Good idea! of course, this doesn't work if you only want to add up some of the fields in the hash. It sums up all the fields in the receiver. Perhaps this modification to abigail's code would be an improvement, since it allows you to specify the desired fields:

#!/opt/perl/bin/perl -w
use strict;
use Data::Dumper;
use Tie::Hash;
 
package Hash::Add;
 
@Hash::Add::ISA = qw /Tie::StdHash/;

sub sumFields {
 my $self = shift;
 $self->{__summedFields} = [ @_ ];
}

sub TIEHASH {
 my $classname = shift;
 my $self = $classname->SUPER::TIEHASH;
 $self->sumFields(@_);
 $self;
}
 
use overload '+' => sub { 
    my ($self, $other) = @_;
 my @keys = @{$self->{__summedFields}};
 @keys = keys(%$self) if (!@keys);
 
    foreach my $key (@keys) {
  next if $key eq '__summedFields';
        $self -> {$key} += $other -> {$key};                 
    }
};

package main;
 
my @fields = qw /foo bar/;
my $totals = tie my %totals => 'Hash::Add', @fields;
my $delta = tie my %delta => 'Tie::StdHash';
@totals{ 'a', 'z' } = ( 123, 456 );
@delta{ 'a', 'z' } = ( 789, 234 );

@totals {@fields} = (10, 20);
@delta  {@fields} =  (5,  6);

$totals += $delta;
 
print "Foo = $totals{foo}\n";
print "Bar = $totals{bar}\n";

__END__
Foo = 15
Bar = 26
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update: set fields a and z in right place