Incomplete variance checking

[subtyping] [variance] [typecase] [recursive-types]

With declaration-site variance (see Covariant containers), it is possible to define a class C with a covariant parameter A, so that C[X] is a subtype of C[Y] whenever X is a subtype of Y. However, when typechecking C it is important to verify that all uses of the parameter A are actually compatible with covariance. Many soundness issues have arisen from skipping such checks:

  • Private members may not need checking for variance, but this is subtle. See Privacy violation.

  • Constructor parameters do not normally need to be checked for covariance, as they do not form part of an object's interface. However, some language features can expose constructors in the interface, in which case variance checking must be done. In Scala1, constructors of inner classes are exposed by an object and can refer to the objects' fields, while in Hack2 constructors are accessible through the (assumed covariant) classname type.

    // Counterexample by Martin Odersky
    class C[+A] {
      private[this] var y: A = _
      def getY: A = y
      class Inner(x: A) {
        y = x
    object Test {
      def main(args: Array[String]) = {
        val x = new C[String]
        val y: C[Any] = x
        val i = new y.Inner(1)
        val s: String = x.getY
        // Exception in thread "main" java.lang.ClassCastException:
        // java.lang.Integer cannot be cast to java.lang.String
    // Counterexample by Derek Lam (edited)
    class Base {}
    class Derived extends Base {
        public function __construct(public int $foo) {}
    abstract class A<+T> {
        abstract public function __construct(T $v);
    class B extends A<Derived> {
        public function __construct(Derived $v){echo $v->foo;}
    class C {
        public static function foo(): void {
        public static function bar(classname<A<Base>> $v): void {
            new $v(new Base()); // crashes
  • GADT parameters introduce equations between types when matched on, making it unsound to mark them as either covariant or contravariant. This issue showed up in early versions of OCaml and in Scala3:

    (* Counterexample by Jeremy Yallop *)
    let magic : 'a 'b. 'a -> 'b =
      fun (type a) (type b) (x : a) ->
        let bad_proof (type a) =
          (Refl : (< m : a>, <m : a>) eq :> (<m : a>, < >) eq) in
        let downcast : type a. (a, < >) eq -> < > -> a =
          fun (type a) (Refl : (a, < >) eq) (s : <>) -> (s :> a) in
        (downcast bad_proof ((object method m = x end) :> < >)) # m
    // Counterexample by Owen Healy
    object Test extends App {
      sealed trait Node[+A]
      case class L[C,D](f: C => D) extends Node[C => D]
      def test[A,B](n: Node[A => B]): A => B = n match {
        case l: L[c,d] => l.f
      println {
        test(new L[Int,Int](identity) with
          Node[Nothing]: Node[Int => String])(3): String

    The details of combining GADTs and declaration-site variance are tricky. Giarusso4 describes the problem in detail, and Scherer and Rémy5 identify several cases where they can be soundly combined.

  • Self types allow a class to refer recursively to the type of this, which may be a subtype of the class being defined. However, if the class has type parameters, any use of a self type must count as a use of those parameters. Failure to do so led to a soundness issue in Hack6:

    // Counterexample by Derek Lam
    class Base {}
    class Derived extends Base {
        public function __construct(public int $derived_prop) {}
    final class ImplCov<+T> {
        public function __construct(private T $v) {}
        public function put(this $v): void {
            $this->v = $v->v;
        public function pull(): T {
            return $this->v;
    class Violate {
        public static function foo(ImplCov<Derived> $v): void {
            echo $v->pull()->derived_prop;
            // Wait... Base doesn't have $derived_prop!
        public static function bar(ImplCov<Base> $v): void {
            $v->put(new ImplCov(new Base()));
    // Violate::foo(new ImplCov(new Derived(42))); crashes
  • Local types that are only used inside a single expression and do not escape do not need variance checking, because they don't form part of the interface. However, it's important to verify that they don't escape! Otherwise, a soundness bug arises, as in Scala7:

    // Counterexample by Paul Phillips
    class A[+T] {
      val foo0 = {
        class AsVariantAsIWantToBe { def contains(x: T) = () }
        new AsVariantAsIWantToBe
    object Test {
      def main(args: Array[String]): Unit = {
        val xs: A[String] = new A[String]
        println(xs.foo0 contains "abc")
        println((xs: A[Any]).foo0 contains 5) // crashes
  • Subclasses may introduce new methods which do not respect covariance, producing an invariant subclass of a covariant class. This is not by itself unsound, but can cause unsoundness if the language also supports downcasting by pattern-matching, allowing covariant use of the invariant derived class through the covariant base class. This problem arose in Kotlin8 and in Scala910:

    // Counterexample by Ilya Gorbunov
    // List is covariant, MutableList is an invariant subclass
    private fun <E> List<E>.addAnything(element: E) {
        if (this is MutableList<E>) {
    arrayListOf(1, 2).addAnything("string")
    // Counterexample by Chung-Kil Hur
    sealed abstract class MyADT[+A]
    case object MyNone extends MyADT[Nothing]
    case class MyFun[A](fun: A=>A) extends MyADT[A]
    def data : MyADT[Any] = MyFun((x:Int)=>x+1)
    val foo : Any =
      data match {
        case MyFun(f) => f("a")
        case _ => 0

GADTs meet subtyping (ESOP '13) Gabriel Scherer and Didier Rémy (2013)