[GHC] #12708: RFC: Representation polymorphic Num

[GHC]

#12708: RFC: Representation polymorphic Num
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        Reporter:  Iceland_jack      |                Owner:
            Type:  feature request   |               Status:  new
        Priority:  normal            |            Milestone:
       Component:  Core Libraries    |              Version:  8.0.1
      Resolution:                    |             Keywords:
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 Iceland_jack):

 This is a pipe dream, `Logic` offers cool possibilities.

 [https://hackage.haskell.org/package/sbv-5.12/docs/src/Data-SBV-
 BitVectors-Model.html sbv] has `EqSymbolic` which is an `Eq a` where
 `Logic a ~ SBool` :

 {{{#!hs
 infix 4 .==, ./=
 class EqSymbolic a where
   (.==), (./=) :: a -> a -> SBool
 }}}

 This could be the regular `Eq` if we had something like (with `Boolean`
 taken from ticket:10592#comment:12)

 {{{#!hs
 class Boolean (Logic a) => Eq (a :: TYPE rep) where
   type Logic a :: TYPE (Rep rep)
   (==) :: a -> a -> Logic a
   a == b = not (a /= b)

   (/=) :: a -> a -> Logic a
   a /= b = not (a == b)

 instance Eq (SBV a) where
   type Logic (SBV a) = SBool
   (==) :: SBV a -> SBV a -> SBool
   SBV a == SBV b = SBV (svEqual a b)

 instance EqSymbolic (SArray a b) where
   type Logic (SArray a b) = SBool
   (==) :: SArray a b -> SArray a b -> SBool
   SArray a == SArray b = SBV (eqSArr a b)
 }}}

 We lose `EqSymbolic Bool` but `... => EqSymbolic [a]` would survive in a
 different form.

--
Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/12708#comment:16>
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