Inconsistent behavior while using nested window functions (first_value, last_value, lead,lag)

MariaDB [test]> create table t1 (a int, b int);

Query OK, 0 rows affected (0.048 sec)

MariaDB [test]> insert into t1 values (1,3), (2,2), (3,1), (1,3), (2,2), (3,1);

Query OK, 6 rows affected (0.017 sec)

Records: 6  Duplicates: 0  Warnings: 0

MariaDB [test]> select  first_value(sum(a)) over () from t1;

ERROR 1111 (HY000): Invalid use of group function

MariaDB [test]> select  first_value(sum(a) over ()) over () from t1; 

+-------------------------------------+

| first_value(sum(a) over ()) over () |

+-------------------------------------+

|                                  12 |

|                                  12 |

|                                  12 |

|                                  12 |

|                                  12 |

|                                  12 |

+-------------------------------------+

6 rows in set (0.002 sec)

MariaDB [test]> select  first_value(sum(a) over (order by null)) over () from t1;

+--------------------------------------------------+

| first_value(sum(a) over (order by null)) over () |

+--------------------------------------------------+

|                                             NULL |

|                                               12 |

|                                               12 |

|                                               12 |

|                                               12 |

|                                               12 |

+--------------------------------------------------+

6 rows in set (0.002 sec)

MariaDB [test]> select  first_value(sum(a) over (order by a)) over () from t1;

ERROR 2013 (HY000): Lost connection to MySQL server during query         ###MDEV MDEV-15180

create table t1 (a int);

insert into t1 values (1), (2), (3);

select  first_value(avg(a)) over () from t1;

MariaDB [test]> select  first_value(avg(a)) over () from t1;

ERROR 1111 (HY000): Invalid use of group function

mysql> select  first_value(avg(a)) over () from t1;

+-----------------------------+

| first_value(avg(a)) over () |

+-----------------------------+

|                      2.0000 |

+-----------------------------+

1 row in set (0.00 sec)