I'm not sure if I'm just reiterating kennethk's solution in the language of lexicals-in-closures rather than globals, but couldn't you do something like: 
package A;
my $self;

my $b = bless \do { my $o } => 'B';

sub foo {
     $self = shift;
     $b->bar;
}

sub caller {
     return $self;
}

package B;

sub bar {
     print "Called by ", (caller)[0]->caller, "\n";
}

package main;

my $a = bless \do { my $o } => 'A';
print "About to call via $a\n";
$a->foo;

[download]

UPDATE: On further thought, you could even confine the messiness of those caller->caller semantics to one place by defining a function like 

sub called_by {
     return ( caller 1 )[0]->caller;
}

[download]

In reply to Re^3: A caller() by any other name by JadeNB
in thread A caller() by any other name by Bloodnok

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