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Date: Fri, 17 May 2013 09:53:07 +0200
From: Georg Bauhaus <rm.dash-bauhaus@futureapps.de>
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Subject: Re: Seeking for papers about tagged types vs access to subprograms
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Date: 2013-05-17T09:53:05+02:00
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On 17.05.13 01:20, Peter C. Chapin wrote:
> On Fri, 17 May 2013, Niklas Holsti wrote:
>
>> A proof ...


Here is one (hint?), from 0122063821 Ch 16, 4. I am abbreviating,
as I guess you academics wouldn't want to see the level of detail
and context that the authors have added for laymen like myself:

Let

  eq : N[⊥] × N[⊥] → N[⊥]

  eq(x, y) = { 1  if x = y
             { 0  if x /= y

(eq is not monotonic, compare eq(⊥, ⊥) to eq(⊥, 0).) Let Φ[⊥] be
the strict extension of the universal function Φ(x, y) (which
takes y to be a program number), let ZERO[⊥] be the strict extension
of ZERO(x) = 0.

  HALT(x, y) = eq(0, ZERO[⊥]( Φ[⊥](x, y) ))

"If ZERO[⊥] and Φ[⊥] are partially computable, then eq certainly
is not".