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Summary

Replacing k -> Type with forall (a :: k) -> Type in a kind of a type constructor should not have any effect. The latter gives a name to the variable, but is otherwise equivalent... or so I thought.

Consider these definitions:

data B1 :: k -> Type

type family F1 :: k -> Type where
  F1 = B1

GHC happily accepts them, unifying the kinds of B1 and F1. However, if I make use of dependent quantification in B but not in F:

data B2 :: forall (a :: k) -> Type

type family F2 :: k -> Type where
  F2 = B2

... GHC gets confused:

    • Expected kind ‘k1 -> Type’,
        but ‘B2’ has kind ‘forall (a :: k0) -> Type’
    • In the type ‘B2’
      In the type family declaration for ‘F2’
   |
14 |   F2 = B2
   |        ^^

Steps to reproduce

Load this in GHCi:

{-# LANGUAGE PolyKinds, TypeFamilies, RankNTypes #-}

module T where

import Data.Kind (Type)

data B1 :: k -> Type

type family F1 :: k -> Type where
  F1 = B1

data B2 :: forall (a :: k) -> Type

type family F2 :: k -> Type where
  F2 = B2

Expected behavior

Both F1 and F2 should be accepted.

Environment

• GHC version used: HEAD