Infinite precision arithmetic repeatedly adds another computer word to
represent numbers that overflow with the current number of words. You were
talking about carries propagating across a word, remember? So if you add 1
to 2^32-1, you get a two word number in 64 bits instead of a one word number
in 32 bits, and the execution time is no longer linear. The number keeps
getting bigger as needed to represent the new value, adding one word of
precision as needed. That makes it recursive in the sense of precision
representation; there is no end to the number of such words that can be
added on overflow. That is what makes it recursive, and that is what makes
it increasing in time and space consumption. (01)
But an iterator, by my definition, for good practice, must not be recursive
in that it is must take a fixed time and space consumption during operation,
otherwise the time and space are not linear for each execution of the
iterator. Recursive calls to the same function results in an unlimited
expense in time and space, and therefore is not good practice for an
iterator. Math is ideal in its behavior; computers aren't. So a recursive
function is not an iterator in my sense of that word. Translate to your own
method of expressing that fact to get the point. (02)
-Rich (03)
Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com
9 4 9 \ 5 2 5 - 5 7 1 2 (04)
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Randall R
Schulz
Sent: Thursday, October 14, 2010 9:34 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] HOL decidability [Was: using
SKOSforcontrolledvalues for controlledvocabulary] (05)
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. (06)
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. (07)
Computing the successor of the following number (shown in binary): (08)
11111111111111111111111111111111111111111111111111 (09)
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. (010)
> ....
>
> -Rich (011)
Randall Schulz (012)
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