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Groups > comp.theory > #49731 > unrolled thread

On recursion and infinite recursion (reprise #3)

Started byMr Flibble <flibble@reddwarf.jmc>
First post2022-05-05 17:50 +0100
Last post2022-05-06 16:39 +0300
Articles 20 on this page of 67 — 7 participants

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  On recursion and infinite recursion (reprise #3) Mr Flibble <flibble@reddwarf.jmc> - 2022-05-05 17:50 +0100
    Re: On recursion and infinite recursion (reprise #3) olcott <polcott2@gmail.com> - 2022-05-05 13:58 -0500
      Re: On recursion and infinite recursion (reprise #3) Ben <ben.usenet@bsb.me.uk> - 2022-05-05 20:56 +0100
        Re: On recursion and infinite recursion (reprise #3) olcott <polcott2@gmail.com> - 2022-05-05 17:15 -0500
          Re: On recursion and infinite recursion (reprise #3) Ben <ben.usenet@bsb.me.uk> - 2022-05-06 02:43 +0100
            Re: On recursion and infinite recursion (reprise #3) olcott <polcott2@gmail.com> - 2022-05-05 20:59 -0500
              Re: On recursion and infinite recursion (reprise #3) Ben <ben.usenet@bsb.me.uk> - 2022-05-06 04:08 +0100
    Re: On recursion and infinite recursion (reprise #3) Ben <ben.usenet@bsb.me.uk> - 2022-05-05 20:51 +0100
      Re: On recursion and infinite recursion (reprise #3) Mr Flibble <flibble@reddwarf.jmc> - 2022-05-05 20:52 +0100
        Re: On recursion and infinite recursion (reprise #3) Ben <ben.usenet@bsb.me.uk> - 2022-05-05 21:15 +0100
          Re: On recursion and infinite recursion (reprise #3) Mr Flibble <flibble@reddwarf.jmc> - 2022-05-05 21:16 +0100
        Re: On recursion and infinite recursion (reprise #3) olcott <polcott2@gmail.com> - 2022-05-05 16:35 -0500
      Re: On recursion and infinite recursion (reprise #3) olcott <polcott2@gmail.com> - 2022-05-05 16:37 -0500
        Re: On recursion and infinite recursion (reprise #3) Ben <ben.usenet@bsb.me.uk> - 2022-05-06 02:38 +0100
          Re: On recursion and infinite recursion (reprise #3) olcott <polcott2@gmail.com> - 2022-05-05 20:42 -0500
            Re: On recursion and infinite recursion (reprise #3) Ben <ben.usenet@bsb.me.uk> - 2022-05-06 03:59 +0100
    Re: On recursion and infinite recursion (reprise #3) Richard Damon <Richard@Damon-Family.org> - 2022-05-05 22:33 -0400
      Re: On recursion and infinite recursion (reprise #3) Mr Flibble <flibble@reddwarf.jmc> - 2022-05-06 15:02 +0100
        Re: On recursion and infinite recursion (reprise #3) Python <python@example.invalid> - 2022-05-06 16:18 +0200
          Re: On recursion and infinite recursion (reprise #3) olcott <polcott2@gmail.com> - 2022-05-06 11:55 -0500
        Re: On recursion and infinite recursion (reprise #3) Mikko <mikko.levanto@iki.fi> - 2022-05-07 12:52 +0300
          Re: On recursion and infinite recursion (reprise #3) Mr Flibble <flibble@reddwarf.jmc> - 2022-05-07 13:42 +0100
            Re: On recursion and infinite recursion (reprise #3) Mikko <mikko.levanto@iki.fi> - 2022-05-07 16:59 +0300
              Re: On recursion and infinite recursion (reprise #3) Mr Flibble <flibble@reddwarf.jmc> - 2022-05-07 15:06 +0100
                Re: On recursion and infinite recursion (reprise #3) Mikko <mikko.levanto@iki.fi> - 2022-05-07 17:16 +0300
                  Re: On recursion and infinite recursion (reprise #3) Mr Flibble <flibble@reddwarf.jmc> - 2022-05-07 15:20 +0100
                    Re: On recursion and infinite recursion (reprise #3) Mikko <mikko.levanto@iki.fi> - 2022-05-07 18:13 +0300
                      Re: On recursion and infinite recursion (reprise #3) Mr Flibble <flibble@reddwarf.jmc> - 2022-05-07 16:19 +0100
                        Re: On recursion and infinite recursion (reprise #3) olcott <polcott2@gmail.com> - 2022-05-07 11:03 -0500
                        Re: On recursion and infinite recursion (reprise #3) Ben <ben.usenet@bsb.me.uk> - 2022-05-07 23:41 +0100
                          Re: On recursion and infinite recursion (reprise #3) Mr Flibble <flibble@reddwarf.jmc> - 2022-05-07 23:43 +0100
                            Re: On recursion and infinite recursion (reprise #3) Richard Damon <Richard@Damon-Family.org> - 2022-05-07 19:59 -0400
                              Re: On recursion and infinite recursion (reprise #3) Mr Flibble <flibble@reddwarf.jmc> - 2022-05-08 01:01 +0100
                                Re: On recursion and infinite recursion (reprise #3) Richard Damon <Richard@Damon-Family.org> - 2022-05-07 20:18 -0400
                                  Re: On recursion and infinite recursion (reprise #3) Mr Flibble <flibble@reddwarf.jmc> - 2022-05-08 01:55 +0100
                        Re: On recursion and infinite recursion (reprise #3) Mikko <mikko.levanto@iki.fi> - 2022-05-08 11:31 +0300
                          Re: On recursion and infinite recursion (reprise #3) Mr Flibble <flibble@reddwarf.jmc> - 2022-05-08 09:49 +0100
                            Re: On recursion and infinite recursion (reprise #3) Mikko <mikko.levanto@iki.fi> - 2022-05-08 13:00 +0300
                              Re: On recursion and infinite recursion (reprise #3) Mr Flibble <flibble@reddwarf.jmc> - 2022-05-08 12:57 +0100
                            Re: On recursion and infinite recursion (reprise #3) Richard Damon <Richard@Damon-Family.org> - 2022-05-08 07:45 -0400
                              Re: On recursion and infinite recursion (reprise #3) Mr Flibble <flibble@reddwarf.jmc> - 2022-05-08 13:02 +0100
                                Re: On recursion and infinite recursion (reprise #3) Richard Damon <Richard@Damon-Family.org> - 2022-05-08 08:31 -0400
                                  Re: On recursion and infinite recursion (reprise #3) Mr Flibble <flibble@reddwarf.jmc> - 2022-05-08 13:39 +0100
                                    Re: On recursion and infinite recursion (reprise #3) Richard Damon <Richard@Damon-Family.org> - 2022-05-08 14:10 -0400
                                      Re: On recursion and infinite recursion (reprise #3) Mr Flibble <flibble@reddwarf.jmc> - 2022-05-08 20:06 +0100
                                        Re: On recursion and infinite recursion (reprise #3) Richard Damon <Richard@Damon-Family.org> - 2022-05-08 15:39 -0400
                                          Re: On recursion and infinite recursion (reprise #3) Mr Flibble <flibble@reddwarf.jmc> - 2022-05-08 21:14 +0100
                                            Re: On recursion and infinite recursion (reprise #3) Richard Damon <Richard@Damon-Family.org> - 2022-05-08 17:40 -0400
                                              Re: On recursion and infinite recursion (reprise #3) Mr Flibble <flibble@reddwarf.jmc> - 2022-05-08 23:04 +0100
                                                Re: On recursion and infinite recursion (reprise #3) Ben <ben.usenet@bsb.me.uk> - 2022-05-09 00:26 +0100
                                                Re: On recursion and infinite recursion (reprise #3) Richard Damon <Richard@Damon-Family.org> - 2022-05-08 19:40 -0400
                                                Re: On recursion and infinite recursion (reprise #3) olcott <NoOne@NoWhere.com> - 2022-05-09 10:55 -0500
                                                  Re: On recursion and infinite recursion (reprise #3) Richard Damon <Richard@Damon-Family.org> - 2022-05-09 20:13 -0400
                                    Re: On recursion and infinite recursion (reprise #3) olcott <NoOne@NoWhere.com> - 2022-05-09 10:51 -0500
                                      Re: On recursion and infinite recursion (reprise #3) Mr Flibble <flibble@reddwarf.jmc> - 2022-05-09 18:31 +0100
                                        Re: On recursion and infinite recursion (reprise #3) olcott <NoOne@NoWhere.com> - 2022-05-09 12:36 -0500
                                          Re: On recursion and infinite recursion (reprise #3) Richard Damon <Richard@Damon-Family.org> - 2022-05-09 20:15 -0400
                                      Re: On recursion and infinite recursion (reprise #3) Richard Damon <Richard@Damon-Family.org> - 2022-05-09 20:14 -0400
                            Re: On recursion and infinite recursion (reprise #3) olcott <NoOne@NoWhere.com> - 2022-05-09 10:49 -0500
                              Re: On recursion and infinite recursion (reprise #3) Mr Flibble <flibble@reddwarf.jmc> - 2022-05-09 18:31 +0100
                                Re: On recursion and infinite recursion (reprise #3) olcott <NoOne@NoWhere.com> - 2022-05-09 12:37 -0500
                          Re: On recursion and infinite recursion (reprise #3) olcott <NoOne@NoWhere.com> - 2022-05-09 10:47 -0500
                            Re: On recursion and infinite recursion (reprise #3) Mikko <mikko.levanto@iki.fi> - 2022-05-09 19:33 +0300
                              Re: On recursion and infinite recursion (reprise #3) olcott <NoOne@NoWhere.com> - 2022-05-09 11:36 -0500
                                Re: On recursion and infinite recursion (reprise #3) Richard Damon <Richard@Damon-Family.org> - 2022-05-09 20:17 -0400
                    Re: On recursion and infinite recursion (reprise #3) olcott <polcott2@gmail.com> - 2022-05-07 11:06 -0500
    Re: On recursion and infinite recursion (reprise #3) Mikko <mikko.levanto@iki.fi> - 2022-05-06 16:39 +0300

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#49931

FromMikko <mikko.levanto@iki.fi>
Date2022-05-07 12:52 +0300
Message-ID<t55fhq$u5e$1@dont-email.me>
In reply to#49846
On 2022-05-06 14:02:53 +0000, Mr Flibble said:

> The decider could never be compiled and run in the first place due to
> the category error in the definition of the proof.

An error in the definition of the proof does not prevent compilation
and execution of the program.

Mikko

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#49934

FromMr Flibble <flibble@reddwarf.jmc>
Date2022-05-07 13:42 +0100
Message-ID<20220507134250.00007acc@reddwarf.jmc>
In reply to#49931
On Sat, 7 May 2022 12:52:58 +0300
Mikko <mikko.levanto@iki.fi> wrote:

> On 2022-05-06 14:02:53 +0000, Mr Flibble said:
> 
> > The decider could never be compiled and run in the first place due
> > to the category error in the definition of the proof.  
> 
> An error in the definition of the proof does not prevent compilation
> and execution of the program.

In this case the error in the definition of the proof does prevent
compilation unless the decider is made part of the program that is
being decided in which case we get a function call-like infinite
recursion instead (as described by Pete Olcott) and we are attempting
(and failing) to decide if a procedure halts rather than if a program
halts.

/Flibble

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#49935

FromMikko <mikko.levanto@iki.fi>
Date2022-05-07 16:59 +0300
Message-ID<t55u0r$7lf$1@dont-email.me>
In reply to#49934
On 2022-05-07 12:42:50 +0000, Mr Flibble said:

> On Sat, 7 May 2022 12:52:58 +0300
> Mikko <mikko.levanto@iki.fi> wrote:
> 
>> On 2022-05-06 14:02:53 +0000, Mr Flibble said:
>> 
>>> The decider could never be compiled and run in the first place due
>>> to the category error in the definition of the proof.
>> 
>> An error in the definition of the proof does not prevent compilation
>> and execution of the program.
> 
> In this case the error in the definition of the proof

No part of the proof is identified as errorneous, so the rest
is irrelevant. Anyway,

> does prevent compilation unless

There is no option here, so the "unless" is void.

> the decider is made part of the program that is being decided

The decider is made a part of the program discussed in the proof.

> in which case we get a function call-like infinite recursion
> instead

We get or we don't get, depending on how the halt decider candidate
attempts to decide.

> (as described by Pete Olcott) and we are attempting (and failing)
> to decide if a procedure halts rather than if a program halts.

In any case, the decider candidate fails to give the correct answer,
and therefore is not a halt decider. Note that this is correctly
inferred in the proof. Therefore either the conclusion of the proof
is correct or you are wrong.

Mikko

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#49936

FromMr Flibble <flibble@reddwarf.jmc>
Date2022-05-07 15:06 +0100
Message-ID<20220507150612.00003fab@reddwarf.jmc>
In reply to#49935
On Sat, 7 May 2022 16:59:55 +0300
Mikko <mikko.levanto@iki.fi> wrote:

> On 2022-05-07 12:42:50 +0000, Mr Flibble said:
> 
> > On Sat, 7 May 2022 12:52:58 +0300
> > Mikko <mikko.levanto@iki.fi> wrote:
> >   
> >> On 2022-05-06 14:02:53 +0000, Mr Flibble said:
> >>   
> >>> The decider could never be compiled and run in the first place due
> >>> to the category error in the definition of the proof.  
> >> 
> >> An error in the definition of the proof does not prevent
> >> compilation and execution of the program.  
> > 
> > In this case the error in the definition of the proof  
> 
> No part of the proof is identified as errorneous, so the rest
> is irrelevant. Anyway,
> 
> > does prevent compilation unless  
> 
> There is no option here, so the "unless" is void.
> 
> > the decider is made part of the program that is being decided  
> 
> The decider is made a part of the program discussed in the proof.
> 
> > in which case we get a function call-like infinite recursion
> > instead  
> 
> We get or we don't get, depending on how the halt decider candidate
> attempts to decide.
> 
> > (as described by Pete Olcott) and we are attempting (and failing)
> > to decide if a procedure halts rather than if a program halts.  
> 
> In any case, the decider candidate fails to give the correct answer,
> and therefore is not a halt decider. Note that this is correctly
> inferred in the proof. Therefore either the conclusion of the proof
> is correct or you are wrong.

No answer is ever given due to the infinite recursion.

/Flibble

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#49937

FromMikko <mikko.levanto@iki.fi>
Date2022-05-07 17:16 +0300
Message-ID<t55uvv$fpf$1@dont-email.me>
In reply to#49936
On 2022-05-07 14:06:12 +0000, Mr Flibble said:

> On Sat, 7 May 2022 16:59:55 +0300
> Mikko <mikko.levanto@iki.fi> wrote:
> 
>> On 2022-05-07 12:42:50 +0000, Mr Flibble said:
>> 
>>> On Sat, 7 May 2022 12:52:58 +0300
>>> Mikko <mikko.levanto@iki.fi> wrote:
>>> 
>>>> On 2022-05-06 14:02:53 +0000, Mr Flibble said:
>>>> 
>>>>> The decider could never be compiled and run in the first place due
>>>>> to the category error in the definition of the proof.
>>>> 
>>>> An error in the definition of the proof does not prevent
>>>> compilation and execution of the program.
>>> 
>>> In this case the error in the definition of the proof
>> 
>> No part of the proof is identified as errorneous, so the rest
>> is irrelevant. Anyway,
>> 
>>> does prevent compilation unless
>> 
>> There is no option here, so the "unless" is void.
>> 
>>> the decider is made part of the program that is being decided
>> 
>> The decider is made a part of the program discussed in the proof.
>> 
>>> in which case we get a function call-like infinite recursion
>>> instead
>> 
>> We get or we don't get, depending on how the halt decider candidate
>> attempts to decide.
>> 
>>> (as described by Pete Olcott) and we are attempting (and failing)
>>> to decide if a procedure halts rather than if a program halts.
>> 
>> In any case, the decider candidate fails to give the correct answer,
>> and therefore is not a halt decider. Note that this is correctly
>> inferred in the proof. Therefore either the conclusion of the proof
>> is correct or you are wrong.
> 
> No answer is ever given due to the infinite recursion.

True about some candidates, false about others. For example, a
candidate that always says "no" is not infinitely recursive but
is wrong in the particular case discussed in the proof. But anyway,
you have confirmed the conclusion of the proof.

Mikko

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#49938

FromMr Flibble <flibble@reddwarf.jmc>
Date2022-05-07 15:20 +0100
Message-ID<20220507152017.00000990@reddwarf.jmc>
In reply to#49937
On Sat, 7 May 2022 17:16:31 +0300
Mikko <mikko.levanto@iki.fi> wrote:

> On 2022-05-07 14:06:12 +0000, Mr Flibble said:
> 
> > On Sat, 7 May 2022 16:59:55 +0300
> > Mikko <mikko.levanto@iki.fi> wrote:
> >   
> >> On 2022-05-07 12:42:50 +0000, Mr Flibble said:
> >>   
> >>> On Sat, 7 May 2022 12:52:58 +0300
> >>> Mikko <mikko.levanto@iki.fi> wrote:
> >>>   
> >>>> On 2022-05-06 14:02:53 +0000, Mr Flibble said:
> >>>>   
> >>>>> The decider could never be compiled and run in the first place
> >>>>> due to the category error in the definition of the proof.  
> >>>> 
> >>>> An error in the definition of the proof does not prevent
> >>>> compilation and execution of the program.  
> >>> 
> >>> In this case the error in the definition of the proof  
> >> 
> >> No part of the proof is identified as errorneous, so the rest
> >> is irrelevant. Anyway,
> >>   
> >>> does prevent compilation unless  
> >> 
> >> There is no option here, so the "unless" is void.
> >>   
> >>> the decider is made part of the program that is being decided  
> >> 
> >> The decider is made a part of the program discussed in the proof.
> >>   
> >>> in which case we get a function call-like infinite recursion
> >>> instead  
> >> 
> >> We get or we don't get, depending on how the halt decider candidate
> >> attempts to decide.
> >>   
> >>> (as described by Pete Olcott) and we are attempting (and failing)
> >>> to decide if a procedure halts rather than if a program halts.  
> >> 
> >> In any case, the decider candidate fails to give the correct
> >> answer, and therefore is not a halt decider. Note that this is
> >> correctly inferred in the proof. Therefore either the conclusion
> >> of the proof is correct or you are wrong.  
> > 
> > No answer is ever given due to the infinite recursion.  
> 
> True about some candidates, false about others. For example, a
> candidate that always says "no" is not infinitely recursive but
> is wrong in the particular case discussed in the proof. But anyway,
> you have confirmed the conclusion of the proof.

False. The proof is not cognisant of the presence of the infinite
recursion.  The decider can never return an answer of halts/doesn't
halt due to the infinite recursion.

/Flibble

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#49944

FromMikko <mikko.levanto@iki.fi>
Date2022-05-07 18:13 +0300
Message-ID<t562a4$9ao$1@dont-email.me>
In reply to#49938
On 2022-05-07 14:20:17 +0000, Mr Flibble said:

> On Sat, 7 May 2022 17:16:31 +0300
> Mikko <mikko.levanto@iki.fi> wrote:
> 
>> On 2022-05-07 14:06:12 +0000, Mr Flibble said:
>> 
>>> On Sat, 7 May 2022 16:59:55 +0300
>>> Mikko <mikko.levanto@iki.fi> wrote:
>>> 
>>>> On 2022-05-07 12:42:50 +0000, Mr Flibble said:
>>>> 
>>>>> On Sat, 7 May 2022 12:52:58 +0300
>>>>> Mikko <mikko.levanto@iki.fi> wrote:
>>>>> 
>>>>>> On 2022-05-06 14:02:53 +0000, Mr Flibble said:
>>>>>> 
>>>>>>> The decider could never be compiled and run in the first place
>>>>>>> due to the category error in the definition of the proof.
>>>>>> 
>>>>>> An error in the definition of the proof does not prevent
>>>>>> compilation and execution of the program.
>>>>> 
>>>>> In this case the error in the definition of the proof
>>>> 
>>>> No part of the proof is identified as errorneous, so the rest
>>>> is irrelevant. Anyway,
>>>> 
>>>>> does prevent compilation unless
>>>> 
>>>> There is no option here, so the "unless" is void.
>>>> 
>>>>> the decider is made part of the program that is being decided
>>>> 
>>>> The decider is made a part of the program discussed in the proof.
>>>> 
>>>>> in which case we get a function call-like infinite recursion
>>>>> instead
>>>> 
>>>> We get or we don't get, depending on how the halt decider candidate
>>>> attempts to decide.
>>>> 
>>>>> (as described by Pete Olcott) and we are attempting (and failing)
>>>>> to decide if a procedure halts rather than if a program halts.
>>>> 
>>>> In any case, the decider candidate fails to give the correct
>>>> answer, and therefore is not a halt decider. Note that this is
>>>> correctly inferred in the proof. Therefore either the conclusion
>>>> of the proof is correct or you are wrong.
>>> 
>>> No answer is ever given due to the infinite recursion.
>> 
>> True about some candidates, false about others. For example, a
>> candidate that always says "no" is not infinitely recursive but
>> is wrong in the particular case discussed in the proof. But anyway,
>> you have confirmed the conclusion of the proof.
> 
> False. The proof is not cognisant of the presence of the infinite
> recursion.  The decider can never return an answer of halts/doesn't
> halt due to the infinite recursion.

The correct term is decider candidate. It is not a decider because
the infinite recursion prevents it from halting in finite time.

You cannot call the proof incorrect merely because it agrees with you.

Mikko

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#49945

FromMr Flibble <flibble@reddwarf.jmc>
Date2022-05-07 16:19 +0100
Message-ID<20220507161901.00002e54@reddwarf.jmc>
In reply to#49944
On Sat, 7 May 2022 18:13:08 +0300
Mikko <mikko.levanto@iki.fi> wrote:

> On 2022-05-07 14:20:17 +0000, Mr Flibble said:
> 
> > On Sat, 7 May 2022 17:16:31 +0300
> > Mikko <mikko.levanto@iki.fi> wrote:
> >   
> >> On 2022-05-07 14:06:12 +0000, Mr Flibble said:
> >>   
> >>> On Sat, 7 May 2022 16:59:55 +0300
> >>> Mikko <mikko.levanto@iki.fi> wrote:
> >>>   
> >>>> On 2022-05-07 12:42:50 +0000, Mr Flibble said:
> >>>>   
> >>>>> On Sat, 7 May 2022 12:52:58 +0300
> >>>>> Mikko <mikko.levanto@iki.fi> wrote:
> >>>>>   
> >>>>>> On 2022-05-06 14:02:53 +0000, Mr Flibble said:
> >>>>>>   
> >>>>>>> The decider could never be compiled and run in the first place
> >>>>>>> due to the category error in the definition of the proof.  
> >>>>>> 
> >>>>>> An error in the definition of the proof does not prevent
> >>>>>> compilation and execution of the program.  
> >>>>> 
> >>>>> In this case the error in the definition of the proof  
> >>>> 
> >>>> No part of the proof is identified as errorneous, so the rest
> >>>> is irrelevant. Anyway,
> >>>>   
> >>>>> does prevent compilation unless  
> >>>> 
> >>>> There is no option here, so the "unless" is void.
> >>>>   
> >>>>> the decider is made part of the program that is being decided  
> >>>> 
> >>>> The decider is made a part of the program discussed in the proof.
> >>>>   
> >>>>> in which case we get a function call-like infinite recursion
> >>>>> instead  
> >>>> 
> >>>> We get or we don't get, depending on how the halt decider
> >>>> candidate attempts to decide.
> >>>>   
> >>>>> (as described by Pete Olcott) and we are attempting (and
> >>>>> failing) to decide if a procedure halts rather than if a
> >>>>> program halts.  
> >>>> 
> >>>> In any case, the decider candidate fails to give the correct
> >>>> answer, and therefore is not a halt decider. Note that this is
> >>>> correctly inferred in the proof. Therefore either the conclusion
> >>>> of the proof is correct or you are wrong.  
> >>> 
> >>> No answer is ever given due to the infinite recursion.  
> >> 
> >> True about some candidates, false about others. For example, a
> >> candidate that always says "no" is not infinitely recursive but
> >> is wrong in the particular case discussed in the proof. But anyway,
> >> you have confirmed the conclusion of the proof.  
> > 
> > False. The proof is not cognisant of the presence of the infinite
> > recursion.  The decider can never return an answer of halts/doesn't
> > halt due to the infinite recursion.  
> 
> The correct term is decider candidate. It is not a decider because
> the infinite recursion prevents it from halting in finite time.
> 
> You cannot call the proof incorrect merely because it agrees with you.

Try actually reading what Strachey wrote: a contradiction arises based
on the result of evaluating T[P] however T[P] is never evaluated due to
the infinite recursion: a fact ignored by the proof.

/Flibble

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#49947

Fromolcott <polcott2@gmail.com>
Date2022-05-07 11:03 -0500
Message-ID<t56585$uq$1@dont-email.me>
In reply to#49945
On 5/7/2022 10:19 AM, Mr Flibble wrote:
> On Sat, 7 May 2022 18:13:08 +0300
> Mikko <mikko.levanto@iki.fi> wrote:
> 
>> On 2022-05-07 14:20:17 +0000, Mr Flibble said:
>>
>>> On Sat, 7 May 2022 17:16:31 +0300
>>> Mikko <mikko.levanto@iki.fi> wrote:
>>>    
>>>> On 2022-05-07 14:06:12 +0000, Mr Flibble said:
>>>>    
>>>>> On Sat, 7 May 2022 16:59:55 +0300
>>>>> Mikko <mikko.levanto@iki.fi> wrote:
>>>>>    
>>>>>> On 2022-05-07 12:42:50 +0000, Mr Flibble said:
>>>>>>    
>>>>>>> On Sat, 7 May 2022 12:52:58 +0300
>>>>>>> Mikko <mikko.levanto@iki.fi> wrote:
>>>>>>>    
>>>>>>>> On 2022-05-06 14:02:53 +0000, Mr Flibble said:
>>>>>>>>    
>>>>>>>>> The decider could never be compiled and run in the first place
>>>>>>>>> due to the category error in the definition of the proof.
>>>>>>>>
>>>>>>>> An error in the definition of the proof does not prevent
>>>>>>>> compilation and execution of the program.
>>>>>>>
>>>>>>> In this case the error in the definition of the proof
>>>>>>
>>>>>> No part of the proof is identified as errorneous, so the rest
>>>>>> is irrelevant. Anyway,
>>>>>>    
>>>>>>> does prevent compilation unless
>>>>>>
>>>>>> There is no option here, so the "unless" is void.
>>>>>>    
>>>>>>> the decider is made part of the program that is being decided
>>>>>>
>>>>>> The decider is made a part of the program discussed in the proof.
>>>>>>    
>>>>>>> in which case we get a function call-like infinite recursion
>>>>>>> instead
>>>>>>
>>>>>> We get or we don't get, depending on how the halt decider
>>>>>> candidate attempts to decide.
>>>>>>    
>>>>>>> (as described by Pete Olcott) and we are attempting (and
>>>>>>> failing) to decide if a procedure halts rather than if a
>>>>>>> program halts.
>>>>>>
>>>>>> In any case, the decider candidate fails to give the correct
>>>>>> answer, and therefore is not a halt decider. Note that this is
>>>>>> correctly inferred in the proof. Therefore either the conclusion
>>>>>> of the proof is correct or you are wrong.
>>>>>
>>>>> No answer is ever given due to the infinite recursion.
>>>>
>>>> True about some candidates, false about others. For example, a
>>>> candidate that always says "no" is not infinitely recursive but
>>>> is wrong in the particular case discussed in the proof. But anyway,
>>>> you have confirmed the conclusion of the proof.
>>>
>>> False. The proof is not cognisant of the presence of the infinite
>>> recursion.  The decider can never return an answer of halts/doesn't
>>> halt due to the infinite recursion.
>>
>> The correct term is decider candidate. It is not a decider because
>> the infinite recursion prevents it from halting in finite time.
>>
>> You cannot call the proof incorrect merely because it agrees with you.
> 
> Try actually reading what Strachey wrote: a contradiction arises based
> on the result of evaluating T[P] however T[P] is never evaluated due to
> the infinite recursion: a fact ignored by the proof.
> 
> /Flibble
> 

Yes and a fact that is documented that I first discovered in 2016.

it looks like the original specification provided in the Linz text may 
be infinitely recursive in that each TM requires its own input.

https://www.researchgate.net/publication/307509556_Self_Modifying_Turing_Machine_SMTM_Solution_to_the_Halting_Problem_concrete_example

-- 
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

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#49979

FromBen <ben.usenet@bsb.me.uk>
Date2022-05-07 23:41 +0100
Message-ID<87pmkpvuce.fsf@bsb.me.uk>
In reply to#49945
Mr Flibble <flibble@reddwarf.jmc> writes:

> Try actually reading what Strachey wrote: a contradiction arises based
> on the result of evaluating T[P] however T[P] is never evaluated due to
> the infinite recursion: a fact ignored by the proof.

It's a central part of the argument.  If T[X] does not always return in
finite time, T fails to be a halt decider.  If the call to T[P] results
in non-terminating recursion, then T has been badly written.  There are
lots of ways the attempt to implement T can fail.

-- 
Ben.

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#49980

FromMr Flibble <flibble@reddwarf.jmc>
Date2022-05-07 23:43 +0100
Message-ID<20220507234312.00005179@reddwarf.jmc>
In reply to#49979
On Sat, 07 May 2022 23:41:37 +0100
Ben <ben.usenet@bsb.me.uk> wrote:

> Mr Flibble <flibble@reddwarf.jmc> writes:
> 
> > Try actually reading what Strachey wrote: a contradiction arises
> > based on the result of evaluating T[P] however T[P] is never
> > evaluated due to the infinite recursion: a fact ignored by the
> > proof.  
> 
> It's a central part of the argument.  If T[X] does not always return
> in finite time, T fails to be a halt decider.  If the call to T[P]
> results in non-terminating recursion, then T has been badly written.
> There are lots of ways the attempt to implement T can fail.
 
You are completely and utterly missing the point. You are completely
and utterly oblivious to the nature of the infinite recursion.

/Flibble

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#49992

FromRichard Damon <Richard@Damon-Family.org>
Date2022-05-07 19:59 -0400
Message-ID<RJDdK.19199$h6X.16518@fx04.iad>
In reply to#49980
On 5/7/22 6:43 PM, Mr Flibble wrote:
> On Sat, 07 May 2022 23:41:37 +0100
> Ben <ben.usenet@bsb.me.uk> wrote:
> 
>> Mr Flibble <flibble@reddwarf.jmc> writes:
>>
>>> Try actually reading what Strachey wrote: a contradiction arises
>>> based on the result of evaluating T[P] however T[P] is never
>>> evaluated due to the infinite recursion: a fact ignored by the
>>> proof.
>>
>> It's a central part of the argument.  If T[X] does not always return
>> in finite time, T fails to be a halt decider.  If the call to T[P]
>> results in non-terminating recursion, then T has been badly written.
>> There are lots of ways the attempt to implement T can fail.
>   
> You are completely and utterly missing the point. You are completely
> and utterly oblivious to the nature of the infinite recursion.
> 
> /Flibble
> 

No, YOU are missing that if T succombs to this sort of infinite 
recursion, then it has failed to meet the requirements of being a 
decider to answer in finite time.

Infinite Recursion can not exist in finite time, so T, if it is a 
decider, can't get infinitely recursive with ANY input, and the mere 
fact that some input can make it so, proves that the candidate T fails 
its test.

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#49993

FromMr Flibble <flibble@reddwarf.jmc>
Date2022-05-08 01:01 +0100
Message-ID<20220508010142.00007bf1@reddwarf.jmc>
In reply to#49992
On Sat, 7 May 2022 19:59:45 -0400
Richard Damon <Richard@Damon-Family.org> wrote:

> On 5/7/22 6:43 PM, Mr Flibble wrote:
> > On Sat, 07 May 2022 23:41:37 +0100
> > Ben <ben.usenet@bsb.me.uk> wrote:
> >   
> >> Mr Flibble <flibble@reddwarf.jmc> writes:
> >>  
> >>> Try actually reading what Strachey wrote: a contradiction arises
> >>> based on the result of evaluating T[P] however T[P] is never
> >>> evaluated due to the infinite recursion: a fact ignored by the
> >>> proof.  
> >>
> >> It's a central part of the argument.  If T[X] does not always
> >> return in finite time, T fails to be a halt decider.  If the call
> >> to T[P] results in non-terminating recursion, then T has been
> >> badly written. There are lots of ways the attempt to implement T
> >> can fail.  
> >   
> > You are completely and utterly missing the point. You are completely
> > and utterly oblivious to the nature of the infinite recursion.
> > 
> > /Flibble
> >   
> 
> No, YOU are missing that if T succombs to this sort of infinite 
> recursion, then it has failed to meet the requirements of being a 
> decider to answer in finite time.
> 
> Infinite Recursion can not exist in finite time, so T, if it is a 
> decider, can't get infinitely recursive with ANY input, and the mere 
> fact that some input can make it so, proves that the candidate T
> fails its test.

You also are completely and utterly missing the point. You also are
completely and utterly oblivious to the nature of the infinite
recursion.

/Flibble

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#49996

FromRichard Damon <Richard@Damon-Family.org>
Date2022-05-07 20:18 -0400
Message-ID<h%DdK.6916$t72a.5563@fx10.iad>
In reply to#49993
On 5/7/22 8:01 PM, Mr Flibble wrote:
> On Sat, 7 May 2022 19:59:45 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
> 
>> On 5/7/22 6:43 PM, Mr Flibble wrote:
>>> On Sat, 07 May 2022 23:41:37 +0100
>>> Ben <ben.usenet@bsb.me.uk> wrote:
>>>    
>>>> Mr Flibble <flibble@reddwarf.jmc> writes:
>>>>   
>>>>> Try actually reading what Strachey wrote: a contradiction arises
>>>>> based on the result of evaluating T[P] however T[P] is never
>>>>> evaluated due to the infinite recursion: a fact ignored by the
>>>>> proof.
>>>>
>>>> It's a central part of the argument.  If T[X] does not always
>>>> return in finite time, T fails to be a halt decider.  If the call
>>>> to T[P] results in non-terminating recursion, then T has been
>>>> badly written. There are lots of ways the attempt to implement T
>>>> can fail.
>>>    
>>> You are completely and utterly missing the point. You are completely
>>> and utterly oblivious to the nature of the infinite recursion.
>>>
>>> /Flibble
>>>    
>>
>> No, YOU are missing that if T succombs to this sort of infinite
>> recursion, then it has failed to meet the requirements of being a
>> decider to answer in finite time.
>>
>> Infinite Recursion can not exist in finite time, so T, if it is a
>> decider, can't get infinitely recursive with ANY input, and the mere
>> fact that some input can make it so, proves that the candidate T
>> fails its test.
> 
> You also are completely and utterly missing the point. You also are
> completely and utterly oblivious to the nature of the infinite
> recursion.
> 
> /Flibble
> 

Then try to expalin it in well defined terms.

You won't be able to in a way that makes the proof invalid.

YOU are the one that doesn't understand the "Point", the "reveled" 
"infinite recursion" is just proving that the simulation method to try 
and solve that halting problem was doomed from the start, and that such 
a "decider" can't work.

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#50001

FromMr Flibble <flibble@reddwarf.jmc>
Date2022-05-08 01:55 +0100
Message-ID<20220508015553.000016a8@reddwarf.jmc>
In reply to#49996
On Sat, 7 May 2022 20:18:21 -0400
Richard Damon <Richard@Damon-Family.org> wrote:

> On 5/7/22 8:01 PM, Mr Flibble wrote:
> > On Sat, 7 May 2022 19:59:45 -0400
> > Richard Damon <Richard@Damon-Family.org> wrote:
> >   
> >> On 5/7/22 6:43 PM, Mr Flibble wrote:  
> >>> On Sat, 07 May 2022 23:41:37 +0100
> >>> Ben <ben.usenet@bsb.me.uk> wrote:
> >>>      
> >>>> Mr Flibble <flibble@reddwarf.jmc> writes:
> >>>>     
> >>>>> Try actually reading what Strachey wrote: a contradiction arises
> >>>>> based on the result of evaluating T[P] however T[P] is never
> >>>>> evaluated due to the infinite recursion: a fact ignored by the
> >>>>> proof.  
> >>>>
> >>>> It's a central part of the argument.  If T[X] does not always
> >>>> return in finite time, T fails to be a halt decider.  If the call
> >>>> to T[P] results in non-terminating recursion, then T has been
> >>>> badly written. There are lots of ways the attempt to implement T
> >>>> can fail.  
> >>>    
> >>> You are completely and utterly missing the point. You are
> >>> completely and utterly oblivious to the nature of the infinite
> >>> recursion.
> >>>
> >>> /Flibble
> >>>      
> >>
> >> No, YOU are missing that if T succombs to this sort of infinite
> >> recursion, then it has failed to meet the requirements of being a
> >> decider to answer in finite time.
> >>
> >> Infinite Recursion can not exist in finite time, so T, if it is a
> >> decider, can't get infinitely recursive with ANY input, and the
> >> mere fact that some input can make it so, proves that the
> >> candidate T fails its test.  
> > 
> > You also are completely and utterly missing the point. You also are
> > completely and utterly oblivious to the nature of the infinite
> > recursion.
> > 
> > /Flibble
> >   
> 
> Then try to expalin it in well defined terms.
> 
> You won't be able to in a way that makes the proof invalid.
> 
> YOU are the one that doesn't understand the "Point", the "reveled" 
> "infinite recursion" is just proving that the simulation method to
> try and solve that halting problem was doomed from the start, and
> that such a "decider" can't work.

You are confusing me with Olcott: I have never mentioned the simulation
method. It is obvious that you are still missing the point.

/Flibble

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#50015

FromMikko <mikko.levanto@iki.fi>
Date2022-05-08 11:31 +0300
Message-ID<t57v4c$7do$1@dont-email.me>
In reply to#49945
On 2022-05-07 15:19:01 +0000, Mr Flibble said:

> On Sat, 7 May 2022 18:13:08 +0300
> Mikko <mikko.levanto@iki.fi> wrote:
> 
>> On 2022-05-07 14:20:17 +0000, Mr Flibble said:
>> 
>>> On Sat, 7 May 2022 17:16:31 +0300
>>> Mikko <mikko.levanto@iki.fi> wrote:
>>> 
>>>> On 2022-05-07 14:06:12 +0000, Mr Flibble said:
>>>> 
>>>>> On Sat, 7 May 2022 16:59:55 +0300
>>>>> Mikko <mikko.levanto@iki.fi> wrote:
>>>>> 
>>>>>> On 2022-05-07 12:42:50 +0000, Mr Flibble said:
>>>>>> 
>>>>>>> On Sat, 7 May 2022 12:52:58 +0300
>>>>>>> Mikko <mikko.levanto@iki.fi> wrote:
>>>>>>> 
>>>>>>>> On 2022-05-06 14:02:53 +0000, Mr Flibble said:
>>>>>>>> 
>>>>>>>>> The decider could never be compiled and run in the first place
>>>>>>>>> due to the category error in the definition of the proof.
>>>>>>>> 
>>>>>>>> An error in the definition of the proof does not prevent
>>>>>>>> compilation and execution of the program.
>>>>>>> 
>>>>>>> In this case the error in the definition of the proof
>>>>>> 
>>>>>> No part of the proof is identified as errorneous, so the rest
>>>>>> is irrelevant. Anyway,
>>>>>> 
>>>>>>> does prevent compilation unless
>>>>>> 
>>>>>> There is no option here, so the "unless" is void.
>>>>>> 
>>>>>>> the decider is made part of the program that is being decided
>>>>>> 
>>>>>> The decider is made a part of the program discussed in the proof.
>>>>>> 
>>>>>>> in which case we get a function call-like infinite recursion
>>>>>>> instead
>>>>>> 
>>>>>> We get or we don't get, depending on how the halt decider
>>>>>> candidate attempts to decide.
>>>>>> 
>>>>>>> (as described by Pete Olcott) and we are attempting (and
>>>>>>> failing) to decide if a procedure halts rather than if a
>>>>>>> program halts.
>>>>>> 
>>>>>> In any case, the decider candidate fails to give the correct
>>>>>> answer, and therefore is not a halt decider. Note that this is
>>>>>> correctly inferred in the proof. Therefore either the conclusion
>>>>>> of the proof is correct or you are wrong.
>>>>> 
>>>>> No answer is ever given due to the infinite recursion.
>>>> 
>>>> True about some candidates, false about others. For example, a
>>>> candidate that always says "no" is not infinitely recursive but
>>>> is wrong in the particular case discussed in the proof. But anyway,
>>>> you have confirmed the conclusion of the proof.
>>> 
>>> False. The proof is not cognisant of the presence of the infinite
>>> recursion.  The decider can never return an answer of halts/doesn't
>>> halt due to the infinite recursion.
>> 
>> The correct term is decider candidate. It is not a decider because
>> the infinite recursion prevents it from halting in finite time.
>> 
>> You cannot call the proof incorrect merely because it agrees with you.
> 
> Try actually reading what Strachey wrote: a contradiction arises based
> on the result of evaluating T[P] however T[P] is never evaluated due to
> the infinite recursion: a fact ignored by the proof.

If you can prove that the program does give the correct result in that
case you have proven Strachey wrong. Otherwise you haven't.

Mikko

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#50016

FromMr Flibble <flibble@reddwarf.jmc>
Date2022-05-08 09:49 +0100
Message-ID<20220508094913.00002e7c@reddwarf.jmc>
In reply to#50015
On Sun, 8 May 2022 11:31:08 +0300
Mikko <mikko.levanto@iki.fi> wrote:

> On 2022-05-07 15:19:01 +0000, Mr Flibble said:
> 
> > On Sat, 7 May 2022 18:13:08 +0300
> > Mikko <mikko.levanto@iki.fi> wrote:
> >   
> >> On 2022-05-07 14:20:17 +0000, Mr Flibble said:
> >>   
> >>> On Sat, 7 May 2022 17:16:31 +0300
> >>> Mikko <mikko.levanto@iki.fi> wrote:
> >>>   
> >>>> On 2022-05-07 14:06:12 +0000, Mr Flibble said:
> >>>>   
> >>>>> On Sat, 7 May 2022 16:59:55 +0300
> >>>>> Mikko <mikko.levanto@iki.fi> wrote:
> >>>>>   
> >>>>>> On 2022-05-07 12:42:50 +0000, Mr Flibble said:
> >>>>>>   
> >>>>>>> On Sat, 7 May 2022 12:52:58 +0300
> >>>>>>> Mikko <mikko.levanto@iki.fi> wrote:
> >>>>>>>   
> >>>>>>>> On 2022-05-06 14:02:53 +0000, Mr Flibble said:
> >>>>>>>>   
> >>>>>>>>> The decider could never be compiled and run in the first
> >>>>>>>>> place due to the category error in the definition of the
> >>>>>>>>> proof.  
> >>>>>>>> 
> >>>>>>>> An error in the definition of the proof does not prevent
> >>>>>>>> compilation and execution of the program.  
> >>>>>>> 
> >>>>>>> In this case the error in the definition of the proof  
> >>>>>> 
> >>>>>> No part of the proof is identified as errorneous, so the rest
> >>>>>> is irrelevant. Anyway,
> >>>>>>   
> >>>>>>> does prevent compilation unless  
> >>>>>> 
> >>>>>> There is no option here, so the "unless" is void.
> >>>>>>   
> >>>>>>> the decider is made part of the program that is being decided
> >>>>>>>  
> >>>>>> 
> >>>>>> The decider is made a part of the program discussed in the
> >>>>>> proof. 
> >>>>>>> in which case we get a function call-like infinite recursion
> >>>>>>> instead  
> >>>>>> 
> >>>>>> We get or we don't get, depending on how the halt decider
> >>>>>> candidate attempts to decide.
> >>>>>>   
> >>>>>>> (as described by Pete Olcott) and we are attempting (and
> >>>>>>> failing) to decide if a procedure halts rather than if a
> >>>>>>> program halts.  
> >>>>>> 
> >>>>>> In any case, the decider candidate fails to give the correct
> >>>>>> answer, and therefore is not a halt decider. Note that this is
> >>>>>> correctly inferred in the proof. Therefore either the
> >>>>>> conclusion of the proof is correct or you are wrong.  
> >>>>> 
> >>>>> No answer is ever given due to the infinite recursion.  
> >>>> 
> >>>> True about some candidates, false about others. For example, a
> >>>> candidate that always says "no" is not infinitely recursive but
> >>>> is wrong in the particular case discussed in the proof. But
> >>>> anyway, you have confirmed the conclusion of the proof.  
> >>> 
> >>> False. The proof is not cognisant of the presence of the infinite
> >>> recursion.  The decider can never return an answer of
> >>> halts/doesn't halt due to the infinite recursion.  
> >> 
> >> The correct term is decider candidate. It is not a decider because
> >> the infinite recursion prevents it from halting in finite time.
> >> 
> >> You cannot call the proof incorrect merely because it agrees with
> >> you.  
> > 
> > Try actually reading what Strachey wrote: a contradiction arises
> > based on the result of evaluating T[P] however T[P] is never
> > evaluated due to the infinite recursion: a fact ignored by the
> > proof.  
> 
> If you can prove that the program does give the correct result in that
> case you have proven Strachey wrong. Otherwise you haven't.

Strachey is wrong because he neglected to account for the infinite
recursion; this should be obvious to anyone who has actually read and
understood what Strachey wrote: it seems that you haven't.

/Flibble

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#50019

FromMikko <mikko.levanto@iki.fi>
Date2022-05-08 13:00 +0300
Message-ID<t584ba$d38$1@dont-email.me>
In reply to#50016
On 2022-05-08 08:49:13 +0000, Mr Flibble said:

> Strachey is wrong because he neglected to account for the infinite
> recursion; this should be obvious to anyone who has actually read and
> understood what Strachey wrote: it seems that you haven't.

Don't forget that Strachey is not presenting a new proof but merely
offering another point of view to an already existing proof. Therefore
it is not important that his presentantion be complete. More important
is that it covers the main idea in a way that is easy to understand.

Mikko

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#50023

FromMr Flibble <flibble@reddwarf.jmc>
Date2022-05-08 12:57 +0100
Message-ID<20220508125704.00001b8f@reddwarf.jmc>
In reply to#50019
On Sun, 8 May 2022 13:00:10 +0300
Mikko <mikko.levanto@iki.fi> wrote:

> On 2022-05-08 08:49:13 +0000, Mr Flibble said:
> 
> > Strachey is wrong because he neglected to account for the infinite
> > recursion; this should be obvious to anyone who has actually read
> > and understood what Strachey wrote: it seems that you haven't.  
> 
> Don't forget that Strachey is not presenting a new proof but merely
> offering another point of view to an already existing proof. Therefore
> it is not important that his presentantion be complete. More important
> is that it covers the main idea in a way that is easy to understand.

It is a pretty stunning omission. No, Occams's Razor suggests it is an
oversight. The proof is invalid.

/Flibble

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#50022

FromRichard Damon <Richard@Damon-Family.org>
Date2022-05-08 07:45 -0400
Message-ID<Q3OdK.15730$Bm21.3438@fx07.iad>
In reply to#50016
On 5/8/22 4:49 AM, Mr Flibble wrote:
> On Sun, 8 May 2022 11:31:08 +0300
> Mikko <mikko.levanto@iki.fi> wrote:
> 
>> On 2022-05-07 15:19:01 +0000, Mr Flibble said:
>>
>>> On Sat, 7 May 2022 18:13:08 +0300
>>> Mikko <mikko.levanto@iki.fi> wrote:
>>>    
>>>> On 2022-05-07 14:20:17 +0000, Mr Flibble said:
>>>>    
>>>>> On Sat, 7 May 2022 17:16:31 +0300
>>>>> Mikko <mikko.levanto@iki.fi> wrote:
>>>>>    
>>>>>> On 2022-05-07 14:06:12 +0000, Mr Flibble said:
>>>>>>    
>>>>>>> On Sat, 7 May 2022 16:59:55 +0300
>>>>>>> Mikko <mikko.levanto@iki.fi> wrote:
>>>>>>>    
>>>>>>>> On 2022-05-07 12:42:50 +0000, Mr Flibble said:
>>>>>>>>    
>>>>>>>>> On Sat, 7 May 2022 12:52:58 +0300
>>>>>>>>> Mikko <mikko.levanto@iki.fi> wrote:
>>>>>>>>>    
>>>>>>>>>> On 2022-05-06 14:02:53 +0000, Mr Flibble said:
>>>>>>>>>>    
>>>>>>>>>>> The decider could never be compiled and run in the first
>>>>>>>>>>> place due to the category error in the definition of the
>>>>>>>>>>> proof.
>>>>>>>>>>
>>>>>>>>>> An error in the definition of the proof does not prevent
>>>>>>>>>> compilation and execution of the program.
>>>>>>>>>
>>>>>>>>> In this case the error in the definition of the proof
>>>>>>>>
>>>>>>>> No part of the proof is identified as errorneous, so the rest
>>>>>>>> is irrelevant. Anyway,
>>>>>>>>    
>>>>>>>>> does prevent compilation unless
>>>>>>>>
>>>>>>>> There is no option here, so the "unless" is void.
>>>>>>>>    
>>>>>>>>> the decider is made part of the program that is being decided
>>>>>>>>>   
>>>>>>>>
>>>>>>>> The decider is made a part of the program discussed in the
>>>>>>>> proof.
>>>>>>>>> in which case we get a function call-like infinite recursion
>>>>>>>>> instead
>>>>>>>>
>>>>>>>> We get or we don't get, depending on how the halt decider
>>>>>>>> candidate attempts to decide.
>>>>>>>>    
>>>>>>>>> (as described by Pete Olcott) and we are attempting (and
>>>>>>>>> failing) to decide if a procedure halts rather than if a
>>>>>>>>> program halts.
>>>>>>>>
>>>>>>>> In any case, the decider candidate fails to give the correct
>>>>>>>> answer, and therefore is not a halt decider. Note that this is
>>>>>>>> correctly inferred in the proof. Therefore either the
>>>>>>>> conclusion of the proof is correct or you are wrong.
>>>>>>>
>>>>>>> No answer is ever given due to the infinite recursion.
>>>>>>
>>>>>> True about some candidates, false about others. For example, a
>>>>>> candidate that always says "no" is not infinitely recursive but
>>>>>> is wrong in the particular case discussed in the proof. But
>>>>>> anyway, you have confirmed the conclusion of the proof.
>>>>>
>>>>> False. The proof is not cognisant of the presence of the infinite
>>>>> recursion.  The decider can never return an answer of
>>>>> halts/doesn't halt due to the infinite recursion.
>>>>
>>>> The correct term is decider candidate. It is not a decider because
>>>> the infinite recursion prevents it from halting in finite time.
>>>>
>>>> You cannot call the proof incorrect merely because it agrees with
>>>> you.
>>>
>>> Try actually reading what Strachey wrote: a contradiction arises
>>> based on the result of evaluating T[P] however T[P] is never
>>> evaluated due to the infinite recursion: a fact ignored by the
>>> proof.
>>
>> If you can prove that the program does give the correct result in that
>> case you have proven Strachey wrong. Otherwise you haven't.
> 
> Strachey is wrong because he neglected to account for the infinite
> recursion; this should be obvious to anyone who has actually read and
> understood what Strachey wrote: it seems that you haven't.
> 
> /Flibble
> 

No, because if T gets stuck in an infinite recursion, it is wrong, 
because it failed to answer in finite time.

If T does answer in finite time, then there never was an infinite recursion.

All you have shown is that there exists a WRONG method to build a T that 
gets stuck, Like a T that needs to run its input to completion to answer 
about it.

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