Section 4.4 in Structure and Implementation of Computer Programs [1] presents an implementation of a Prolog-like logic programming language in Scheme. It is very instructive to contrast it to the meta-circular evaluator of Scheme in that same book to see the similarities and differences.

Paradigms of Artificial Programming by Norvig also contains a chapter implementing Prolog in Common Lisp. The code can be found at [2].

[1] https://mitpress.mit.edu/sicp/full-text/book/book-Z-H-29.htm...

[2] http://norvig.com/paip/prolog.lisp

you can start by looking for "warren abstract machine" (usually shortened as WAM). It's an intermediate format for compiling prolog programs (sets of Horn clauses, that is, rules). It makes every operation very explicit, including unification (to match the current goal against each rule's conclusion) and backtracking (to enumerate solutions; this involves stacks, unsurprisingly). I think most state of the art prolog implementations are then able to compile this format to native code. Of course prolog also requires that the runtime has a GC (to collect dead terms) and that it can dynamically add/remove rules, use reflection to observe the shape of a term, etc.

https://en.wikipedia.org/wiki/XSB is an implementation to which Warren contributes, with additional features such as tabling (a powerful form of memoization that avoids many infinite recursions).

You should have a look at https://mitpress.mit.edu/books/reasoned-schemer