$str = "aBcD12ef7812g";
print is_alphabetical($str);

sub is_alphabetical {
    (my $str = lc(shift)) =~ s/([^a-z])//g;
    my @c = split //, $str;
    $c[$_] ge $c[$_ - 1] or return 0 for 1 .. $#c;
    return 1;
}