Translate/encode Haskell's `data Obj = forall

Question

I've not been able to come up with how to encode Obj in Scala:

{-# LANGUAGE ExistentialQuantification #-}

data Obj = forall a. (Show a) => Obj a

instance Show Obj where show (Obj a) = "Obj " ++ show a

main = print $ show [Obj "hello", Obj 3, Obj True]

when run, the above produces the following output:

[Obj "hello",Obj 3,Obj True]

In Scala, however, this does not seem to compile:

forSome { type T; implicit val ev: Show[T] }

and neither does this:

forSome { type T : Show[T] }

Is this even possible at the type system level, or do I need to "capture" the type class instance using something like this:

class Obj[T](val x: T)(implicit val: Show[T])  // ...or similar

Any insight would be appreciated!

Answer 1

You got it almost right:

import scalaz._
import scalaz.Scalaz._

trait Obj {
  type T // existential type
  val x: T
  implicit val show: Show[T]
}

implicit val objSow: Show[Obj] = Show.shows[Obj] { (x: Obj) =>
  x.show.shows(x.x)
}

object Obj {
  /* "constructor" */
  def apply[U](_x: U)(implicit _show: Show[U]): Obj = new Obj {
    type T = U
    val x = _x
    val show = _show
  }
}

val test: List[Obj] = List(Obj(1), Obj(true), Obj("foo"))

/*
scala> test.shows
res0: String = [1,true,"foo"]
*/

P.S I'd like to use T and show in apply; not U and _show. If someone knows how to avoid shadowing, I'll appreciate!

---

Alternatively you could use forSome:

import scala.language.existentials

trait ObjE {
  val pair: Tuple2[T, Show[T]] forSome { type T }
}

/* And to define Show instance we have to help compiler unify `T` in pair components. */
def showDepPair[T] = Show.shows[Tuple2[T, Show[T]]] { x => x._2.shows(x._1) }
implicit val showObjE = Show.shows[ObjE] { x => showDepPair.shows(x.pair) }

Here we have to use Tuple2 (or other auxillary type) to capture Show. I like the previous variant more. For me it's easier to wrap a mind around a type member.

Also in Scala "Don Giovanni" forSome syntax will be eliminated in favour of val pair: ({ type λ[T] = Tuple2[T, Show[T]] })#λ[_] }, which works already too. I hope there will be some syntax support for type lambdas as well. kind-projector doesn't help in this situation (repeated use of T). Maybe something like in Typelevel scalac: val pair: ([T] => Tuple2[T, Show[T])[_]).

Another foundational change will be:

A single fundamental concept – type members – can give a precise meaning to generics, existential types, wildcards, and higher-kinded types.

So the both forms will be equivalent from the point of view of the compiler (in former we unpack the tuple). I'm not 100% sure what are the differences currently, if there are any.

P.S. The Troubles with Types helped me understand scala's current type system quirks.

Answer 2

I've "packaged" Oleg's answer into this generic and (seemingly) reusable structure:

import scala.language.{ higherKinds, implicitConversions }

trait AnyWithTC[TC[_]] { type T; val x: T; implicit val ev: TC[T] }

// don't like the 'implicit' here; suggestions welcome
implicit def AnyWithTC[T, TC[_]](x: T)(implicit ev: TC[T]) = {
  type T0 = T; val x0 = x; val ev0 = ev
  new AnyWithTC[TC] { type T = T0; val x = x0; val ev = ev0 }
}

then, data Obj = forall a. (Show a) => Obj a can be implemented like this:

type Obj = AnyWithTC[Show]
implicit val objShow = Show.shows[Obj] { x => "Obj " + x.show.shows(x.x)   }
val xs: List[Obj] = List(1, true, "hello")
println(xs.shows) // prints [Obj 1,Obj true, Obj hello]