Re: [GHC] #8516: Add (->) representation and the Invariant class to GHC.Generics

30 Nov 2016


      ...
We currently disallow any use of the parameter in the domain of (->).
{{{
newtype F a = F ((a -> Int) -> Int) deriving Generic1
<interactive>:4:38:
    Can't make a derived instance of `Generic1 (F g)':
      Constructor `F' must use the last type parameter only as the last
 argument of a data type, newtype, or (->)
    In the data declaration for `F'
}}}
!DeriveFunctor succeeds for this F.
I'd like to add this representation type to GHC.Generics and
 !DeriveGeneric.
{{{
newtype (f :->: g) a = FArrow1 (f a -> g a)
}}}
We could then represent the first example above. We could also derive
#8516: Add (->) representation and the Invariant class to GHC.Generics
-------------------------------------+-------------------------------------
        Reporter:  nfrisby           |                Owner:
            Type:  feature request   |               Status:  new
        Priority:  low               |            Milestone:
       Component:  Compiler (Type    |              Version:  7.7
  checker)                           |
      Resolution:                    |             Keywords:  Generics
Operating System:  Unknown/Multiple  |         Architecture:
                                     |  Unknown/Multiple
 Type of failure:  None/Unknown      |            Test Case:
      Blocked By:                    |             Blocking:
 Related Tickets:                    |  Differential Rev(s):
       Wiki Page:                    |
-------------------------------------+-------------------------------------
Changes (by songzh):

 * cc: songzh (added)


Comment:

 Replying to [ticket:8516 nfrisby]:
 the more interesting Generic1 (F g).
...
{{{
newtype F g a = F (g a -> Int) deriving Generic1
type instance Rep1 (F g) = Rec1 g :->: Rec0 Int
instance Generic1 (F g) where
  to x = F $ unRec0 . unArrow1 x . Rec1
  from (F x) = FArrow1 $ Rec0 . x . unRec1
}}}
Admittedly, there's not many generic definitions impeded by not having
(:->:). Contra- and in-variant  types are uncommon.
...
I'm suggesting this feature without strong motivating examples because I
think this would streamline the implementation of -XDeriveGenerics in some
 ways while also making it more general — assuming that we added the
 Invariant class to base or ghc-prim.
...
{{{
class Invariant t where
  invmap :: (a -> b) -> (b -> a) -> t a -> t b
invmap_covariant :: Functor t => (a -> b) -> (b -> a) -> t a -> t b
invmap_covariant f _ = fmap f
instance (Invariant f,Invariant g) => Invariant (FArrow f g) where
  invmap co contra (FArrow h) = FArrow $ invmap co contra . h . invmap
contra co
...
}}}
(Of course, Invariant should be a super class of Functor. :/ )
Now we can handle quite involved examples:
{{{
newtype F g h a = F (g (h a)) deriving Generic1
instance Invariant g => Generic1 (F g h) where
  to x = invmap unRec1 Rec1 $ unComp1 x
  from (F x) = Comp1 $ invmap Rec1 unRec1
}}}
All of that said, I'm mostly opening this ticket so I can get feedback
 on difficulties I might not be anticipating and have a place to reference
 from the compiler source code comments.
--
Ticket URL: http://ghc.haskell.org/trac/ghc/ticket/8516#comment:14
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