null behavior for null people

nulls.txt

lol=# select
  null = true as null_eq_true,
  null = false as null_eq_false,
  null != true as null_neq_true,
  null != false as null_neq_false,
  null = null as null_eq_null,
  null != null as null_neq_null,
  null is true as null_is_true,
  null is false as null_is_false,
  null is null as null_is_null,
  null is not true as null_is_not_true,
  null is not false as null_is_not_false,
  null is not null as null_is_not_null,
  (null) is null as parenthetical_null_is_null,
  (not null) is null as parenthetical_not_null_is_null,
  null = ALL (ARRAY[]::int[]) as null_eq_all_empty_array,
  null = ANY (ARRAY[]::int[]) as null_eq_any_empty_array,
  null != ALL (ARRAY[]::int[]) as null_neq_all_empty_array,
  null != ANY (ARRAY[]::int[]) as null_neq_any_empty_array
  ;
-[ RECORD 1 ]------------------+--
null_eq_true                   |
null_eq_false                  |
null_neq_true                  |
null_neq_false                 |
null_eq_null                   |
null_neq_null                  |
null_is_true                   | f
null_is_false                  | f
null_is_null                   | t
null_is_not_true               | t
null_is_not_false              | t
null_is_not_null               | f
parenthetical_null_is_null     | t
parenthetical_not_null_is_null | t
null_eq_all_empty_array        | t
null_eq_any_empty_array        | f
null_neq_all_empty_array       | t
null_neq_any_empty_array       | f