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If i have a column say column a of any given values, and i want another column column b to have a default value according to the value of column a

In another words:
if column a = 'peter' then column b default value = 'doctor'.

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This is not possible with a simple DEFAULT value, as the manual clearly states:

The value is any variable-free expression (subqueries and cross-references to other columns in the current table are not allowed).

You could use a trigger instead:

CREATE OR REPLACE FUNCTION trg_foo_b_default()
  RETURNS trigger
  LANGUAGE plpgsql AS
$func$
BEGIN
   -- For just a few constant options, CASE does the job:
   NEW.b := CASE NEW.a
               WHEN 'peter'  THEN 'doctor'
               WHEN 'weirdo' THEN 'shrink'
               WHEN 'django' THEN 'undertaker'
               ELSE NULL
            END;

   /*
   -- For more, or dynamic options, consider a lookup table:
   SELECT INTO NEW.b  t.b
   FROM   def_tbl t
   WHERE  t.a = NEW.a;
   */

   RETURN NEW;
END
$func$;


CREATE TRIGGER b_default
BEFORE INSERT ON foo
FOR EACH ROW
WHEN (NEW.b IS NULL AND NEW.a IS NOT NULL)
EXECUTE PROCEDURE trg_foo_b_default();

To make it more efficient use a WHEN clause in the trigger definition (available since Postgres 9.0): This way the trigger function is only executed, when it's actually useful. (Assuming we can let b IS NULL slide if a IS NULL.)

Works in a similar, but subtly different fashion from a DEFAULT value.
With a default value, you can explicitly insert NULL to overrule the default. That's not possible here, NULL in b is replaced with the value derived from a.


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