Re: Flibble’s Leap: Why Behavioral Divergence Implies a Type Distinction in the Halting Problem

On 11/05/2025 18:14, olcott wrote:

On 5/11/2025 11:54 AM, dbush wrote:

On 5/11/2025 12:49 PM, olcott wrote:

The category error is actually the fact that everyone
here expects a termination analyzer to report on behavior
other than the behavior that its input finite string
actually specifies.

>
That's because it's whether or not the algorithm described by the input halts when executed directly.
>
No one cares what "the behavior that its input finite string specifies" because that's not what we asked about.

 int sum(int x, int y) { return x + y ; }
when you ask about the sum of 5 + 7 using sum(3,2)
you are asking the wrong question.

By the same token, when asked what DDD's halting behavior is when executed and you answer with what you think it's halting behaviour is when simulated, you'd better be sure that the two answers are the same or you're answering the wrong question.

HHH reports on the behavior that DDD specifies.

What it should be reporting on is the behaviour that DDD manifests when directly executed.

sum reports on the sum that its inputs specify.

Often, yes. But it isn't hard to devise a way to break it so that it reports the wrong result. Is that the parallel with DDD that you intended to draw?
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
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