Please, can someone explain how is it posible for ALTER TABLE to add a primary key column to a table without some intruction that would make it a real PK (NOT NULL and UNIQUE).

prueba=> CREATE TABLE nopk (
prueba(> textito varchar
prueba(> );
CREATE TABLE
prueba=> INSERT INTO nopk VALUES ('algo de texto');
INSERT 0 1
prueba=> INSERT INTO nopk VALUES ('otro texto');
INSERT 0 1
prueba=> ALTER TABLE nopk ADD COLUMN id INT PRIMARY KEY;
NOTICE: ALTER TABLE / ADD PRIMARY KEY creará el índice implícito «nopk_pkey» para la tabla «nopk»
ALTER TABLE
prueba=> \d nopk
             Tabla «martin.nopk»
 Columna |       Tipo        | Modificadores
---------+-------------------+---------------
 textito | character varying |
 id      | integer           | not null
Índices:
    «nopk_pkey» PRIMARY KEY, btree (id)

prueba=> SELECT * FROM nopk WHERE id IS NULL;
    textito    | id
---------------+----
 algo de texto |
 otro texto    |
(2 filas)


So id is a pk with NULL values, which isn't right.

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