Defunctionalization symbols should be given fixity declarations

[RyanGlScott]

singletons provides a promoted version of the familiar composition function:

(.) :: (b -> c) -> (a -> b) -> (a -> c)
infixr 9 (.)

The promoted version is given the name (:.) and (after #322) is given a fixity of infixr 9. However, you can't really take advantage of the fact that (:.) is infixr 9. Why? To do so, you'd need to be able to write something like this:

f :. g :. h

But those aren't fully saturated uses of (:.) (which is a type family that takes three arguments), so GHC will reject that. On the other hand, you can use defunctionalization symbols to write:

f .@#@$$$ g .@#@$$$ h

However, this will associate to the left, not the right! This is because while (:.) is given a fixity of infixr 9, none of its defunctionalization symbols are. It seems like they ought to, though, especially since that's effectively the only way to exploit this right-associativity.

[RyanGlScott]

Implementing this wouldn't be too hard. However, we would need to change significantly less code if we had #319 merged first, so this is blocked on that.

[RyanGlScott]

Never mind, this wasn't as bad as I thought it would be. See #327.

On the way, though, I discovered that there's more problems lurking beneath the surface. See #326.

[goldfirere]

Forgive me if I'm being dense, but is f .@#@$$$ g .@#@$$$ h at all useful? There's no call to Apply anywhere in there...

[RyanGlScott]

Forgive me if I'm being dense, but is f .@#@$$$ g .@#@$$$ h at all useful?

Sure. I frequently write types of the form Sigma a (f .@#@$$$ g .@#@$$$ h), whose second field would have the type Apply (f .@#@$$$ g .@#@$$$ h) x for some x :: a.

[goldfirere]

OK. Merge away, then. :)