Curry–Howard correspondence
So proofs and programs are isomorphic. We know there are programs which never halt and we know there are programs for which we can not algorithmically decide whether they halt or not. What is the equivalent thing in proofs? Are there proofs which never halt?<p>Is a proof really isomorphic with a program as written in source-code, or is it isomorphic with the EXECUTION of a program with a given input?<p>A program and its execution are not the same thing are they? But with proofs I find it hard to think about the difference between the &quot;source-code&quot; of a proof and the &quot;execution&quot; of a proof. Is there such a thing as distinction between the execution of a proof and the &quot;source-code&quot; of it?