = (caller(0))[7];

if($is_require) {
    print "I'm a module!\n";
} else {
    print "I'm a program!\n";
}
[download]

caller rocks.

bbfu
Seasons don't fear The Reaper.
Nor do the wind, the sun, and the rain.
We can be like they are.