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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: I have always been correct about emulating termination analyzers
 --- PROOF
Date: Tue, 22 Oct 2024 09:02:01 -0500
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On 10/22/2024 2:13 AM, Mikko wrote:
> On 2024-10-21 13:52:28 +0000, olcott said:
> 
>> On 10/21/2024 3:41 AM, Mikko wrote:
>>> On 2024-10-20 15:32:45 +0000, olcott said:
>>>
>>>> The actual barest essence for formal systems and computations
>>>> is finite string transformation rules applied to finite strings.
>>>
>>> Before you can start from that you need a formal theory that
>>> can be interpreted as a theory of finite strings.
>>
>> Not at all. The only theory needed are the operations
>> that can be performed on finite strings:
>> concatenation, substring, relational operator ...
> 
> You may try with an informal foundation but you need to make sure
> that it is sufficicently well defined and that is easier with a
> formal theory.
> 
>> The minimal complete theory that I can think of computes
>> the sum of pairs of ASCII digit strings.
> 
> That is easily extended to Peano arithmetic.
> 
> As a bottom layer you need some sort of logic. There must be unambifuous
> rules about syntax and inference.
> 

I already wrote this in C a long time ago.
It simply computes the sum the same way
that a first grader would compute the sum.

I have no idea how the first grade arithmetic
algorithm could be extended to PA.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer