Re: The simple essence of Proof Theoretic Semantics

On 7/3/2026 3:08 PM, olcott wrote:
> On 7/3/2026 1:27 PM, dbush wrote:
>> On 7/3/2026 2:10 PM, olcott wrote:
>>> On 7/3/2026 12:10 PM, dbush wrote:
>>>> On 7/3/2026 12:52 PM, olcott wrote:
>>>>> On 7/3/2026 10:50 AM, dbush wrote:
>>>>>> On 7/3/2026 11:36 AM, olcott wrote:
>>>>>>> On 7/3/2026 4:22 AM, Mikko wrote:
>>>>>>>> On 02/07/2026 17:51, olcott wrote:
>>>>>>>>>
>>>>>>>>> Do you know enough about C to understand that
>>>>>>>>> dbush example was foolish nonsense when proposed
>>>>>>>>> to show the halting problem counter-example?
>>>>>>>>
>>>>>>>> It is a valid example of a C program. It was present as a part of a
>>>>>>>> claim about you, and your response was the false claim that "That
>>>>>>>> is just nonsense". Later in the discussion you offer more evidence
>>>>>>>> to support his claim.
>>>>>>>>
>>>>>>>
>>>>>>> His halt decider did not look at its input.
>>>>>>
>>>>>> Nor is it required to.  All it needs to do is map inputs to outputs.
>>>>>>
>>>>>
>>>>> So a piece of metal sitting on the ground is an automobile.
>>>>
>>>> Does algorithm H map machine description X and machine input Y to an 
>>>> output of either 0 or 1?
>>>>
>>> Ignoring the input IS NOT A MAPPING
>>>
>>
>> A mapping is nothing more than an association of inputs to outputs, so 
>> there is nothing to ignore.  What an algorithm might do to *compute* 
>> the mapping has nothing to do with the mapping.
>>
> 
> It is conventionally construed as a mapping.
> It is not even conventionally construed as a halt
> function, not even a halt function that gets the
> wrong answer.


Here's a simpler example. Consider the following mapping, with the 
domain being integers from 0 to 255:

input | output
--------------
0     | 4
1     | 4
2     | 4
3     | 4
...
253   | 4
254   | 4
255   | 4

i.e. for all inputs in the domain, output 4.

Requirement: an algorithm that computes the above mapping.

The following algorithm meets this requirement:

int foo(unsigned char x)
{
     return 4;
}