Data families vs Injective type families

Question

Now that we have injective type families, is there any remaining use case for using data families over type families?

Looking at past StackOverflow questions about d

Answer 1

The answer by Reid Barton explains the distinction between my two examples perfectly. It has reminded me of something I read in Richard Eisenberg's thesis about adding dependent types to Haskell and I thought that since the heart of this question is injectivity and generativity, it would be worth mentioning how DependentHaskell will deal with this (when it eventually gets implemented, and if the quantifiers proposed now are the ones eventually implemented).

What follows is based on pages 56 and 57 (4.3.4 Matchability) of the aforementioned thesis:

Definition (Generativity). If f and g are generative, then f a ~ g b implies f ~ g

Definition (Injectivity). If f is injective, then f a ~ f b implies a ~ b

Definition (Matchability). A function f is matchable iff it is generative and injective

In Haskell as we know it now (8.0.1) the matchable (type-level) functions consist exactly of newtype, data, and data family type constructors. In the future, under DependentHaskell, one of the new quantifiers we will get will be '-> and this will be used to denote matchable functions. In other words, there will be a way to inform the compiler a type-level function is generative (which currently can only be done by making sure that function is a type constructor).