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

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Partially applied type synonyms are not allowed in Haskell at all. A partially applied synonym is effectively a function whose inputs are the un-applied types and whose output is a type. For example, here is an encoding of boolean logic:

type True x y = x
type False x y = y
type Not b x y = b y x
type And b1 b2 x y = b1 (b2 x y) y
type Or b1 b2 x y = b1 x (b2 x y)

To decide whether two partially applied type synonyms are equal, the type checker would have to decide whether functions are equal. This is a hard problem, and in general it is undecidable.

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