#!/usr/bin/perl

package Dummy;

use strict;
use warnings;

use overload '==' => \&iseq;
sub new  { return bless [ $_[1] ], $_[0];}
sub iseq { return $_[0]->[0] == $_[1]->[0] ;}

package MyTie;

use strict;
use warnings;
use Carp;

our $AUTOLOAD;

sub TIEARRAY {
  my $class = shift;
  return bless [ map { Dummy->new($_) } @_ ], $class;
}
sub FETCH     { $_[0]->[ $_[1] ]; }
sub FETCHSIZE { scalar @{$_[0]}; }
sub AUTOLOAD  { croak "Undefined method $AUTOLOAD called in " . __PACKAGE__;}

package main;

use strict;
use warnings;

use Data::Dumper;
use Devel::Peek;

tie my @arr, 'MyTie', 1,3,4;

for my $i (@arr){
  for my $j (@arr){
# uncomment this row and comment out the next one, and it works
#    if($i->iseq($j)){
    if($i == $j){
      print $i->[0] . " == " . $j->[0] . "\n";
    } else {
      print $i->[0] . " != " . $j->[0] . "\n";
    }
  }
}

exit 0;

##</code><code>##

Operation `0+': no method found, argument in overloaded package Dummy at 5perltie.pl line 42.

##</code><code>##

use overload '==' => \&iseq, '0+' => \&num;
...
sub num  { print "Someone wants me (" . $_[0]->[0] . ") in numeric context\n"; }

##</code><code>##

Someone wants me (1) in numeric context
Someone wants me (1) in numeric context
1 == 1
1 != 3
1 != 4
Someone wants me (1) in numeric context
Someone wants me (3) in numeric context
3 == 1
3 == 3
3 != 4
Someone wants me (1) in numeric context
Someone wants me (4) in numeric context
4 == 1
4 != 3
4 == 4