Where can I see an example of an actual prompt that is produced?
Per query, the LMQL runtime calls the underlying LM several times, to execute the complete specified (multi-part) query program.
It does not only translate to only one LM prompt, but rather a sequence of prompts, where during generation additional constraining of the LM is applied, to ensure the LM behaves according to the provided template. That's how it support control-flow and external function calls during generation, it actually executes the queries with a proper runtime and only uses LLMs on the backend.