如何让 GHC 识别此代码段中的 SingI 实例？

Question

had a question about singletons

I have a promoted data type a where I instanced data family Sing (a :: Foo) appropriately.

I also have a type family Bar (a :: Foo) (b :: Foo) :: Foo

In the middle of a busy function, I have:

(\(x :: Sing n) (y :: Sing m) -> doThingsWith (sing :: Sing (Bar n m)))

But I'm not sure where I should put my SingI constraint.

For more details, my type is

data PNat = NZ | NS PNat

data instance Sing (n :: PNat) where
  SNZ :: Sing 'NZ
  SNS :: Sing (m :: PNat) -> Sing ('NS m)

and my type family is

type family NPlus (n :: PNat) (m :: PNat) :: PNat where
  NPlus NZ y = y
  NPlus (NS x) y = NS (NPlus x y)

Now, I'm actually able to manually write out explicit singleton shuffling:

nPlus :: forall n m nm. (NPlus n m ~ nm) => Sing n -> Sing m -> Sing nm
nPlus SNZ y = y
nPlus (SNS x) y = SNS (nPlus x y)

And this compiles fine...I can do

\x y -> nPlus x y

but I feel like I should be able to just use singI here and let the type family do both of the work. Besides, I have a lot of functions like this, too, and would prefer to not have to do it for each one.

I do have ScopedTypeVariables turned on.

thank you all

---

Edit: Ah, I just realized that SingI instances aren't automatically derived; I whipped one up:

instance SingI NZ where
  sing = SNZ

instance SingI n => SingI (NS n) where
  sing = SNS sing

Unfortunately, GHC is still telling me that there is no instance of SingI when I use sing in the lambda above :/

Answer 1

I feel like I should be able to just use singI here and let the type family do both of the work.

This can't be done. The reason why we have the many TH facilities in singletons is that data and function definitions must be duplicated in the current state of affairs.

The idiomatic usage would be defining everything on the term level once, and deriving the rest with TH.

-- LANGUAGE KitchenSink
import Data.Singletons.TH
import Data.Singletons.Prelude

$(singletons [d|
  data PNat = NZ | NS PNat deriving (Eq, Show, Ord)

  nPlus :: PNat -> PNat -> PNat
  nPlus NZ y = y
  nPlus (NS x) y = NS (nPlus x y)  |])

This creates the Sing definition,the type family for nPlus , SingI instances, SingKind instances, the kind-restricted SPNat type synonym for Sing , defunctionalization symbols for type families and constructors, and also type-level analogues for Eq and Ord , and also decidable equality . You can hit :bro on the module and :i PNat to find out exactly what got generated.

Now nPlus and the type family NPlus work as intended.

To provide a bit of explanation regarding SingI : SingI a => t is equivalent to Sing a -> t . They even compile to the exact same Core code. The only difference between them is that Sing -s are passed explicitly and SingI -s implicitly. sing provides conversion from SingI to Sing , and singInstance converts backwards.

In the light of this, something like

(SingI (NPlus n m)) => Sing n -> Sing m -> Sing (NPlus n m)

is pretty awkward, since it's equivalent to

Sing (NPlus n m) -> Sing n -> Sing m -> Sing (NPlus n m)

which can be implemented as a constant function that doesn't do any addition.

So when should we use SingI or Sing ? The most convenient way is to perform computation on Sing -s, since we can pattern match on them, and use SingI only when we just need to plug in or pass along a value somewhere, but don't need to pattern match or recurse.