I'm generally interested in this, but (even as somebody who knows intermediate Haskell), I don't have a good intuition about the scope of dependent types: - ho

I'm generally interested in this, but (even as somebody who knows intermediate Haskell), I don't have a good intuition about the scope of dependent types: - how much of the burden of writing the proof falls on me, and how much falls to the compiler? I've seen Idris type signatures, and I didn't find them super easy to grasp. - What are the full range of things I can express? What can't I express, even with dependent types? I come from math, so I'm used to have infinite flexibility to define what goes into my set of possible values. When I first learned Haskell I was surprised that I couldn't easily define types like "this set, modulo an equivalence relation". Or something like: "Int, but only even numbers". - how huch more effort falls to me when structuring my code, in order to pass the properties or proofs through? I already run into this all the time in Haskell, with Maybes thay I _know_ to contain a value, or Lists that I know not to be empty. There is a real trade off between writing clear code, and wrapping/unwrapping values all the time everywhere. Length-indexed vectors is a great example, because it is such a non-story in math, and yet for programming I have to front-load all this complexity to express something so utterly trivial. It's part infuriating, part enlightening how surprisingly tricky seemingly small things can be.