...Update: I won't. It's not needed in the solution. You should use the documented API, i.e. Parent and get_leaves.

Good luck :)

#!/usr/bin/perl --
use strict;
use warnings;
use Data::Dump qw/ dd /;

dd( deef( [ qw/ Cobra /] , [qw/ Fox /] ) );
dd( deef( [ qw/ Dog Fox Wolf /] , [qw/ Fox /] ) );


sub deef {
    my( $got, $want) = @_;
    my %have; undef @have{ @$got };
    my @add = grep { !exists $have{$_} } @$want;
    undef %have; undef @have{ @$want };
    my @del = grep { !exists $have{$_} } @$got;
    [deeef( @add )], [deeef( @del )];
}

sub deeef {
    my( @animals ) = @_;
    my %catcatdog = (
      Mammal  => {
                   Bovine => ["Cow", "Bison"],
                   Canine => ["Dog", "Fox", "Wolf"],
                   Equine => ["Horse", "Zebra", "Pony"],
                 },
      Reptile => {
                   Bird   => ["Pigeon", "Canary", "Owl"],
                   Lizard => ["Salamander", "Chameleon"],
                   Snake  => ["Python", "Cobra"],
                 },
    );
    my %dogcatcat;
    for my $cat ( keys %catcatdog ){
        for my $catcat ( keys %{ $catcatdog{ $cat } } ){
            for my $dog( @{ $catcatdog{$cat}{$catcat} } ){
                push @{ $dogcatcat{$dog} }, $catcat, $cat, ;
            }
        }
    }
    return map {; [ $_, @{ $dogcatcat{$_} } ]  } @animals;
}
__END__
(
  [["Fox", "Canine", "Mammal"]],
  [["Cobra", "Snake", "Reptile"]],
)
(
  [],
  [["Dog", "Canine", "Mammal"], ["Wolf", "Canine", "Mammal"]],
)
[download]

(_i_)

#!/usr/bin/perl --
use strict;
use warnings;
use Data::Dump qw/ dd /;
dd( Zoo->new( qw/ Cobra / ), Zoo->new( qw/ Fox / ) );
dd( Zoo->diff( Zoo->new( qw/ Cobra / ), Zoo->new( qw/ Fox / ) ) );
dd( Zoo->diff( Zoo->new( qw/ Dog Fox Wolf / ), Zoo->new( qw/ Fox / ) )
+ );

Zoo->new( 'Jabbawockeez' );


BEGIN {
    $INC{'Zoo.pm'} = __FILE__;
    package Zoo;
    my %catcatdog = (
      Mammal  => {
                   Bovine => ["Cow", "Bison"],
                   Canine => ["Dog", "Fox", "Wolf"],
                   Equine => ["Horse", "Zebra", "Pony"],
                 },
      Reptile => {
                   Bird   => ["Pigeon", "Canary", "Owl"],
                   Lizard => ["Salamander", "Chameleon"],
                   Snake  => ["Python", "Cobra"],
                 },
    );
    my %dogcatcat; _dogcatcat();
    sub _dogcatcat {
        for my $cat ( keys %catcatdog ){
            for my $catcat ( keys %{ $catcatdog{ $cat } } ){
                for my $dog( @{ $catcatdog{$cat}{$catcat} } ){
                    push @{ $dogcatcat{$dog} }, $catcat, $cat, ;
                }
            }
        }
    }
#~     (    
#~       Bison      => ["Bovine", "Mammal"],
#~       Canary     => ["Bird", "Reptile"],
#~       Chameleon  => ["Lizard", "Reptile"],
#~       Cobra      => ["Snake", "Reptile"],
#~       Cow        => ["Bovine", "Mammal"],
#~       Dog        => ["Canine", "Mammal"],
#~       Fox        => ["Canine", "Mammal"],
#~       Horse      => ["Equine", "Mammal"],
#~       Owl        => ["Bird", "Reptile"],
#~       Pigeon     => ["Bird", "Reptile"],
#~       Pony       => ["Equine", "Mammal"],
#~       Python     => ["Snake", "Reptile"],
#~       Salamander => ["Lizard", "Reptile"],
#~       Wolf       => ["Canine", "Mammal"],
#~       Zebra      => ["Equine", "Mammal"],
#~     );;
    sub new {
        my( $class, @muts ) = @_;
        for my $mut ( @muts ){
            die "what is a $mut?" if ! exists $dogcatcat{ $mut };
        }
        return bless \@muts, $class;
    }
    sub cat     { $dogcatcat{$_[1]}->[0]; }
    sub catcat  { $dogcatcat{$_[1]}->[1]; }
    sub Parent {
        my( $class , $mut ) = @_;
        return $dogcatcat{$mut}->[0];
    }
    sub get_leaves {
        my( $self ) = @_;
        return @{ $self };
    }
    
    sub diff {
        my( $class, $got, $want) = @_;
        my %have; undef @have{ @$got };
        my @add = grep { !exists $have{$_} } @$want;
        undef %have; undef @have{ @$want };
        my @del = grep { !exists $have{$_} } @$got;
#~         \@add, \@del;
        return
            [ map {; [ $_, @{ $dogcatcat{$_} } ]  } @add ],
            [ map {; [ $_, @{ $dogcatcat{$_} } ]  } @del ],
        ;;
    }
    1;
}

__END__
(bless(["Cobra"], "Zoo"), bless(["Fox"], "Zoo"))
(
  [["Fox", "Canine", "Mammal"]],
  [["Cobra", "Snake", "Reptile"]],
)
(
  [],
  [["Dog", "Canine", "Mammal"], ["Wolf", "Canine", "Mammal"]],
)
what is a Jabbawockeez? at - line 57.
[download]