Problems with ISubset in vinyl

Question

I have the following code:

type Drawable = '["object" ::: Object, "transform" ::: M44 GL.GLfloat]
objXfrm :: "transform" ::: M44 GL.GLfloat
objXfrm = Field
objRec :: "object" ::: Object
objRec = Field

drawObject :: (Drawable `ISubset` a) => M44 GL.GLfloat -> PlainRec a -> IO ()
drawObject camera obj =
    withVAO vao $ do
        GL.currentProgram $= Just (program shdr)
        setUniforms shdr (modelView =: (rGet objXfrm obj !*! camera))
        GL.polygonMode $= (GL.Line, GL.Line)
        GL.drawElements GL.Triangles inds GL.UnsignedInt nullPtr
    where Object {objVAO = vao, objNumIndices = inds, objShader = shdr}
              = rGet objRec obj

When I get rid of the type on drawObject it compiles fine, but with the type I get

  Could not deduce (IElem * ("transform" ::: V4 (V4 GL.GLfloat)) a)
      arising from a use of `rGet'
    from the context (ISubset * Drawable a)
...
  Could not deduce (IElem * ("object" ::: Object) a)
      arising from a use of `rGet'
    from the context (ISubset * Drawable a)

The type that GHC deduces for me is

drawObject
  :: (IElem * ("object" ::: Object) rs,
      IElem * ("transform" ::: V4 (V4 GL.GLfloat)) rs) =>
     V4 (V4 GL.GLfloat)
     -> Rec rs Data.Functor.Identity.Identity -> IO ()

And that works fine as a type signature, but the one with ISubset does not. The error is exactly the same if I interchange the arguments to ISubset. What is going on here?

Answer 1

Looking at the source code for Vinyl, IElem x xs (which is a synonym for Implicit (Elem x xs)) has two instances:

instance Implicit (Elem x (x ': xs)) where
    implicitly = Here
instance Implicit (Elem x xs) => Implicit (Elem x (y ': xs)) where
    implicitly = There implicitly

Note that there is no mention of Subset here. Logically, (x ∈ xs) ∧ (xs ⊆ ys) ⇒ (x ∈ ys), but since there is no instance with the signature Implicit (Subset xs ys), Implicit (Elem x xs) => Implicit (Elem x ys), Haskell has no way of inferring the appropriate instance. Furthermore, no such instance can be written because doing so would result in some nasty instance overlap.

As a possible workaround, we can manipulate the membership witnesses (Elem and Subset) directly in order to force the appropriate instances (this is totally untested, and may fail miserably):

{-# LANGUAGE RankNTypes, ScopedTypeVariables, and possibly more... #-}

-- Lift an Elem value to a constraint.
withElem :: Elem x xs -> (forall r. IElem x xs => r) -> r
withElem Here x = x
withElem (There e) x = withElem e x

-- Witness of (x ∈ xs) ⇒ (xs ⊆ ys) ⇒ (x ∈ ys)
subsetElem :: Elem x xs -> Subset xs ys -> Elem x ys
subsetElem Here (SubsetCons e _) = e
subsetElem (There e) (SubsetCons _ s) = There (subsetElem e s)

-- Utility for retrieving Elem values from Fields (:::).
fieldElem :: IElem x xs => x -> Elem x xs
fieldElem _ = implicitly

inSubset :: IElem x xs => x -> Subset xs ys -> (forall r. IElem x ys => r) -> r
inSubset f s x = withElem (subsetElem (fieldElem f) s) x

drawObject :: forall a. (Drawable `ISubset` a) => M44 GL.GLfloat-> PlainRec a -> IO ()
drawObject camera obj =
    inSubset objRec subset $
    inSubset objXfrm subset $
        -- The desired instances should now be available here
        ...
  where
    subset = implicitly :: Subset Drawable a
    ...