It doesn't have to be a new language. I'm sure some existing language can be used to create a DSL that serves this purpose.
It can obviously never be complete. Some parts of the spec will always have to be natural language if we want to make the best use of LLMs.
If only there was an entire class of well-studied languages which don't have any such ambiguity. They'd be perfect for programming LLMs! We could call them "programming languages" perhaps.