How to add FK on a column of composite type in PostgreSQL?

I have a table which contains a composite type and I am trying to connect a column of it to another table's PK.

CREATE TABLE aaa (col1 SERIAL PRIMARY KEY);

CREATE TYPE bbb AS (col2 INTEGER);
CREATE TABLE ccc (col3 bbb);

I tried to add FK but it was syntax error.

CREATE TABLE ccc (col3 bbb, FOREIGN KEY col3.col2 REFERENCES aaa col1);

ERROR:  syntax error at or near "col3"
LINE 1: CREATE TABLE ccc (col3 bbb, FOREIGN KEY col3.col2 REFERENCES…

This is also a syntax error.

CREATE TABLE ccc (col3 bbb, FOREIGN KEY (col3.col2) REFERENCES aaa (col1));

ERROR:  syntax error at or near "."
LINE 1: CREATE TABLE ccc (col3 bbb, FOREIGN KEY (col3.col2) REFERENC…

Also this…

CREATE TABLE ccc (col3 bbb, FOREIGN KEY ((col3).col2) REFERENCES aaa (col1));

ERROR:  syntax error at or near "("
LINE 1: CREATE TABLE ccc (col3 bbb, FOREIGN KEY ((col3).col2) REFERE…

How can I add FK to a sub-column which is a column of a composite type?
I am not trying to make multi-column FK. I wan to link a single INTEGER column to another INTEGER column.

I am using PostgreSQL 9.3.

Update

This is simplified version of my current schema. I am essentially abstracting tables into hierarchical key-value set.

``
CREATE DOMAIN "AlwaysSUID" AS BIGINT NOT NULL;
CREATE DOMAIN "OptionalSUID" AS BIGINT DEFAULT NULL;

CREATE DOMAIN "AlwaysString" AS TEXT NOT NULL;
CREATE DOMAIN "OptionalString" AS TEXT DEFAULT NULL;

-- More similar domains...

CREATE TYPE "Account" AS
(
"socialName" "AlwaysString",
"mailAddress" "AlwaysString",
"passcodeHash" "AlwaysString"
);

CREATE TYPE "Session" AS
(
"accountID" "AlwaysSUID", -- This needs to be linked to AccountMap.ID` as FK.
"chracterID" "AlwaysSUID",
"initiationTime" "AlwaysTimestamp",
"deviceNameID" "AlwaysString"
);

CREATE TABLE "Acco

This avoids the syntax error:

create type bbb as (col2 int);

create table aaa (
  col1 serial primary key
);

create table ccc (
  id serial primary key,
  col3 bbb references aaa --will reference the primary key of aaa
);

Even without the syntax error, you still get:

"Schema Creation Failed: ERROR: foreign key constraint "ccc_col3_fkey" cannot be implemented
  Detail: Key columns "col3" and "col1" are of incompatible types: bbb and integer.: "

This works though:

create type bbb as (col2 int);

create table aaa (
  col1 bbb primary key
);

create table ccc (
  id serial primary key,
  col3 bbb references aaa
);

But now you don't have a sequence. Also, you can't create sequence as...

So you are going to have to live without sequences on those tables or just use an int instead of a bbb.

StackExchange Database Administrators Q#52352, answer score: 2