Union types in scala

Posted on January 27, 2013

I’ve done some research  a while ago on union types and found a nice implementation by Miles Sabin but it only works for declaring types of function parameters. And you can also do this with with type classes. What do I mean with “only function parameters”? In “everything is a function” kind of view there are three places to put types

  1. function parameters
  2. value(val or let binding in haskell and the like)
  3. function return type

Even though Miles’ encoding with Curry-Howard isomorphism is ingenious it only applies to point 1. Let’s fix that! Oh yeah you could also use Either but that adds up boilerplate(even with implicits!) and packing. And I want my union types unboxed.

Enter type tags

I first saw this idea in Scalaz and immediately clicked with me. The idea is to combine structural types with existing types. You don’t touch the value, just enhance the compile-time type with a tag. Structural types are, well types that care about structure not name(JVM has nominal type system) and (sadly) use reflection to do stuff at runtime. You can even use it do do clean-ish method invocation with reflection.

type HasFoo = { def foo(): Bar }
//or even
(a:Any).asInstanceOf[{def bar: Int}].bar

But at compile-time they play along very nicely. Only concern if you don’t want reflection is not to use anything at runtime. But you can use type members! They only appear at compilation so this works out perfect. From scalaz

type Tagged[U] = {type Tag=U}
type @@[V,T] = V with Tagged[T]

type ExampleTaggedType = Foo @@ Bar

implicit class Taggable[A](value: A){
  def tag[T] = value.asInstanceOf[A @@ T]

val a = SomeType @@ Baz = someValue.tag[Baz]

Tagged is just a conversion between a regular generic and a structural type with Tag member Type. This allows you to define @@ - that’s simple too: it takes the type and mixes in the structural tag. Foo @@ Bar now means type Foo but with tag Bar, the only difference between them is that values of type Foo @@ Bar now have a member type Tag that will equal Bar. And I threw in an implicit for easier tagging.

Subtyping with existentials

We need one more tool to get everything in place - subtyping. I mean subtyping as in “if A is subtype of B and C is subtype of D then A @@ C is also subtype of B @@ D”. Technical term for this is covariance. And with classes is done by simply adding pluses to type signature like type @@[+V,+T]=… but this doesn’t work for types. You get a compile error as type parameters are used in non-covariant positions. Luckily we can work around this with use-site subtyping. Instead of using type A @@ B you can use X @@ Y for some types X and Y. Quite literaly with this syntax

type Something = X @@ Y forSome {type X; type Y}

And these are existential types. Because X and Y have to exist. Simple. There is some sugar with _(as usual) but it doesn’t work at all places; let’s not get into detail.

Either, or should I say Union

Now that we have the necessary foundation lets take a look at making unboxed version of Either from scala standard library. Conversion is pretty simple: instead of boxing into Left and Right, tag with Left and Right. And instead of being of type Either a value will be some type tagged with Either. I first implemented this with my type hierarchy only to realize I reimplemented(without real functionality) Either.

type Or[A,B] = @@[_, _ <: Either[A,B]]

implicit def any2taggedLeft[A](a:A): A Or Nothing = a.tag[Left[A,Nothing]]

implicit def any2taggedRight[A](a:A): Nothing Or A= a.tag[Right[Nothing,A]]

There is Or type(intended for inline use) that equals something tagged with something that’s a subtype of Either[A,B] - this is anonymous use site subtyping, a workaround for not being able to make tags covariant. And that’s pretty much all there is to it. The two implicits are just for automatic tagging so you can use regular types and compiler will tag them for you to type check union types. And when this code compiled and worked I started cheering. Let me replace my current lack of enthusiasm by use examples to let you fully gasp the implications on your own.

def id[A](a:A):A=a //a helper for testing parameter types

val a: Int Or String = 1
val b: Int Or String = "hi"
val c: Int Or String = 1.2 //does not compile

id[Int Or String](1)
id[Int Or String]("hi")
id[Int Or String[(1.2) //does not compile

def f(n: Int): Int Or String = 
    n: Int Or String 
    "n is negative": Int Or String

As you can see all three requirements from the intro are satisfied while keeping values unboxed. There are some rough edges unfortunately. Compiler refuses to insert tags without explicit type annotations that inform it to insert implicit conversions. Which is kinda weird because it work for regular Either. Still looking into that. And the real letdown is pattern matching. You can’t match against types…compiler just complains about these types not being possible. And it’s kinda right since String isn’t in fact a subtype of Or[String,Int]. Luckily there’s a workaround that’s not too ugly.

(a:Any) match { 
  case _:String => "string"
  case _:Int => "int"

I have an idea how to solve both issues but it involves forking scala standard library and is thus (much) less portable. Of course if anyone has an idea how to convince the compiler to accept (fake) subtypes or how to steer type inference please let me know.

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