[GHC] #9123: Need for higher kinded roles

[GHC]

#9123: Need for higher kinded roles
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        Reporter:  simonpj           |            Owner:
            Type:  bug               |           Status:  new
        Priority:  normal            |        Milestone:
       Component:  Compiler          |          Version:  7.8.2
      Resolution:                    |         Keywords:
Operating System:  Unknown/Multiple  |     Architecture:  Unknown/Multiple
 Type of failure:  None/Unknown      |       Difficulty:  Unknown
       Test Case:                    |       Blocked By:
        Blocking:                    |  Related Tickets:
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Comment (by goldfire):

 The question, as I see it, is this:

 If we know `(Rep m, Coercible a b)` can we derive `Coercible (s -> m (a,
 s)) (s -> m (b, s))`? We assume that the ''only'' way we can use `Rep` is
 in the following rule: `(Rep m, Coercible x y)` implies `Coercible (m x)
 (m y)`. Call that rule (*).

 Yes:

 1. Decompose the `(->)` to get that we need to show `Coercible (m (a, s))
 (m (b, s))`.

 2. Use (*) to get that we need to show `Coercible (a, s) (b, s)`.

 3. By the roles of `(,)`, this reduces to `Coercible a b`.

 4. We are done by assumption.

 What have I missed? Where did the asymmetry come into play? I'm not saying
 that the current solver does this, but it seems possible. You may also
 want to see the original post in #9117 which may be of interest. (Much of
 the ensuing commentary is not as relevant.)

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Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/9123#comment:15>
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