> "ideal programs" that halt when any program input to them halt Nit, but this can certainly exist. "Accept program as input, run input program" is one such p

> "ideal programs" that halt when any program input to them halt Nit, but this can certainly exist. "Accept program as input, run input program" is one such program. You can always (eventually) halt and say "this halted" for any program that halts. The hard part is distinguishing "this will never halt" from "this has not halted yet", and that will always be impossible for some inputs.