What is the precedence of ~, and why?

Question

The following snippet compiles:

{-# LANGUAGE TypeFamilies #-}
type family Foo a b

f :: (Foo a b ~ Int) => a -> b -> b
f = error ""

but infix type operators seem to behave differently:

{-# LANGUAGE TypeFamilies #-}
type family a \\ b

f :: (a \\ b ~ Int) => a -> b -> b
f = error ""

GHC complains that the second argument to \\ should have kind *, but b ~ Int has kind Constraint. Of course this can be fixed with parens, but I'm wondering if there's another way.

I've tried setting the precedence of my operator with the fixity declaration infixl 9 \\, but that doesn't fix the problem, indicating that the precedence of ~ is at least 9 (if I'm interpreting that correctly). I tried using the trick from this answer to make GHCi tell me the precedence of ~, but it didn't work.

Technically speaking, ~ probably isn't a type operator, it's more of a lexical construct similar to ,, but the questions still stand:

1. Why do infix and prefix operators exhibit different behavior?
2. Why does ~ bind so tightly?
3. Is there something I can do to make my own operators bind even tighter?

(Note: This question asks about the precedence of type functions, but it doesn't say anything about ~.)

Answer 1

~ isn't an operator, it's a keyword, like module or case, so I think you could only alter the precedence using parentheses.

See more here: https://wiki.haskell.org/Keywords#.7E