[Haskell-cafe] [ghc-proposals/cafe] Partially applied type families

[Richard Eisenberg]

> On May 12, 2017, at 6:46 AM, Anthony Clayden <anthony_clayden at clear.net.nz> wrote:
> 
> So please explain here in what way 
> type families are "half baked".

My interpretation of mniip’s use of this descriptor was a reference to the fact that type families aren’t just functions, don’t support `case`, can’t be partially applied, etc. Instead, we should just be able to use functions in types. :)

I agree that closed type families are bizarre and perhaps a misfeature -- though I think they are a good incremental step toward something better. What would be far better is if we could just use `case`, and then the closed type family syntax would desugar into case statements, much like how normal functions work. So 

type family F a b where
  F Int b    = b
  F a   Bool = a

(AntC’s example) would really mean

type F a b = case a of
  Int -> b
  _   -> case b of
           Bool -> a
           _    -> F a b

We understand the semantics of case expressions, so this would avoid the bizarreness of closed type families. (We would also have to eliminate non-linear patterns, replacing them with some other first-class test for equality. It’s currently unclear to me how to do this right. Section 5.13.2 of my thesis dwells on this, without much in the way of a concrete way forward.)

AntC’s proposed disequality constraints then become straightforward pattern guards.

Richard