package ParentClass;
BEGIN {
  my %constants = (
    FOO => 'foo',
    BAR => 'bar',
    BAZ => 'baz',
  );
  foreach my $name ( keys %constants ) {
    no strict 'refs';
    *{$name} = sub () { $constants{$name} };
  }
  our @EXPORT = keys %constants;
}

# -------- new file --------

package ChildClass;
use base 'ParentClass';
BEGIN {
  ParentClass->import();
}
sub doStuff {
  my ($self, @otherArguments) = @_;
  print FOO; # Yay, it works this time!
  ...
}