[GHC] #10832: Generalize injective type families

[GHC]

#10832: Generalize injective type families
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        Reporter:  jstolarek         |                Owner:  jstolarek
            Type:  feature request   |               Status:  new
        Priority:  normal            |            Milestone:
       Component:  Compiler (Type    |              Version:  7.11
  checker)                           |             Keywords:  TypeFamilies,
      Resolution:                    |  InjectiveFamilies
Operating System:  Unknown/Multiple  |         Architecture:
                                     |  Unknown/Multiple
 Type of failure:  None/Unknown      |            Test Case:
      Blocked By:                    |             Blocking:
 Related Tickets:  #6018             |  Differential Rev(s):  Phab:D1287
       Wiki Page:                    |
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Comment (by AntC):

 comment:13 is asking for injectivity from result with ''either'' argument
 to the other.

 Notice the O.P. for `AddTF` only considers result & first argument `->`
 second arg.

 I see a problem. In instances

 {{{
 type family xs :++: ys = r | r xs -> ys, r ys -> xs where  -- both
 injectivities
   '[]       :++: ys = ys
   (x ': xs) :++: ys = x ': (xs :++: ys)
 }}}

 Under the injection `r ys -> xs`, I think GHC will not be able to see the
 'apartness' in the two equations. That is, it won't be able to disprove
 `ys ~ (x ': (xs :++: ys))`. Yes we know they can't unify, but GHC sees
 `:++:` as a Type Function, not a (proto-)constructor.

 Speculative remedy [https://github.com/AntC2/ghc-proposals/blob/instance-
 apartness-guards/proposals/0000-instance-apartness-guards.rst#injective-
 type-families proposed here], for the `AddTF` example.

--
Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/10832#comment:17>
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