haskellpolykinds

What is the kind of the function arrow in haskell?

Until now, i have thought that the (->) type has the kind * -> * -> *. But what confuses me is that it also works for unlifted types (e. g. Int#).

I inspected the type with ghci and got * -> * -> * like expected. This was all I could figure out but I don't understand how the arrow is kind polymorphic.

ghci> :k (->)
(->) :: * -> * -> *
ghci> :k Int#
Int# :: TYPE IntRep
ghci> :k (->) Int#
(->) Int# :: * -> *
Solution

  • Indeed the kind is polymorphic over any RuntimeRep, that’s just hidden by default. There are a few flags that enable showing the details.

    λ :set -fprint-explicit-foralls
λ :set -fprint-explicit-kinds
λ :set -fprint-explicit-runtime-reps
λ :set -XNoStarIsType
λ :kind (->)
(->) :: forall {q :: GHC.Types.RuntimeRep}
               {r :: GHC.Types.RuntimeRep}.
        TYPE q -> TYPE r -> Type