Incremental sum ?

I have a problem that requires what I call a incremental sum, lets say
I have the folowing table (for simplicity):

table invoices_not_paid(cust_id int, invoice_id int, val numeric, paid
numeric);

with the folowing values:

cust_id   invoice_id   val    paid
----------------------------------
1             23      10.50   3.40
1             34       5.70   0.0
1             67      23.89   4.50


I want show a list like this:

cust_id   invoice_id   val    paid  incremental_not_paid_sum
-----------------------------------------------------------------
1             23      10.50   3.40     (10.50 - 3.40)        7.10
1             34       5.70   0.0    (7.10 + 5.70 - 0.0)    12.80
1             67      23.89   4.50  (12.80 + 23.89 - 4.50)  31.19

The operations betwen () are showed only to explain how the
incremental_not_paid_sum is calculated, The operation requires a
reference to a previous column or a partial sum of columns till that
moment, someone has an idea how this can be done using sql ?