I have a large table that I don't want to lock for more than couple
seconds. I want to add a nullable column to the table, the type of the
column is a domain with a check constraint.

It appears that the check constraint is being checked for each row, even
though the column can be nullable? Is there a way around this?

BEGIN
  Timing is on.

create domain test_enum numeric check (value > 0);
  CREATE DOMAIN
  Time: 1.817 ms

create table test_enum_table (id serial primary key);
  CREATE TABLE
  Time: 2.213 ms

insert into test_enum_table select * from generate_series(1, 2000000);
  INSERT 0 2000000
  Time: 4299.000 ms

alter table test_enum_table add column t test_enum;
  ALTER TABLE
  Time: 3165.869 ms -- Takes 3 seconds in this test example

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