I am trying to create a data type that is an vector of values, but internally uses an unboxed vector when possible and a boxed array otherwise. If this already exists, let me know. For example, any easily unboxed type is stored in an unboxed array, but also any type that is a product type of only easily unboxed types like (Int, Int) is stored in multiple unboxed arrays. I don’t think there is a smart way of doing this for sum types, so those are stored in boxed arrays.

I’m trying to create a typeclass

class VectorElement a where

  data Vector a

  replicate :: Int -> a -> Vector a

  length :: Vector a -> Int

to represent things that can be stored in Vectors. I can then implement it for specific types that I know can be stored in unboxed vectors:

instance VectorElement Int where
  newtype Vector Int = VectorInt (U.Vector Int)
                     deriving Show
  replicate len x = VectorInt $ U.replicate len x
  length (VectorInt v) = U.length v

I also want to automatically derive instances of this class for other types using the Generic typeclass. Ideally these instances would be the most efficient possible, so that for example the instance for (Int, Int) used two unboxed arrays but the instance for Maybe Int uses a boxed array. To that end I created another typeclass and wrote instances for the Generic data constructors:

class VectorElementG (r :: * -> *) where

  data VectorG r

  replicateG :: Int -> r a -> VectorG r

  lengthG :: VectorG r -> Int

instance VectorElementG V1 where

  data VectorG V1

  replicateG = undefined

  lengthG = undefined

instance VectorElementG U1 where

  newtype VectorG U1 = VectorGUnit Int

  replicateG i U1 = VectorGUnit i

  lengthG (VectorGUnit i) = i

instance VectorElement a => VectorElementG (K1 i a) where

  newtype VectorG (K1 i a) = VectorGK (Vector a)

  replicateG i (K1 x) = VectorGK $ replicate i x

  lengthG (VectorGK v) = length v

instance (VectorElementG r1, VectorElementG r2) => VectorElementG (r1 :*: r2) where

  data VectorG (r1 :*: r2) = VectorGProd (VectorG r1) (VectorG r2)

  replicateG i (a :*: b) = VectorGProd (replicateG i a) (replicateG i b)

  lengthG (VectorGProd v _) = lengthG v

instance VectorElement ((r1 :+: r2) p) where

  newtype Vector ((r1 :+: r2) p) = VectorSum (V.Vector ((r1 :+: r2) p))

  replicate i x = VectorSum $ V.replicate i x

  length (VectorSum v) = V.length v

instance VectorElementG f => VectorElementG (M1 i c f) where

  newtype VectorG (M1 i c f) = VectorGMeta (VectorG f)

  replicateG i (M1 f) = VectorGMeta $ replicateG i f

  lengthG (VectorGMeta v) = lengthG v

I’m not sure if these are correct, especially the one for :+:. I want basically base cases to be any type that already has an instance of VectorElement or a sum type which is automatically boxed, and the recursive case to basically just use parallel vectors for product types.

I think this sort of worked insofar as it allowed me to write an instance for tuples:

instance (VectorElement a, VectorElement b) => VectorElement (a,b) where

  newtype Vector (a, b) = VectorTuple (VectorG (Rep (a, b)))

  replicate i x = VectorTuple $ replicateG i (from x)

  length (VectorTuple v) = lengthG v

Ideally, however, the compiler would automatically derive this instance using the Generic instance. Is there a way to do that also?

I would welcome any thoughts on this entire idea and approach.

Thanks,

Jake Waksbaum

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