Constructing a Quine from Kleene's Second Recursion Theorem

Kleene's second recursion theorem guarantees the existence of Quines (self-reproducing programs), and this article formalizes the practical construction of such a program in untyped lambda calculus. The author demonstrates that formalizing this classical theoretical result provides clearer insights into the theorem than traditional hand-wavy presentations, which often obscure details through tedious numerical encodings of computational structures.