[GHC] #13341: Lift constraint products

[GHC]

#13341: Lift constraint products
-------------------------------------+-------------------------------------
           Reporter:  Iceland_jack   |             Owner:  (none)
               Type:  feature        |            Status:  new
  request                            |
           Priority:  normal         |         Milestone:
          Component:  Compiler       |           Version:  8.0.1
           Keywords:                 |  Operating System:  Unknown/Multiple
       Architecture:                 |   Type of failure:  None/Unknown
  Unknown/Multiple                   |
          Test Case:                 |        Blocked By:
           Blocking:                 |   Related Tickets:
Differential Rev(s):                 |         Wiki Page:
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 I want to get a discussion going, could we lift constraint products
 automatically.

 Although not partially applicable, we can consider `(,)` as having kind

 {{{#!hs
 (,) :: Constraint -> Constraint -> Constraint
 }}}

 I propose also giving it kinds

 {{{#!hs
 (,) :: (k -> Constraint) -> (k -> Constraint) -> (k -> Constraint)

 (,) :: (k -> k' -> Constraint) -> (k -> k' -> Constraint) -> (k -> k' ->
 Constraint)

 -- etc.
 }}}

 == Translation

 {{{#!hs
 (Eq, Num, Show)
 (Monad, Foldable)
 (Category, Profunctor)
 }}}

 gets turned into something like

 {{{#!hs
 class    (c a, d a) => (c :&: d) a
 instance (c a, d a) => (c :&: d) a
 infixl 7 :&:

 Eq:&:Num:&:Show
 Monad:&:Foldable
 Category:&:Profunctor
 }}}

 == Uses

 Very often I need to be able to combine constraints.

 A small modification of [https://hackage.haskell.org/package/free-
 functors-0.7.2/docs/Data-Constraint-Class1.html SuperClasses]

 {{{#!hs
 type c :~ d = forall xx. c x :- d xx

 class HasSuperClasses (c :: k -> Constraint) where
   type SuperClasses c :: k -> Constraint
   type SuperClasses c = c

   superClasses :: c :~ SuperClasses c
   containsSelf :: SuperClasses c :~ c

 instance HasSuperClasses Functor where
   superClasses :: Functor :~ Functor
   superClasses = Sub Dict

   containsSelf :: Functor :~ Functor
   containsSelf = Sub Dict

 instance HasSuperClasses Foldable where
   superClasses :: Foldable :~ Foldable
   superClasses = Sub Dict

   containsSelf :: Foldable :~ Foldable
   containsSelf = Sub Dict
 }}}

 I want to be able to write

 {{{#!hs
 instance HasSuperClasses Traversable where
   type Traversable = (Traversable, Functor, Foldable)

   superClasses :: Traversable :~ (Traversable, Functor, Foldable)
   superClasses = Sub Dict

   containsSelf :: (Traversable, Functor, Foldable) :~ Traversable
   containsSelf = Sub Dict
 }}}

 If this doesn't pose any difficulties I'll open a GHC proposal.

--
Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/13341>
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