Prove the halting problem is undecidable using Rice's theorem Is it possible to prove that the Halting problem is undecidable using Rice's theorem? Here's what I've tried and failed:


We want to reduce Rice's Theorem (decide if a language has the nontrivial property P) to the Halting Problem
We want to say "if the Halting Problem can be solved, then we can decide if a language as nontrivial property P"


Here's how I thought the proof might go:


Suppose we have a machine H that solves the halting problem. We want to use this machine to decide if a language has property P. 
We construct a machine that uses H to decide a language has property P. 


Example: Take P to be "language contains the string 1". 

We want to use H to decide if the language of a TM M contains the string 1, i.e that the TM halts and accepts when given input 1. 

Now, if M halts on 1, that doesn't mean it accepts 1, so we don't know if L(M) contains 1. On the other hand if M does not halt on 1, that certainly means that L(M) does not contain 1. 

And that's where I'm stuck. Is it actually possible to use Rice's theorem to prove that the halting problem is undecidable?
Your question contains a few hints at misunderstandings of the fundamentals that would take several pages to address. So let's focus on your final question:


  Is it actually possible to use Rice's theorem to prove that the halting problem is undecidable? 


No. Rice's theorem can only be used to show undecidability of index sets and the (usual) Halting problem can not be expressed as such. For details, see here and here.