How to implement Functor[Dataset]

Question

I am struggling on how to create an instance of Functor[Dataset]... the problem is that when you map from A to B the Encoder[B] must be in the implicit scope but I am not sure how to do it.

implicit val datasetFunctor: Functor[Dataset] = new Functor[Dataset] {
    override def map[A, B](fa: Dataset[A])(f: A => B): Dataset[B] = fa.map(f)
  }

Of course this code is throwing a compilation error since Encoder[B] is not available but I can't add Encoder[B] as an implicit parameter because it would change the map method signature, how can I solve this?

Landonlandor

Answer 1

You cannot apply f right away, because you are missing the Encoder. The only obvious direct solution would be: take cats and re-implement all the interfaces, adding an implict Encoder argument. I don't see any way to implement a Functor for Dataset directly.

However maybe the following substitute solution is good enough. What you could do is to create a wrapper for the dataset, which has a map method without the implicit Encoder, but additionally has a method toDataset, which needs the Encoder in the very end.

For this wrapper, you could apply a construction which is very similar to the so-called Coyoneda-construction (or Coyo? What do they call it today? I don't know...). It essentially is a way to implement a "free functor" for an arbitrary type constructor.

Here is a sketch (it compiles with cats 1.0.1, replaced Spark traits by dummies):

import scala.language.higherKinds
import cats.Functor

/** Dummy for spark-Encoder */
trait Encoder[X]

/** Dummy for spark-Dataset */
trait Dataset[X] {
  def map[Y](f: X => Y)(implicit enc: Encoder[Y]): Dataset[Y]
}

/** Coyoneda-esque wrapper for `Dataset` 
  * that simply stashes all arguments to `map` away
  * until a concrete `Encoder` is supplied during the
  * application of `toDataset`.
  *
  * Essentially: the wrapped original dataset + concatenated
  * list of functions which have been passed to `map`.
  */
abstract class MappedDataset[X] private () { self =>
  type B
  val base: Dataset[B]
  val path: B => X
  def toDataset(implicit enc: Encoder[X]): Dataset[X] = base map path

  def map[Y](f: X => Y): MappedDataset[Y] = new MappedDataset[Y] {
    type B = self.B
    val base = self.base
    val path: B => Y = f compose self.path
  }
}

object MappedDataset {
  /** Constructor for MappedDatasets.
    * 
    * Wraps a `Dataset` into a `MappedDataset` 
    */
  def apply[X](ds: Dataset[X]): MappedDataset[X] = new MappedDataset[X] {
    type B = X
    val base = ds
    val path = identity
  }

}        

object MappedDatasetFunctor extends Functor[MappedDataset] {
  /** Functorial `map` */
  def map[A, B](da: MappedDataset[A])(f: A => B): MappedDataset[B] = da map f
}

Now you can wrap a dataset ds into a MappedDataset(ds), then map it using the implicit MappedDatasetFunctor as long as you want, and then call toDataset in the very end, there you can supply a concrete Encoder for the final result.

Note that this will combine all functions inside map into a single spark stage: it won't be able to save the intermediate results, because the Encoders for all intermediate steps are missing.

---

I'm not quite there yet with studying cats, I cannot guarantee that this is the most idiomatic solution. Probably there is something Coyoneda-esque already in the library.

EDIT: There is Coyoneda in the cats library, but it requires a natural transformation F ~> G to a functor G. Unfortunately, we don't have a Functor for Dataset (that was the problem in the first place). What my implementation above does is: instead of a Functor[G], it requires a single morphism of the (non-existent) natural transformation at a fixed X (this is what the Encoder[X] is).

Isadoraisadore

thank you, I am going to investigate more about Coyoneda, it seems to be the cleanest solution, right? – Landonlandor

@Mikel: This seems to be the go-to solution if you want to build a Functor instance for an F[A] which "cannot map right away, but can map later". There is also a dual Yoneda-construction for building Functor for F[A]s which "can map initially, but lose this capability later on". I'm pretty sure that this is standard, I swear I saw it in Bjarnason/Chiusano's book, but I can't find it right now. – Isadoraisadore

@Mikel: Here is the original Coyoneda from the cats library: Coyoneda.scala. I don't see immediately how you could use it directly, because it requires an F ~> G to a G with a functor, but again, you don't have a Functor, you have a single Encoder[X] for a fixed type X. I added a comment on that. – Isadoraisadore

@Mikel Added an edit about why it could be that this thing is not exactly the full-blown Coyoneda, but rather a Coyoneda which works with a single morphism of a natural transformation, instead of the entire natural transformation (which would be a family of functions which could encode all the X at once). – Isadoraisadore