Correct. There are awful tricks to write [1] dependent Haskell but even then it isn't powerful enough and has a significantly worse user experience then a proper dependently typed proof checker (as bad as the UX is on those!).

That said there are other languages such as Agda, Idris, and Rocq that would be fantastic replacements to Lean, especially if you care about staying constructive.

1. https://homepages.inf.ed.ac.uk/slindley/papers/hasochism.pdf

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ux266478 an hour ago | parent [-]

I mentioned in another comment, but that worse user experience is also going to exist with Idris. It's not a theorem prover, you can just use it as one.

	▲	solomonb 21 minutes ago \| parent [-]
		Idris has pi and sigma types, dependent pattern matching, view patterns, totality checking, proof search, interactive case splitting, etc, etc. It is orders of magnitude better then Haskell where the best you can do is hacky bullshit with singletons, GADTs, and type families.