Make new rows dependent on previous row values in Presto - sql

Question

I have new users being added to my table each day and I want to check for new users. However, the table's data removes old rows after reaching a certain number of rows. To keep my new rows accurate, I want to calculate the new users BASED on the PREVIOUS ROWS values. So as long as I have one previous row available, my new row will always be accurate. If there is no previous row, the row should have a default value.
Date
users_Today
New_users
All_users_To_Date
Dec 6
Allie, Jon
Allie, Jon
Allie, Jon
Dec 7
Allie, Jon, Zach
Zach
Allie, Jon, Zach
Currently I have:
WITH user_log_response AS (
SELECT
CAST(JSON_PARSE(user_log) AS MAP<VARCHAR, VARCHAR>) AS user_map,
date
FROM user_log_response_table
),
names_and_dates AS (
SELECT DISTINCT
user_name AS user_name,
date
FROM user_log_response
CROSS JOIN UNNEST(user_map) AS u(user_name, user_age)
),
user_names AS (
SELECT
date,
ARRAY_JOIN(
ARRAY_AGG(
user_name
ORDER BY
user_name
),
','
) users_today,
FROM names_and_dates
GROUP BY
date
ORDER BY
date DESC
)
SELECT
date,
users_today
FROM user_names
Which results in this
Date
users_Today
Dec 6
Allie, Jon
Dec 7
Allie, Jon, Zach
If I store "all users to date" how can I calculate "new users" to equal previous row's "all users to date" minus "users today"
Also how can I calculate "all users to date" to equal previous row's "all users to date" plus current row's "new users"