You have a program. It has input and output, and is either running or done. With abstraction, you can have a view of the program that is just a bidirectional data pipe. You give it information, you request information back. At some point you're done talking to it and drop the reference. The entire idea of 'halting' is gone.
No, that doesn't work, because programs in general don't give one output bit per input bit, and they can also take a very long time to come up with their answer.
E.g. input stream: stream of description of Turing machines and their input tape. Output stream: A stream of booleans that are true iff the respective machine holds.
I guess I should have addressed that idea specifically. If you transfer total control to a subprogram that directly looks for halting, you've just moved the problem, you haven't really abstracted it.
Apply indirection to anything with unspecified runtime. When you need a result, put a reasonable waiting time on it, and if it doesn't happen assume the source has died and handle it as an error code.
