Re: The simple essence of Proof Theoretic Semantics

On 04/07/2026 04:52, olcott wrote:
> On 7/3/2026 5:51 PM, André G. Isaak wrote:
>> On 2026-07-03 16:37, olcott wrote:
>>> On 7/3/2026 1:47 PM, André G. Isaak wrote:
>>>> On 2026-07-03 12:36, olcott wrote:
>>>>> On 7/3/2026 1:18 PM, dbush wrote:
>>>>
>>>>>> If an algorithm takes an input and produces an output, that is by 
>>>>>> definition a mapping. 
>>>>> That only proves that the definition is incoherent.
>>>>> The coherent way that it actually works is that
>>>>> inputs are transformed into outputs by applying
>>>>> finite string transformation rules to inputs to
>>>>> derive outputs.
>>>>
>>>> Apparently you don't understand the difference between a mapping and 
>>>> an algorithm. They are two different things.
>>>>
>>>> André
>>>>
>>>
>>> A function that ignores its input and only returns 0
>>> is not any sort of halt function.
>>
>> He was defining 'mapping', not 'halt function'.
>>
>> André

> A actual halt function must compute the mapping from
> its actual input according to the operational semantics
> of this input to the behavior that this input actually
> specifies. No function can report on the behavior of
> its caller because it has no idea who its caller is.

A function does not compute. An algrothm may compute a function.
However, no algrithm computes the halt function.

The halt functions maps a computation to a truth value
but so do many other functions, too.

-- 
Mikko