A simple desugaring example may illustrate:

    {-# LANGUAGE Arrows, GADTs #-}

    import Control.Arrow

    data X a where
      X :: Bool -> Int -> X (Bool, Int)

    ex1 :: Arrow a => a (X x) (Int, Bool)
    ex1 = proc (X b i) -> returnA -< (i, b)

    ex1expl :: Arrow a => a (X x) (Int, Bool)
    ex1expl =
        arr f >>> -- pattern match
        arr g >>> -- expression
        returnA
      where
        f :: X a -> (Bool, Int)
        f (X b i) = (b, i)

        g :: (Bool, Int) -> (Int, Bool)
        g (b, i) = (i, b)

If we want to desugar Alexis' example

    data T where
        T :: a -> T

    panic :: (Arrow arrow) => arrow T T
    panic = proc (T x) -> do returnA -< T x

which has the same shape, what would the type of `f` be?

    f :: T -> a -- doesn't work

If we had sigmas, i.e. dependent pairs and type level lambdas, we could have

    f :: T -> Sigma Type (\a -> a) -- a pair like (Bool, Int) but fancier

i.e. the explicit desugaring could look like

    panicExplicit :: (Arrow arrow) => arrow T T
    panicExplicit =
        arr f >>>
        arr g >>>
        returnA
      where
        f :: T -> Sigma Type (\a -> a)
        f (T @a x) = (@a, x)

        g :: Sigma Type (\a -> a)
        g (@a, x) = T @a x

My gut feeling says that the original arrow desugaring would just work,
but instead of tuples for context, we'd need to use telescopes.
Not that earth-shattering of a generalization.

The evidence could be explicitly bound already today,
but I guess it's not, and simply thrown away:

    {-# LANGUAGE Arrows, GADTs, ConstraintKinds #-}

    import Control.Arrow

    data Showable a where
        Showable :: Show a => a -> Showable a

    data Dict c where
        Dict :: c => Dict c

    ex2explicit :: Arrow a => a (Showable x) (Showable x)
    ex2explicit =
        arr f >>> -- pattern match
        arr g >>> -- expression
        returnA 
      where
        f :: Showable x -> (x, Dict (Show x))
        f (Showable x) = (x, Dict)

        g :: (x, Dict (Show x)) -> Showable x
        g (x, Dict) = Showable x

The

    ex2 :: Arrow a => a (Showable x) (Showable x)
    ex2 = proc (Showable x) -> returnA -< Showable x

works today, surprisingly. Looks like GHC does something as above,
if I read the -ddump-ds output correctly:

    ex2
      :: forall (a :: * -> * -> *) x.
         Arrow a =>
         a (Showable x) (Showable x)
    [LclIdX]
    ex2
      = \ (@ (a_a2ja :: * -> * -> *))
          (@ x_a2jb)
          ($dArrow_a2jd :: Arrow a_a2ja) ->
          break<1>()
          let {
            arr' :: forall b c. (b -> c) -> a_a2ja b c
            [LclId]
            arr' = arr @ a_a2ja $dArrow_a2jm } in
          let {
            (>>>>) :: forall a b c. a_a2ja a b -> a_a2ja b c -> a_a2ja a c
            [LclId]
            (>>>>) = GHC.Desugar.>>> @ a_a2ja $dArrow_a2jn } in
          (>>>>)
            @ (Showable x_a2jb)
            @ ((Show x_a2jb, x_a2jb), ())
            @ (Showable x_a2jb)
            (arr'
               @ (Showable x_a2jb)
               @ ((Show x_a2jb, x_a2jb), ()) -- this is interesting
               (\ (ds_d2kY :: Showable x_a2jb) ->
                  case ds_d2kY of { Showable $dShow_a2je x_a2hL ->
                  (($dShow_a2je, x_a2hL), ghc-prim-0.5.3:GHC.Tuple.())
                  }))
            ((>>>>)
               @ ((Show x_a2jb, x_a2jb), ())
               @ (Showable x_a2jb)
               @ (Showable x_a2jb)
               (arr'
                  @ ((Show x_a2jb, x_a2jb), ())
                  @ (Showable x_a2jb)
                  (\ (ds_d2kX :: ((Show x_a2jb, x_a2jb), ())) ->
                     case ds_d2kX of { (ds_d2kW, _ [Occ=Dead]) ->
                     case ds_d2kW of { ($dShow_a2jl, x_a2hL) ->
                     break<0>() Main.Showable @ x_a2jb $dShow_a2jl x_a2hL
                     }
                     }))
               (returnA @ a_a2ja @ (Showable x_a2jb) $dArrow_a2jd))

- Oleg

I think the real difference is whether new type variables are brought into scope. It seems that GHC can't deal with a proc-pattern-match that introduces type variables, but it *can* deal with introduced constraints. I have no idea *why* this is the case, but it seems a plausible (if accidental) resting place for the implementation.

Richard

On Oct 3, 2021, at 12:19 PM, Alexis King <lexi.lambda@gmail.com> wrote:

Hi,

I’ve been working on bringing my reimplementation of arrow notation back up to date, and I’ve run into some confusion about the extent to which arrow notation is “supposed” to support matching on GADT constructors. Note [Arrows and patterns] in GHC.Tc.Gen.Pat suggests they aren’t supposed to be supported at all, which is what I would essentially expect. But issues #17423 and #18950 provide examples of using GADT constructors in arrow notation, and there seems to be some expectation that in fact they ought to be supported, and some recently-added test cases verify that’s the case.

But this is quite odd, because it means the arrows test suite now includes test cases that verify both that this is supported and that it isn’t… and all of them pass! Here’s my understanding of the status quo:

• Matching on constructors that bind bona fide existential variables is not allowed, and this is verified by the arrowfail004 test case, which involves the following program:

  data T = forall a. T a
  
  panic :: (Arrow arrow) => arrow T T
  panic = proc (T x) -> do returnA -< T x

  This program is rejected with the following error message:

  arrowfail004.hs:12:15:
      Proc patterns cannot use existential or GADT data constructors
      In the pattern: T x

• Despite the previous point, matching on constructors that bind evidence is allowed. This is enshrined in test cases T15175, T17423, and T18950, which match on constructors like these:

  data DecoType a where
    DecoBool :: Maybe (String, String) -> Maybe (Int, Int) -> DecoType Bool
  data Point a where
    Point :: RealFloat a => a -> Point a

This seems rather contradictory to me. I don’t think there’s much of a meaningful distinction between these types of matches, as they create precisely the same set of challenges from the Core point of view… right? And even if I’m wrong, the error message in arrowfail004 seems rather misleading, since I would definitely call DecoBool and Point above “GADT data constructors”.

So what’s the intended story here? Is matching on GADT constructors in arrow notation supposed to be allowed or not? (I suspect this is really just yet another case of “nobody really knows what’s ‘supposed’ to happen with arrow notation,” but I figured I might as well ask out of hopefulness that someone has some idea.)

Thanks,
Alexis

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