Richard wrote and the asshole (PO) snipped
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Right. but some infinite structures might actually have meaning. The
fact that Prolog uses certain limited method to figure out meaning
doesn't mean that other methods can't find the meaning.
Just like:
Fact(n) := (N == 1) ? 1 : N*Fact(n-1);
if naively expanded has an infinite expansion.
But, based on mathematical knowledge, and can actually be proven from
the definition, something like Fact(n+1)/fact(n), even for an unknown n,
can be reduced without the need to actually expend infinite operations.
Note, this is actual shown in your case of H(H^,H^). Yes, if H doesn't
abort its simulation, then for THAT H^, we have that H^(H^) is
non-halting, but so is H(H^,H^), and thus THAT H / H^ pair fails to be a
counter example
When you program H to abort its simulation of H^ at some point, and
build your H^ on that H, then H(H^,H^), will return the non-halting
answer, and H^(H^) when PROPERLY run or simulated halts, because H has
the same "cut off" logic at the factorial above.
The naive expansion thinks it is infinite, but the correct expansion
sees the cut off and sees that it is actually finite.
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A good symbolic manipulation system or a theorem prover with appropriate
axioms and rules of inference could surely handle forms such as
Fact(n+1)/fact(n) without breathing hard. It is only you, an ignorant
fool, who seems to think that the unthinking infinite unrolling of a
form must occur. Only you would think that a solver system would
completely unroll a form before analyzing it and applying
transformations to it.
Son, it don't work that way (unless you are defining and making a mess
trying to write the system yourself). Systems usually have rules that
make small incremental transformations and usually search breadth first
with perhaps a limited amount of depth first interludes. If they don't
use a breadth first strategy, they will not be able to claim the
completeness property. (See resolution theorem prover literature for
some explanation. You wont understand it but you can cite as if you did!)
Richard was trying to explain this to you in the snipped portion I
recited just above. Question for Peter holding his pecker: How do you
always and I mean always manage to delete the part of a message you
respond too that addresses the point you now try to make?
A typically subsequence you might see in the trace: would include in
order but not necessarily consecutively:
Fact(n+1)/Fact(n)
(n+1)*Fact(n)/Fact(n)
(n+1)
Some interspersed terms such as Fact(n+1)/(n*Fact(n-1)) would be found
too. In some circumstances, these other terms might be helpful. A
theorem prover or manipulator does all of this, breadth first, hoping to
blindly stumble on a solution. You can provide heuristics that might
speed up the process but no advice short of an oracle will get you even
one more result. (Another manifestation of HP.) It's the slow grinding
through the possibilities that guarantees that if a result can be found,
it will be found. And all the theory that you don't understand says
that's the best you can do.
Ben and I disagree on reasons for your type of total dishonesty. He
thinks that you are so self deluded that you actual believe what you are
saying; that you are so self deluded that the dishonest utterances are
just your subconscious protecting your already damaged ego. To that, I
say phooey; you are just a long term troll who lies a lot about math,
about your history and health, and about your accomplishments.
I don't believe that you will read this before you start to respond but
that's okay. Understanding is not required. Neither is respect in
either direction.
--
Jeff Barnett