The aj function at its heart is a bin (https://code.kx.com/q/ref/bin/) search between the two tables, on the requested columns, to find the indices of the right table to zip onto the left table.
aj[`sym`time;t;q]
becomes
t,'(`sym`time _q)(`sym`time#q)bin`sym`time#t
The rest of the aj function internals are there to handle edge cases, handling missing columns and options for filling nulls.
A lot of the joins can be distilled to the core operators/functions in a similar manner. For example the plus-join is
A lot of the joins can be distilled to the core operators/functions in a similar manner. For example the plus-join is