Add helper for hand-written SDecide instances?

[Shea Levy]

I just found myself reaching for this in defining a simple SDecide instance:

type RefuteHelper :: forall k1 k2 . k1 -> k2 -> Type
type family RefuteHelper x y where
  RefuteHelper a a = ()
  RefuteHelper _ _ = Void

refuted :: Sing a -> Sing b -> a :~: b -> RefuteHelper a b
refuted a _ Refl = ()

Would this, or some appropriately more general version, be useful upstream in Data.Singletons.Decide?

[Ryan Scott]

Can you elaborate on how you're using RefuteHelper to define an SDecide instance? It's not obvious to me what the connection is.

[Shea Levy]

instance SingKind Longevity where
  type Demote Longevity = Longevity

  fromSing SShort = Short
  fromSing SLong = Long

  toSing Short = SomeSing SShort
  toSing Long = SomeSing SLong

instance SDecide Longevity where
  SShort %~ SShort = Proved Refl
  SLong %~ SLong = Proved Refl
  SShort %~ SLong = Disproved (refuted SShort SLong)
  SLong %~ SShort = Disproved (refuted SLong SShort)

Perhaps this approach is not Haskelly enough, it's the closest analogue to what I'd write in Agda/coq

[Ryan Scott]

The way that singletons-th would generate an SDecide instance for that data type would be by using EmptyCase, i.e.,

instance SDecide Longevity where
  SShort %~ SShort = Proved Refl
  SLong %~ SLong = Proved Refl
  SShort %~ SLong = Disproved (\p -> case p of {})
  SLong %~ SShort = Disproved (\p -> case p of {})

This is shorter (and could be made even shorter with LambdaCase), but more importantly, it works without needing any auxiliary definitions. I wonder if this would work for your use case? I'm inclined to just recommend that instead.

[Shea Levy]

Ah, this works, thanks!