Contravariance and val

Question

How and why does 'val' and 'case' affect the type system? (Especially the variance)

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scala> class E[-A]
defined class E

scala> class F[-A](val f: E[A] => Unit)
<console>:6: error: contravariant type A occurs in covariant position in type => (E[A]) => Unit of value f
class F[-A](val f: E[A] => Unit)
                       ^  
scala> case class C[-A](f: E[A] => Unit)
<console>:6: error: contravariant type A occurs in covariant position in type => (E[A]) => Unit of value f
   case class C[-A](f: E[A] => Unit)

scala> class F[-A](f: E[A] => Unit)    
defined class F

Answer 1

Consider this:

trait Equal[-A] { def eq(a1: A, a2: A): Boolean }
val e = new Equal[Option[Int]] { 
    def eq(a1: Option[Int], a2: Option[Int]) = a1 forall (x => a2 forall (x ==)) 
}

// Because Equal is contra-variant, Equal[AnyRef] is a subtype of Equal[String]
// Because T => R is contra-variant in T, Equal[AnyRef] => Unit is a supertype
// of Equal[String] => Unit
// So the follow assignment is valid
val f: Equal[AnyRef] => Unit = (e1: Equal[String]) => println(e1.eq("abc", "def"))


// f(e) doesn't compile because of contra-variance
// as Equal[Option[Int]] is not a subtype of Equal[AnyRef]

// Now let's tell Scala we know what we are doing
class F[-A](val f: Equal[A @uncheckedVariance] => Unit)

// And then let's prove we are not:
// Because F is contra-variant, F[Option[Int]] is a subtype of F[AnyRef]
val g: F[Option[Int]] = new F(f)

// And since g.f is Equal[Option[Int]] => Unit, we can pass e to it.
g.f(e) // compiles, throws exception

If f is not visible outside F, this problem can't happen.

Answer 2

Here's a contravariant "output channel" that just prints to the console:

class OutputChannel[-T] {   
  def write(t:T) = println(t); 
}

Here it is in action:

val out:OutputChannel[Any] = new OutputChannel[Any]
out.write(5)

Nothing interesting yet. The cool thing about contravariance is you can now safely assign this output channel to one that accepts any subclass of T:

val out2:OutputChannel[String] = out
out2.write("five")
out2.write(55) //wont compile

Now, imagine if we added a history tracking to the output channel - to give back a List of things that have been sent out thus far.

//!!! as you've seen code like this won't compile w/ contravariant types!!!!
class OutputChannel[-T] {   
  var history:List[T] = Nil
  def write(t:T) = { 
    history = history :+ t;  
    println(t); 
  } 
}

If the above did compile, the user of the String-based output channel would have a problem:

//history(0) is an Int - runtime exception (if scala allowed it to compile)
val firstStringOutputted:String = out2.history(0) 

Since contravariance allows this "narrowing" of types (ie from Any to String here), the type system cannot expose values of type T, such as this "history" field I did, or the "f" field you had.

Other famous "contrarians" are Function and Comparators:

val strHashCode:String => Int = { s:Any => s.hashCode }  //function which works with any object
val strComp:Comparator<String> = new HashCodeComparator()   //comparator object which works with any object

Answer 3

Are you asking what variance is? If you know what variance is, this is self-explanatory. The example without "val" or "case" has no externally visible members involving A, so it can't induce a variance error.

Answer 4

The 'val' means that the field is externally visible. Consider:

val f: E[Any] => Unit = { ... }
val broken: F[Int] = new F[Any](f) // allowed by -A annotation
val f2: E[Int] => Unit = broken.f // must work (types match)
val f3: E[Int] => Unit = f // type error

Basically, we managed to unsafely cast f without acting for it explicitly. This only works is f is visible, i.e. if you define it as a val or use a case class.