In APL the circle functions are a little bit special. They are used to fulfil different functions. In APL2 this is extended to handle the complex numbers. This part is regarded here in more detail and some remarks seem to be in place here to avoid uncontrolled use. A kind of system in "typing" is proposed here to stay open even to other possible enhancements to APL. It may be a hint for the possible future inclusion of the complex numbers in APL2/PC.
/lp/association-for-computing-machinery/some-reflections-on-the-circle-functions-qFjz6xWPNo