I've hear many times that a major result in Recursion Theory is the equivalence of Turing and Godel's models: the functions implementable on a Turing machine are precisely the functions that can be built from the primitive recursive functions via composition and primitive recursion.
I am interested in the proof in the direction Turing $\to$ Godel. How do we take a Turing machine and come up with a recursive definition of a function that is equivalent to the language decided by the Turing machine?
An explanation or a pointer to the paper(s) that prove this result would be much appreciated. Thanks!