When you think about it, any dependently typed language has to have an interpreter inside it, because you can put function applications inside a type and the typechecker will probably need to evaluate the application at some point. The go-to technique is to use Normalization by Evaluation [0], where you convert the AST version of a function in the interpreted language to an actual function in the host language, and piggyback off the host language's (presumably very fast) function application.
[0]: https://en.wikipedia.org/wiki/Normalisation_by_evaluation
