"Imagine a world in which logic, programming, and mathematics are unified, in which every proof corresponds to a program, every program to a mapping, every mapping to a proof!"
The thing I never understood about statements of this sort is that in my understanding of model theory, Godel's theorem and so-forth, a proof is a rare thing. Most of the true statements in a given model don't have proofs. Any consistent proof system admits an uncountable sets of independent theorems and so-forth.
The thing I never understood about statements of this sort is that in my understanding of model theory, Godel's theorem and so-forth, a proof is a rare thing. Most of the true statements in a given model don't have proofs. Any consistent proof system admits an uncountable sets of independent theorems and so-forth.