> On 20 Dec 2018, at 01:04, Brent Meeker <[email protected]> wrote:
> 
> 
> 
> On 12/19/2018 7:27 AM, Jason Resch wrote:
>> The output of a computation is not the computation, and we make use of 
>> non-halting programs all the time.  For example, Operating Systems, Web 
>> Servers, Virtual Machines, etc.  Ideally, these programs never halt, and 
>> usually they never output anything, unless they crash.
> 
> Those are programs in the vernacular, but they are not programs in the Turing 
> sense unless you count all their inputs/outputs as part of the "program".  
> They are open systems.

Open digital system are Turing emulable. The usual CT is extensional, but it is 
also intensional. All universal machine compute all partial computable 
functions, but they emulate also all digital processes, and they can compute 
all functions *in all possible manners*

Bruno




> 
> Brent
> 
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