How to create aggregate function, like sum, with an implicit DISTINCT?
Is it possible to create an aggregate function (SUM_DISTINCT), that returns the same result as as SUM(DISTINCT foo), so SUM_DISTINCT(foo) = SUM(DISTINCT foo)?


Yes, it is possible — you need a User-defined Aggregate, such as this:

create or replace function f_sum_distinct (numeric[], numeric) returns numeric[]
    language sql as $$
select $1||$2;
$$;

create or replace function f_sum_distinct_final (numeric[]) returns numeric 
    language sql as $$
select sum(v) from (select distinct unnest($1) v) z;
$$;

create aggregate sum_distinct(numeric)
( sfunc     = f_sum_distinct
 ,stype     = numeric[]
 ,finalfunc = f_sum_distinct_final
);

with w(v) as (select 2 union all select 2 union all select 3)
select sum(v) "Plain SUM", sum(distinct v) "SUM(DISTINCT)", sum_distinct(v) "SUM_DISTINCT" from w;

/*
|Plain SUM|SUM(DISTINCT)|SUM_DISTINCT|
|--------:|------------:|-----------:|
|        7|            5|           5|
*/


dbfiddle here

Note though (thanks @Erwin), that performance is going to be very substantially worse than the built-in aggregates. If this matters you will have to consider writing the helper functions in C, which is much more of an undertaking.