> There needs to be a way to write a query that runs on an abstract interface, rather than an actual table.

Proper use of SQL inverts control. Instead of parameterizing query by table, you write a query and at the actual use site you join it on the table you need by fields your query provides. VIEWs allows you to not repeat yourself too often.

Best thing is that you do not need to even mention that "abstract interface table" as a parameter at all.