Postgres 10

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CREATE TABLE a
             (col1 integer,
              col2 text);
CREATE TABLE b
             (std_id integer,
              name text);
CREATE
 OR REPLACE FUNCTION addrows
                     ()
                     RETURNS TRIGGER
AS
$$
BEGIN
  DELETE FROM b;
  
  INSERT INTO b
              (std_id,
               name)
              SELECT col1,
                     col2
                     FROM inserted;
  RETURN NULL;
END;
$$
LANGUAGE plpgsql;
CREATE TRIGGER test_one
               AFTER INSERT ON a
               REFERENCING NEW TABLE AS inserted
               FOR EACH STATEMENT
               EXECUTE PROCEDURE addrows();
INSERT INTO a
            VALUES (1,
                    'one'),
                   (2,
                    'two');
2 rows affected

SELECT *
       FROM a;


col1
col2


1
one

2
two


SELECT *
       FROM b;


std_id
name


1
one

2
two


INSERT INTO a
            VALUES (3,
                    'three'),
                   (4,
                    'four'),
                   (5,
                    'five');
3 rows affected

SELECT *
       FROM a;


col1
col2


1
one

2
two

3
three

4
four

5
five


SELECT *
       FROM b;


std_id
name


3
three

4
four

5
five