Partition over a sliding date window

Hi,

I have a simple table with 3 fields: date, value and username, which can
hold identical rows.

What I am trying to do is to have for each date the count of distinct
username for the 30 previous days.

I was hoping to get this with a partition, as in the following
non-working exemple

SELECT
t.date
, t.value
, COUNT(DISTINCT t.username) OVER (PARTITION date BETWEEN t.date -
INTERVAL '29 days' and t.date)
FROM
table t
GROUP BY
date
, value
, username
;

There are many issues with this query:
- distinct not implemented for window function
- COUNT () OVER is not seen as an aggregate function, I thus need to add
username in the GROUP BY clause, which leads to wrong result
- I am not convinced that the date BETWEEN is valid either, but the
other issues prevent me to check this.

Is there a way to do what I am looking for with partitions, or should I
just give up and use 'usual' sql?

Thanks,
Guillaume