That's backwards. One proof of rice's theorem relies on the fact that, if you could decide any interesting property of programs in general, then you could solve the halting problem; it doesn't follow that, if you could solve the halting problem, then you could decide any interesting property.
It happens to be true that, if you could solve the halting problem, then you could decide any interesting property of programs; but this is simply because the antecedent is false.
Being able to turn an interesting property solver into a halting problem solver is not the same thing as being able to turn a halting property solver into an interesting problem solver.
My claim or at least intent was you can solve interesting property solver like you can solve a halting problem. I.e. not in a satisfying way (no false negatives or false positives with unlimited iterations).
You can solve it to some extent (e.g. does program terminate in X steps).
But this is vacuous and unrelated to the halting problem or Rice's Thm. A program that emits "Yes" on every input will decide some property of programs with zero false negatives.
"Interesting property", as defined by Rice's Thm, is "any semantic property that is not either always true or always false for all program executions." It does not mean "interesting" as in "interesting to humans."
And I'm talking about the decider, not the program being fed as input.
I'm not a computer scientist, but I am aware Interesting doesn't mean interesting to humans.
> And I'm talking about the decider
EDIT: If by decider you mean program tested for having property P, that's a particular case and not applicable in general, ergo non-important (a program that's a NOP can be shown to leak no memory as well).
So the property P you are testing always returns true? Then it's not interesting per your definition. Leaking memory however is interesting.
No that's not what I mean by decider. The decider is the program that takes the other program as input and tells you whether that input program has the semantic property you want.
The only noninteresting semantic properties of programs that exist are "this is a program" and "this is not a program."
> A program that emits "Yes" on every input will decide some property of programs with zero false negatives.
Followed by
> any semantic property that is not either always true or always false for all program executions
So what you said is your decider always outputs true. That's not an interesting property, because it's true for all inputs.
Btw what is the point of your argument? It still doesn't refute my initial statement. If you want to determine an interesting property of program like leaks, or automatic lifetime calculation or whether output is square of input, you run into Rice Theorem, which makes the problem undecidable. In other words it's impossible to get correct yes and no algorithmically.
It happens to be true that, if you could solve the halting problem, then you could decide any interesting property of programs; but this is simply because the antecedent is false.