Why can't we define closed data families?

Question

All of the following work:

{-# LANGUAGE TypeFamilies #-}

type family TF a
type instance TF Int = String
type instance TF Bool = Char

data family DF a
data inst         


        

Answer 1

(Here I am only guessing, but I want to share this thought.)

Assume we can write

data family CDF a where
  CDF Int = CDFInt String
  CDF Bool = CDFBool Char
  CDF a = CDFOther Double

Now, what is the type of the value constructors induced by this definition? I would be tempted to say:

CDFInt   :: String -> CDF Int
CDFBool  :: Char   -> CDF Bool
CDFOther :: Double -> CDF a

... but the last one feels very wrong, since we would get

CDFOther @ Int :: Double -> CDF Int

which should be disallowed, since in a closed data family one would expect that a (non bottom) value of CDF Int must start with the CDFInt constructor.

Perhaps a proper type would be

CDFOther :: (a /~ Int, a /~ Bool) => Double -> CDF a

involving "inequality constraints", but this would require more typing machinery that currently available in GHC. I have no idea if type checking / inference would remain decidable with such extension.

By contrast, type families involve no value constructors, so this issue does not arise there.