min and if

[#1]

I want to sum qty for a range date . the following expression is wrong:

  sum( {<dealdate={">=min({<data_origin={'purchase'},dealdate={'<=$(=$(var_date1))>=$(=$(var_date2))'}>} dealdate)"} >} qty)

or

  sum(if(dealdate >=min({<data_origin={'purchase'},dealdate={'<=$(=$(var_date1))>=$(=$(var_date2))'}>} dealdate),qty)

First I must find a the min date for type of  'purchase'  , and sum the sales's  qty from that date.