Almost ten years ago I tried to convert the package llvm-tf to use type-level naturals but it did not lead very far. What is the current state of type-level natural number programming and reasoning? I need type-level naturals for vectors of static size. The type checker must know things like: n+n ~ 2*n n*m ~ m*n (Pos - positive natural number) n::Nat, m::Pos -> n+m :: Pos n::Nat, m::Pos -> n*m :: Nat n::Pos, m::Pos -> n*m :: Pos I need to access an element from a heterogeneous list with a typenat index. That is, I need a kind of induction. I know of ghc-typelits-natnormalise, but it has some problems with inequalities that I need: "Could not deduce n~0 from the context n<=0" https://github.com/clash-lang/ghc-typelits-natnormalise/issues/33 "Could not deduce: (n0 + 1) ~ m from the context: 1 <= m" https://github.com/clash-lang/ghc-typelits-natnormalise/issues/59 So, what is the current state of the art? What libraries, what GHC extensions? Any tutorials?