Transactions, references and how to enforce double entry bookkeeping? (PG) Double entry bookkeeping is 


  a set of rules for recording financial information in a financial
  accounting system in which every transaction or event changes at least
  two different nominal ledger accounts.


An account can be "debited" or "credited", and the sum of all credits must be equal to the sum of all debits.

How would you implement this in a Postgres database? Specifying the following DDL:

CREATE TABLE accounts(
    account_id serial NOT NULL PRIMARY KEY,
    account_name varchar(64) NOT NULL
);


CREATE TABLE transactions(
    transaction_id serial NOT NULL PRIMARY KEY,
    transaction_date date NOT NULL
);


CREATE TABLE transactions_details(
    id serial8 NOT NULL PRIMARY KEY,
    transaction_id integer NOT NULL 
        REFERENCES transactions (transaction_id)
        ON UPDATE CASCADE
        ON DELETE CASCADE
        DEFERRABLE INITIALLY DEFERRED,
    account_id integer NOT NULL
        REFERENCES accounts (account_id)
        ON UPDATE CASCADE
        ON DELETE RESTRICT
        NOT DEFERRABLE INITIALLY IMMEDIATE,
    amount decimal(19,6) NOT NULL,
    flag varchar(1) NOT NULL CHECK (flag IN ('C','D'))
);


Note: the transaction_details table does not specify an explicit debit/credit account, because the system should be able to debit/credit more than one account in a single transaction.

This DDL creates the following requirement: After a database transaction commits on the transactions_details table, it must debit and credit the same amount for each transaction_id, e.g:

INSERT INTO accounts VALUES (100, 'Accounts receivable');
INSERT INTO accounts VALUES (200, 'Revenue');

INSERT INTO transactions VALUES (1, CURRENT_DATE);

-- The following must succeed
BEGIN;
    INSERT INTO transactions_details VALUES (DEFAULT, 1, 100, '1000'::decimal, 'D');
    INSERT INTO transactions_details VALUES (DEFAULT, 1, 200, '1000'::decimal, 'C');
COMMIT;


-- But this must raise some error
BEGIN;
    INSERT INTO transactions_details VALUES (DEFAULT, 1, 100, '1000'::decimal, 'D');
    INSERT INTO transactions_details VALUES (DEFAULT, 1, 200, '500'::decimal, 'C');
COMMIT;


Is it possible to implement this in a PostgreSQL database? Without specifying additional tables to store trigger states.
First, this is exactly the question I had in mind when I asked Modelling constraints on subset aggregates? which is certainly the place to start.  That question is more general though than this and so my answer here will have a bit more information regarding practical approaches.

You probably do not want to do this declaratively in PostgreSQL.  The only possible declarative solutions either break 1NF or are extremely complicated and so this means doing it imperatively.

In LedgerSMB we expect to do this enforcement in two stages (both of which are strict).


All journal entries will come in via stored procedures.  These stored procedures will accept a list of line items as an array and check that the sum is equal to 0.  Our model in the db is that we have a single amount column with negative numbers being debits and positive numbers being credits (if I was starting over, I would have positive numbers as debits and negative numbers as credits because this is just a little more natural but the reasons here are obscure).  Debits and credits are merged on storage and separated on retrieval by the presentation layer.  This makes running totals a lot easier.
We will use a deferred constraint trigger which will check on commit based on the system fields on the table.  This means that the lines entered in a given transaction must balance, but we can do this beyond the lines themselves.