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
x+0i^y(cols key y)#x