Some Prolog systems (like Ciao Prolog https://github.com/ciao-lang/ciao/blob/master/core/lib/forei...) implement bidirectional foreign interfaces. Once you have C bindings it is easy to write bindings from Rust, C++, or any other language (that can interoperate with C). I give here some details about Ciao because this is the system I know better but it should be similar for other popular Prolog implementations.
The tradeoffs depend on the complexity of the Prolog code and your needs for performance and features: pure LP, Prolog (search+unification+cut), garbage collection, dynamic database updates, constraint domains, etc. The Ciao Prolog engine is around 300-400KB. Adding a few libraries, compiler, etc. it goes to 2MB. Naive Prolog systems can be one order of magnitude smaller at the cost of sacrificing ISO compatibility, performance, etc. Note that "performance" can be very misleading. Some Prolog programs may run particularly fast in some Prolog system and very badly in others.
The tradeoffs depend on the complexity of the Prolog code and your needs for performance and features: pure LP, Prolog (search+unification+cut), garbage collection, dynamic database updates, constraint domains, etc. The Ciao Prolog engine is around 300-400KB. Adding a few libraries, compiler, etc. it goes to 2MB. Naive Prolog systems can be one order of magnitude smaller at the cost of sacrificing ISO compatibility, performance, etc. Note that "performance" can be very misleading. Some Prolog programs may run particularly fast in some Prolog system and very badly in others.