I assume they meant "all programs are provably halting or non-halting". Which, by the way, isn't true if you take into account the fact that a computer may int

I assume they meant "all programs are provably halting or non-halting". Which, by the way, isn't true if you take into account the fact that a computer may interface with an external, potentially infinite, memory device - such as a memory tape reader-writer, together with a human who responds to the "INSERT NEXT TAPE TO CONTINUE" messages by going out to the store and buying more tape. The whole "acktshually computer is just a finite state machine" is the most annoying "gotcha!" I've ever heard from computer scientists. There's a reason we invented virtual memory and file systems - it's so we can treat real computers like Turing Machines, and increase the memory when needed without having to re-write our whole systems every time.