[GHC] #14362: Allow: Coercing (a:~:b) to (b:~:a)

[GHC]

#14362: Allow: Coercing (a:~:b) to (b:~:a)
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        Reporter:  Iceland_jack      |                Owner:  (none)
            Type:  feature request   |               Status:  new
        Priority:  normal            |            Milestone:
       Component:  Compiler          |              Version:  8.2.1
      Resolution:                    |             Keywords:  roles
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 simonpj):

 Reminder
 {{{
 data Coercion a b where
   Coercion :: Coercible a b => Coercion a b

 data a :~: b where
   Refl :: a :~: a
 }}}
 So you want to be able to prove
 {{{
 [W] (a :~: b)      ~R#  (b :~: a)
 [W] Coercible a b  ~R#  Coercible b a
 }}}
 Once could imagine special cases in the compiler, these are really
 perfectly ordinary data type declarations.  What makes these
 representational type equalities true?

 Well, representationally speaking

 * `Refl :: (a ~# b) => a :~: b` has no represented value arguments. I
 suppose that for such types it's true that `(a :~: b) ~R#  (c :~: d)` for
 any `a, b, c, d`.  Is that right?

 Let's think about that first; I expect that once we figure this one out,
 `Coercible` will follow.

 Richard?

-- 
Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/14362#comment:2>
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