Why doesn't TypeSynonymInstances allow partially applied type synonyms to be used in instance heads?

Question

I know that TypeSynomymInstances only allows fully applied type synonyms to be used in instance heads, but it seems like it would be handy if I could use paritally applied t

Answer 1

Another issue with allowing partially applied type synonyms is that they would make type inference and instance selection essentially impossible. For example, suppose in the context of some program I wanted to use thingy at the type Int -> String -> Int -> (Int, String). thingy has type forall a b e. a -> b -> e a b, so we can unify a with Int and b with String, but if e is allowed to be a partially applied type synonym, we could have

e = FuncSynonym (,)

or

e = FuncSynonym' Int (,) where type FuncSynonym' x f a b = x -> f a b

or even

e = Const2 (Int -> (Int, String)) where Const2 a x y = a

The problem of type inference would become even worse than deciding equality of functions; it would require considering all functions with specified output on a particular input, or similar more complicated problems (imagine simply trying to unify a b with Int).