Heterogeneous Maps and Keys with Phantom Types in Scala

The term “heterogeneous collection” captures a few different ideas, most popularly a set or list where the elements may have different types. This post is not about those, but about a map (or dictionary, or key-value mapping, or whatever else you’d like to call it) where the values may be of different types, but the program does not lose that type information.

I’ve made a preliminary library from these code snippets at https://github.com/kennknowles/scala-heterogeneous-map. Let’s jump right in and do our imports…

import java.net.URI

import org.scalacheck._
import org.scalacheck.Arbitrary._
import org.scalacheck.Prop._
import org.scalacheck.Pretty._

To define a heterogeneous map, instead of Map[Key, Value] as you would normally have in Scala, we need a different type per key. So we embed the type of the value into the key by using a type constructor (function from type to type like List[_] or Set[_]) as our generic parameter to the HMap trait. Scala has some rather idiosyncratic ways of writing higher-kinded types, but here is the definition of the trait:

trait HMap[TypedKey[_]] { self =>
  def get[T](key: TypedKey[T]) : Option[T]
  def put[T](key: TypedKey[T], value: T) : HMap[TypedKey]
}

You can already notice the principle feature: A key can only be used to put/get a value of the appropriate type. Exercise for the reader: Add iteration over key-value pairs.

For this essay I will just use a default implementation layered directly on the existing type of maps and use casting under the hood.

object HMap {
  private class WrappedMap[TypedKey[_]](m: Map[TypedKey[_], AnyRef])
  extends HMap[TypedKey] {
    def get[T](key: TypedKey[T]) = m.get(key).asInstanceOf[Option[T]]
    def put[T](key: TypedKey[T], value: T) =
      new WrappedMap(m + (key -> value.asInstanceOf[AnyRef]))
  }

  def empty[TypedKey[_]] : HMap[TypedKey] = new WrappedMap[TypedKey](Map())
}

Let’s see about playing with this in the console for a bit. I’ll need to improvise a type for the keys. I’ll use integers with an extra type attached for the type of the values they point to.

$ xsbt console

scala> case class TInt[T](i: Int)
defined class TInt

scala> val m = HMap.empty[TInt]
m: HMap[TInt] = HMap$WrappedMap@67bcdb3f

scala> m.put(TInt[String](3), "hello")
res0: HMap[TInt] = HMap$WrappedMap@13216ee9

scala> m.put(TInt[Int](3), "goodbye")
<console>:11: error: type mismatch;
  found   : TInt[Int]
  required: TInt[Any]
  Note: Int <: Any, but class TInt is invariant in type T.
  You may wish to define T as +T instead. (SLS 4.5)
              m.put(TInt[Int](3), "goodbye")
                             ^

scala> m1.get(TInt[String](3))
res2: Option[String] = Some(hello)

scala> m1.get(TInt[String](5))
res3: Option[String] = None

scala> m1.get(TInt[Int](3))
res4: Option[Int] = Some(hello)

What? That last one is definitely wrong. Read on for why and how to fix it. The problem is the Java/Scala/JVM approach to equality – below I solve it via TInt, not HMap.

As was clear in the trait, the type parameter of TInt has to match from key to value. The type parameter is also compile-time only; a good compiler can eliminate the boxing/unboxing, in general. There is probably some object-oriented reason why Scala is not allowed to, but I didn’t check the bytecode.

Now the thing I did with TInt is a well-known pattern called “Phantom Types” (discussed by Foursquare, Neil Mitchell, Ralf Hinze, James Iry, and you should really just search for it and read as much as you like) so I will define a general phantom-type-augmented value. It is basically as simple as “case class WithPhantom[T, Phantom](v: T)” but there are some wrinkles surrounding equality, as we saw earlier. Are equal values boxed with the different phantom types equal? Clearly they should not be, but the best way to implement this was not obvious to me. I would love suggestions on improving these bits. (Direct them to the previously-mentioned github project for this code)

case class WithPhantom[T, Phantom: Manifest](v: T) {
  private val m = implicitly[Manifest[Phantom]]

  override def equals(other: Any) =
    other.isInstanceOf[WithPhantom[T, Phantom]] && {
      val otherPh = other.asInstanceOf[WithPhantom[T, Phantom]]
      (otherPh.m.erasure == this.m.erasure) && (otherPh.v == this.v)
    }

  override def hashCode =
    (v, implicitly[Manifest[Phantom]].hashCode).hashCode
  
  override def toString = "WithPhantom[%s](%s)"
    .format(implicitly[Manifest[Phantom]].erasure.getName, v)
}

Now we can use this to have TInt, TString, and, my favorite, TURI (think of a mime type registry for a crawler)

object WithPhantom {
  type TInt[T] = WithPhantom[Int, T]
  type TString[T] = WithPhantom[String, T]
  type TURI[T] = WithPhantom[URI, T]

  def TInt[T: Manifest](i: Int) = WithPhantom[Int, T](i)
  def TString[T: Manifest](str: String) = WithPhantom[String, T](str)
  def TURI[T: Manifest](uri: URI) = WithPhantom[URI, T](uri)
}

It is fun and all to play around in the scala console, but to make this robust, small as it is, I’ll use ScalaCheck properties. For that, I will need Arbitrary values for WithPhantom and HMap. This is somewhat problematic because to have an arbitrary HMap I need to choose arbitrary types which is another discussion entirely. So for these properties, I just use two types and request that the invoker of the functions ensure that they are different if needed, providing an arbitrary instance that just generates values that of types Int and String.

object ScalaCheckInstances {

  implicit def arbWithPhantom[T: Arbitrary, Phantom: Manifest]
    : Arbitrary[WithPhantom[T, Phantom]] =
    Arbitrary(for(v <- arbitrary[T]) yield WithPhantom[T, Phantom](v))

  def genHMap[Value1, Value2, TypedKey[_]](
    implicit arbV1: Arbitrary[Value1],
             arbV2: Arbitrary[Value2],
             arbK1: Arbitrary[TypedKey[Value1]],
             arbK2: Arbitrary[TypedKey[Value2]]): Gen[HMap[TypedKey]] = {
      for {
        kv1List <- arbitrary[List[(TypedKey[Value1], Value1)]]
        kv2List <- arbitrary[List[(TypedKey[Value2], Value2)]]
      } yield {
        var hmap = HMap.empty[TypedKey]
        for ((k, v) <- kv1List) { hmap = hmap.put(k, v) }
        for ((k, v) <- kv2List) { hmap = hmap.put(k, v) }
        hmap
      }
  }

  // For arbitrary, I just choose Int and String as the two phantom types and TInt for the key
  implicit def arbHMap[TypedKey[_]](
    implicit arbKInt: Arbitrary[TypedKey[Int]],
             arbKString: Arbitrary[TypedKey[String]]) =
    Arbitrary(genHMap[Int, String, TypedKey])
}

The most important test is that WithPhantom[Int, Int](x) != WithPhantom[Int, String](x) because that is the code I was least confident in. My pattern is to define properties without forAll invocations and separately register those properties with the testing framework. As before, generating arbitrary types is beyond the scope of this essay, so I just ask the caller of the prop_typeMiss to provide different types.

object WithPhantomProperties extends Properties("WithPhantom") { 
  // Types must be different
  def prop_typeMiss[T, Value1: Manifest, Value2: Manifest](x: T) : Prop =
    WithPhantom[T, Value1](x) != WithPhantom[T, Value2](x)

  property("typeMiss") =
    forAll { x:Int => prop_typeMiss[Int, Boolean, String](x) }
}

In the github project, you can run these via “xsbt test“, but if you are just following along by copying this into a .scala file, then the easiest way is via “xsbt console“.

$ xsbt console

WithPhantomProperties.check
+ WithPhantom.typeMiss: OK, passed 100 tests.

And then the spec for HMap is more-or-less the same as the spec for Map, but we add an extra check to make sure that lookups in the map for different phantom types also miss.

object HMapProperties extends Properties("HMap") { 
  import ScalaCheckInstances._
  import WithPhantom._ // for TInt, etc

  def prop_empty[TypedKey[_], T](x: TypedKey[T]) : Prop = 
    HMap.empty.get(x) ?= None

  def prop_hit[TypedKey[_], T](m: HMap[TypedKey], x: TypedKey[T], v: T) : Prop = 
    m.put(x, v).get(x) ?= Some(v)

  def prop_miss[TypedKey[_], T](m: HMap[TypedKey], x: TypedKey[T],
                                y: TypedKey[T], v: T) : Prop =
      (x != y) ==> (m.put(y, v).get(x) ?= m.get(x))
    
  // When x == y but T != U
  def prop_typeMiss[TypedKey[_], T, U](m: HMap[TypedKey], x: TypedKey[T],
                                       y: TypedKey[U], v: U) : Prop =
    m.put(y, v).get(x) ?= m.get(x)

  property("empty") = forAll { x:TInt[Int] => prop_empty(x) }

  property("hit") = forAll { (m:HMap[TInt], x: TInt[Int], v: Int) => prop_hit(m, x, v) }
  
  property("miss") = forAll { (m:HMap[TInt], x: TInt[Int], 
                               y: TInt[Int], v: Int) =>
    prop_miss(m, x, y, v)
  }
  
  property("typeMiss") = forAll { (m:HMap[TInt], x: Int, v: Boolean) => 
    prop_typeMiss(m,
                  WithPhantom[Int, Int](x).asInstanceOf[TInt[Int]],
                  WithPhantom[Int, Boolean](x).asInstanceOf[TInt[Boolean]], 
                  v) }
}

And try it in the console

$ xsbt console

scala> HMapProperties.check
+ HMap.empty: OK, passed 100 tests.
+ HMap.hit: OK, passed 100 tests.
+ HMap.miss: OK, passed 100 tests.
+ HMap.typeMiss: OK, passed 100 tests.

All the checks pass! I do have some lingering doubts about equality and hashcodes…

I’m not claiming novelty of idea or implementation; I have simply written these thoughts up as an exercise for myself and hopefully entertainment for you. Here are some other references to similar ideas; please share other related links in the comments.

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