Let’s make that specification Turing complete while at it.
Jokes aside, IMO it will be a good natural progression. Specify the problem statement in LLM specification, generate the code in Go/Rust whatever is the language of your choice and review the generated code to make sure it adheres to the architecture/design principles that you have set.
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.