I found plenty of fantastic LISP implementations which stay close to the original paper. But they are all fully-functional, practical implementations. The original paper builds from deeper fundamentals which it would be possible to write code in, albeit very impractical.
I implemented these earlier iterations, so programmers can follow the paper step-by-step in a more familiar language than 50s mathematical notation.
I am no expert in Lisp or mathematics, and intentionally went into this with no knowledge of Lisp beyond the original paper. I did not write it in the most elegant way, but in the simplest way for me to understand. So please don't take this code as a definitive statement on the language.
However, this code really helped me to understand the original paper better, and to begin using Lisp with a better grasp of the spirit of the language.
I'd welcome any thoughts from those who have more experience with Lisp or comp sci history.