Comment by jasim

With negative/positive, the invariant would be sum(amount) = 0; with your approach, it would be sum(debit-credit)=0. Both are valid, it is just two ways of expressing the same thing.

I think it is useful to think about double-entry book-keeping in two layers. One is the base primitive of the journal - where each transaction has a set of debits and credits to different accounts, which all total to 0.

Then above that there is the chart of accounts, and how real-world transactions are modelled. For an engineer, to build the base primitive, we only need a simple schema for accounts and transactions. You can use either amount (+/-ve), or debit/credit for each line item.

Then if you're building the application layer which creates entries, like your top-up example, then you also need to know how to _structure_ those entries. If you have a transfer between two customer accounts, then you debit the one who's receiving the money (because assets are marked on the debit side) and credit the other (because liabilities are on the credit side). If you receive payment, then cash is debited (due to assets), and the income account is credited (because income balances are on the credit side).

However, all of this has nothing to do with how we structure the fundamental primitive of the journalling system. It is just a list of accounts, and then a list of transactions, where each transaction has a set of accounts that get either debited/credit, with the sum of the entire transaction coming to 0. That's it -- that constraint is all there is to double-entry book-keeping from a schema point.