Postgres 12

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Help with an interesting Postgres question: Why isn't an Index Only Scan used on a partition accessed via the parent table?.

SELECT           now()
UNION ALL SELECT transaction_timestamp()
UNION ALL SELECT current_timestamp;

now

2023-02-23 16:13:07.582346+00

2023-02-23 16:13:07.582346+00

2023-02-23 16:13:07.582346+00

SELECT 3

SELECT           timestamptz 'now'
UNION ALL SELECT timestamptz 'now '
UNION ALL SELECT timestamptz 'now()'
UNION ALL SELECT timestamptz 'now[]'
UNION ALL SELECT timestamptz 'now{}'
UNION ALL SELECT timestamptz 'now}{])))}}{{[[(()'
UNION ALL SELECT timestamptz 'now }{       ]) ) )} } {{[    [(()'
UNION ALL SELECT timestamptz ' }]) now {[( ';

timestamptz

2023-02-23 16:13:07.583133+00

2023-02-23 16:13:07.583133+00

2023-02-23 16:13:07.583133+00

2023-02-23 16:13:07.583133+00

2023-02-23 16:13:07.583133+00

2023-02-23 16:13:07.583133+00

2023-02-23 16:13:07.583133+00

2023-02-23 16:13:07.583133+00

SELECT 8

-- but:
SELECT timestamptz 'now1';

ERROR:  invalid input syntax for type timestamp with time zone: "now1"
LINE 2: SELECT timestamptz 'now1';
                           ^