[GHC] #13403: Derive instances (Applicative, Monad, ...) for structures lifted over functors

[GHC]

#13403: Derive instances (Applicative, Monad, ...) for structures lifted over
functors
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        Reporter:  Iceland_jack      |                Owner:  (none)
            Type:  bug               |               Status:  new
        Priority:  normal            |            Milestone:
       Component:  Compiler          |              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):

 Thanks for taking the time to respond to my proposals

 Replying to [comment:2 RyanGlScott]:
 > This feels extremely //ad hoc// and not nearly formalized enough to
 where I'd be comfortable with it.

 At least it gets a reaction :) the proposal was but we can go into the
 direction of [https://hackage.haskell.org/package/base-4.9.1.0/docs/GHC-
 Generics.html#t:Rep Generic's Rep]

 > I have no idea how you could teach GHC to recognize "product types"

 It's not just for product types, I should have made myself more clear but
 I didn't want to complicate the proposal. This should work for our entire
 polynomial arsenal, `Sum`, `Product`, `Identity`, `Const _`, when we get
 to weirder things like
 [https://hackage.haskell.org/package/bifunctors-5.4.1/docs/Data-Bifunctor-
 Biff.html Biff] things start to collide. Maybe it's a matter of picking a
 comfortable subset.

 > `data Product f g h a = Product (f (g (f a))) (h (f (g a)))`?

 That could be encoded as ↓ and we can still derive a whole host of
 instances

 {{{#!hs
 infixr 9 ·
 type (·) = Compose

 newtype P f g h a = P (Product (f · g · f) (h · f · g) a)
   deriving (Functor, Foldable, Traversable, Applicative, Alternative,
 Contravariant)
 }}}

 In any case it could be implemented incrementally.

 > What if there are constants like `data Product a = Product Int a`?

 They could always be rewritten as (I changed `Int` to `String` to get that
 `Applicative` instance)

 {{{#!hs
 newtype Q a = Q (Product (Const String) Identity a)
   deriving (Functor, Foldable, Traversable, Applicative)
 }}}

 >
 > * `newtype Compose f g a = Compose (f (g a))`
 > * `data Proxy a = Proxy`

 `Compose` and `Proxy` would likely be primitives in what ever subset of
 types we support.

 Are there other discussions about something similar? Or is this the first
 time this is proposed.

--
Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/13403#comment:3>
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