Runtime type misinformation


The typing judgement e:Ae : A is a static, syntactic judgement based on the syntax of ee and AA. Sometimes, it would be useful to have a runtime counterpart, allowing expressions like e  ?  Ae ;?; A which evaluate to true if at runtime the expression ee evaluates to a value of type AA. This "??" operator goes by various names, including typecase and instanceof.

In any but the simplest type systems, this is fraught with difficulties. The trouble is that advanced type systems can make finer distinctions than are visible at runtime, so the runtime type check has incomplete information.

For example, using newtype in Haskell it is possible to define a type EscapedString as a new type based on String:

newtype EscapedString = EscapedString String

Crucially, unlike type aliases (type in Haskell, or typedef in C/C++) the two types String and EscapedString are distinct for type checking purposes, causing a type error whenever one is used where the other is expected and ensuring that a forgotten escaping or unescaping causes a compile failure.

This extra checking has no runtime cost, because newtypes in Haskell (and opaque types in ML, and similar features) introduce no extra wrappers: the String and EscapedString have the same representation.

This is fundamentally incompatible with typecase. The expression e ? EscapedString cannot be expected to return true on escaped strings and false on unescaped ones, because at runtime there is no distinction between them. The situation gets even worse with more advanced type systems, since whether ee has type AA may not even be decidable at runtime.

It is possible to mix typecase with advanced type systems by limiting the typecase operator to those types for which sufficient runtime information is available, either by distinguishing static types from dynamic tags (e.g. ML's exn, OCaml's open types), or by specifying the subset of static types that have dynamically-checkable representations (e.g. Haskell's Typeable, Scala's "checkable types").

When this is not done carefully, unsoundness results, in which a runtime tests identifies two types that are statically known to be distinct. This problem has occurred in Scala1 (where the types checked in patterns did not always match the static ones) and some cases remain in Dotty2. The problem also occurs in Hack3 (where information about generics was erased at runtime, so typecase returned true if asked whether a list of ints was a List<string>), in Flow4 (which also performs typecase on erased generics), and in Kotlin5 (where inner classes share runtime information, even if they depend on generic parameters that may vary).

Java has an issue similar to those in Hack and Kotlin, where instanceof checks ignore generic parameters, but avoids unsoundness by limiting which classes can be used for comparison.

// Counterexample by David R. MacIver
object Test extends Application {
    case class L();
    object N extends L();

    def empty(xs : L) : Unit = xs match {
        case x@N => println(x); println(x);

The compiler inserts a cast of xs to N.type, which is unsound:
The pattern match will succeed for any L, because N == L().
// Counterexample by Andrew Kennedy
function mycast<T>(mixed $x, classname<T> $t) : T {
  if ($x instanceof $t) { return $x; }
  else throw new Exception("Type didn't match");
function expectListOfString(List<string> $x) { ... }

// If I write expectListOfString(mycast($y, List::class))
// but with $y having type List<int> then no exception will
// get thrown at runtime (because of generics erasure).
// Counterexample by William Chargin
// @flow
class Box<T> {
  +field: T;
  constructor(x) {
    this.field = x;

function asBox<T>(x: T | Box<T>): Box<T> {
  if (x instanceof Box) {
    // Here, `x` is refined to be `Box<T>`. This is unsound: `T` could
    // well be `Box<U>` for some other `U`. Example below.
    return x;
  } else {
    // whatever
    return new Box(x);

const stringStringBox: Box<Box<string>> = asBox(new Box("wat"));  // unsound!
stringStringBox.field.field.substr(0);  // runtime error
// Counterexample by Vladimir Reshetnikov
class A<T>(var value: T) {
    fun replaceValue(x: Any) : Any {
        class C(var v: T)
        if(x is C) {
            value = x.v
            return x

        return C(value)

fun main(args: Array<String>) {
    val a = A("string")
    a.replaceValue(A(0).replaceValue("something not of type C"))

    // a.value has type String, but now contains integer 0
    val s = a.value // crashes
// This function would do an unsound conversion from Integer to String
// because the cls.cast always passes: it's only checking List
static String bad(Class<List<String>> cls) {
    List<Integer> i = Arrays.asList(42);
    List<String> badList = cls.cast(i);
    String badString = badList.get(0);
    return badString;

// But Java provides no way to get a Class<List<String>>.
// (Arrays.asList("a").getClass() is a Class<? extends List>)

Runtime type tests are also tricky when the value being tested has a union type: see Polymorphic union refinement.