[GHC] #12057: TypeFamilyDependencies on Data.Type.Bool's `Not`

[GHC]

#12057: TypeFamilyDependencies on   Data.Type.Bool's `Not`
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        Reporter:  Iceland_jack      |                Owner:  Iceland_jack
            Type:  feature request   |               Status:  new
        Priority:  normal            |            Milestone:
       Component:  libraries/base    |              Version:  8.0.1
      Resolution:                    |             Keywords:  TypeFamilies,
                                     |  Injective, newcomer
Operating System:  Unknown/Multiple  |         Architecture:
                                     |  Unknown/Multiple
 Type of failure:  None/Unknown      |            Test Case:
      Blocked By:                    |             Blocking:
 Related Tickets:                    |  Differential Rev(s):
       Wiki Page:                    |
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Comment (by RyanGlScott):

 Replying to [comment:5 Iceland_jack]:
 > Interesting, thank you. Would this be covered by the weaker
 [https://ghc.haskell.org/trac/ghc/ticket/6018#comment:48
 ‘head’-injectivity]?

 In principle, it should be. Ever since we added
 [https://ghc.haskell.org/trac/ghc/ticket/10030 packageName] to the
 generics metadata, every `Rep` instance should be uniquely identified by
 the package, module, and datatype name of the underlying datatype, so I
 think `Rep`s are unique modulo type variables.

 I say "in principle" because although most `Generic` instances (and hence
 `Rep` instances) are derived, a devilish programmer //could// handwrite a
 `Rep` instance that violates injectivity. However, it's strongly
 discouraged to do such a thing (for instance, you can't handwrite
 `Generic` instances in `Safe` code), so I don't know if that would even be
 an issue in practice.

 > Is there any benefit from adding this distinguishing information/kind
 information to the metadata (since `Proxy` is polykinded)?
 >
 > I am perversely working backwards from the perspective of injectivity
 but there may be a use for `TypeRep`s in the `Rep`.

 Well, I've never found myself wanting to put `TypeRep` in `Rep` precisely
 because `Typeable`'s a whole 'nother can of worms, and it does feel
 perverse to jam more stuff into an already cluttered `Rep`. Furthermore, I
 don't think this would solve the problem of making it injective, since
 `TypeRep` values represent monomorphic types.

 > Sure, it can be kept open for more injective type families in base.

 Out of curiosity, are there any other type families in `base` besides
 `Not` that can be injective?

--
Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/12057#comment:7>
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