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

9 Mar 2017

      #13403: Derive instances (Applicative, Monad, ...) for structures lifted over
functors
-------------------------------------+-------------------------------------
           Reporter:  Iceland_jack   |             Owner:  (none)
               Type:  bug            |            Status:  new
           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:
-------------------------------------+-------------------------------------
 I'll start small: Given that we know how to define various instances for
 [https://hackage.haskell.org/package/base-4.9.1.0/docs/Data-Functor-
 Product.html Product] GHC could do it automatically.

 {{{#!hs
 data P f g a = f a ::: g a deriving (Functor, Applicative, Alternative)

 {-
 instance (Applicative f, Applicative g) => Applicative (P f g) where
   pure x = pure x ::: pure x
   (f:::g) <*> (x:::y) = (f <*> x) ::: (g <*> y)
 -}
 }}}

 And for specific constructors as well

 {{{#!hs
 data Q a = [a] :*: Maybe a deriving (Functor, Applicative, Alternative)

 {-
 instance Applicative Q where
   pure x = [x] :*: Just x
   (f:*:g) <*> (x:*:y) = (f <*> x) :*: (g <*> y)
 -}
 }}}

 == Alternative ==

 Use `GeneralizedNewtypeDeriving`

 {{{#!hs
 newtype Q a = Q (Product [] Maybe a)
   deriving (Functor, Applicative, Alternative)

 pattern (:*:) :: [a] -> Maybe a -> Q a
 pattern a :*: b = Q (Pair a b)
 }}}

 == Future Work ==

 This should work for a combination of various things, using `Const _`
 deprives us of `Alternative`

 {{{#!hs
 newtype U e a = U (([] `Product` Maybe `Product` Const e) a)
   deriving (Functor, Applicative)
 }}}

 using sums where
 [https://hackage.haskell.org/package/transformers-0.5.4.0/docs/Control-
 Applicative-Lift.html one summand is identity] gives us `Applicative` /
 `Alternative`

 {{{#!hs
 -- data Lift f a = Pure a | Other (f a)
 import Control.Applicative.Lift

 data V a = V ((Lift [] `Product` Maybe) a)
   deriving (Functor, Applicative, Alternative)
 }}}

 I want to be able to write this directly

 {{{#!hs
 data U e a = U [a] (Maybe a) (Const e a)
   deriving (Functor, Applicative)

 data V a
   = VL a   (Maybe a)
   | VR [a] (Maybe a)
   deriving (Functor, Applicative, Alternative)
 }}}

 == Future, Future Work ==

 [https://hackage.haskell.org/package/kan-extensions-5.0.1/docs/Data-
 Functor-Kan-Lan.html left-Kan extension]

 {{{#!hs
 data Lan g h a where
   Lan :: (g b -> a) -> h b -> Lan g h a
   deriving (Functor, Applicative)
 }}}

 [https://hackage.haskell.org/package/kan-extensions-5.0.1/docs/Control-
 Monad-Codensity.html codensity]

 {{{#!hs
 data Endo a = Endo (a -> a)

 newtype CodEndo a = CE (forall xx. (a -> Endo xx) -> Endo xx)
   deriving (Functor, Applicative, Monad)
 }}}

 and [https://hackage.haskell.org/package/free-4.12.4/docs/Control-Comonad-
 Cofree.html comonad]

 {{{#!hs
 data Rose a = a :< [Rose a]
   deriving (Functor, Applicative, Monad, Comonad, ...)
 }}}

--
Ticket URL: http://ghc.haskell.org/trac/ghc/ticket/13403
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