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Isn't that amazing‽ I wonder if you could guide its search with an LLM...

There is some research work I’m aware of that’s trying to make type-safe LLM generation a thing.

Is that research publically available, and where ?

Not sure if this is what you mean, but 'inductive logic programming' and more generally 'program synthesis' are fairly active research areas.

This paper appeared at PLDI '25: https://arxiv.org/abs/2504.09246