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Re: [ontolog-forum] HOL decidability [Was: using SKOS forcontrolledvalue

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Randall R Schulz <rschulz@xxxxxxxxx>
Date: Thu, 14 Oct 2010 21:34:11 -0700
Message-id: <201010142134.11802.rschulz@xxxxxxxxx>
On Thursday October 14 2010, Rich Cooper wrote:
> There is a version of Lisp which incorporates infinite precision
> arithmetic. You might find an iterator of the kind you are looking
> for there.    (01)

That is a complete nonsequitur. My point is that your criterion about 
the absence of an underlying iterative process for something to be 
iterative cannot be met. Switching to infinite-precision arithmetic 
does not make that go away, it just makes it unbounded.    (02)

Computing the successor of the following number (shown in binary):    (03)

 11111111111111111111111111111111111111111111111111    (04)

on a contemporary computer that uses binary representation of integers 
will require 60 iterations of its carry algorithm. So the INC 
instruction (as well as ADD, MUL, DIV and all the other arithmetic 
operations defined by that processor) of necessity invoke underlying 
iterative processes. So by your criterion, it is impossible to realize 
an iteration on such a processor.    (05)

> ....
> -Rich    (06)

Randall Schulz    (07)

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