I did a close reading of the implementation in the original miniKanren paper; you can see my write-up and implementation here: https://codeberg.org/ashton314/microKanren
miniKanren paper: http://webyrd.net/scheme-2013/papers/HemannMuKanren2013.pdf
Also relevant—a practical use-case for miniKanren: https://aphyr.com/posts/354-unifying-the-technical-interview