miniF2F VS FL

That said, you *can* write down a desired type and have a system write down a ton of type annotations or generate a bunch of code to prove that the type you wrote down is satisfied by your program. There's been recent work on this in deep learning for theorem proving, such as this work which uses GPT for proving theorems in Lean, a dependently type programming language and theorem prover. A better approach though would be to combine this with an actual tree search algorithm to allow a more structured search over the space of proofs, instead of trying to generate full correct proofs in one shot. Hypertree Proof Search does this, using a variant of AlphaZero to search and fine-tune the neural net. Unfortunately it hasn't been open-sourced though, and it's pretty compute intensive, so we can't use this for actual type inference yet. But yeah there's active interest in doing this kind of thing, both as a proving ground for using RL for reasoning tasks and from mathematicians for theorem-proving.

I absolutely agree with the OP. Out of the same frustration I actually ended up designing my own language and wrote a compiler for it, and now I use it for all my ML modelling. It probably only solves my particular problems and I don't expect it to be very useful for anyone else, but here goes, in case anyone is curious: https://github.com/waveworks-ai/fl