Consider a very old single-core CPU that does not support hardware interrupts, and let's say I want to write a multi-tasked operating system. Using a hardware timer, one can poll an IRQ line in order to determine whether the timer has elapsed, and if so then switch threads/processes.
However, in order to be able to poll, the kernel has to have execution attention by the CPU. For a CPU that supports hardware interrupts, an ISR is called upon an interrupt and (correct me if I'm wrong) if the interrupt is by the context-switch timer, the appropriate ISR calls the kernel code that handles context switching.
If a CPU does not support hardware interrupts (again, correct me if I'm wrong), then the kernel has to repeatedly check for interrupts and the appropriate ISR is called in kernel space.
But, if a user thread is currently in execution on this hypothetical processor, the thread has to manually yield execution to the kernel for it to be able check whether the context-switch is due according to the timer through the appropriate IRQ line. This can be done by calling an appropriate kernel function.
Is there a way to implement non-cooperative multithreading on a single-core processor that only supports software interrupts? Are my thoughts correct, or am I missing something?