Science Forums 2

[phillip1882]

"But now you modify hp to make hp'. hp' is adjusted so that if hp would have halted, hp' doesn't; if hp would have gone on forever, hp' halts."

a bit of an inaccurate description, hp always halts, it just it returns doesn't halt. (i think i made the same mistake in my description in the other post.)
this may seem nit picky, but it's an important distinction, because, hp when run on hp' input shouldn't have a problem, as far as whether it halts.

let's say hp algorithm is this, if "if" statements - comments <1 then return doesn't halt. else "if" - comments >=1, return halt. clearly this algorithm is a bad one, but it just for demonstration.
now create h'. h' will have the following algorithm. if "if" statements -comments <1 return halt. "if" - comments >=1 go into infinite loop. what will h return when run on h'? it reads that it has two if statements, and no comments. so it would go into first if statement, return doesn't halt. clearly however h' does halt in this case. if you add two comments to h' code, then h will see that, and return halt. but clearly h' doesn't halt in this case. in short, as you said pryotex, h will always return the wrong answer when run on h'.