This was just going to be a comment on this reddit thread, but then it seemed to take on a life of its own, so I figured I may as well milk it for all it’s worth make a nice post out of it.

Yesterday, the TypeScript guys announced a preview of the new 0.9.0 version of the language featuring generics. I, like a lot of people, was really curious to see what approach they’d take with them. Retrofitting a type system onto a dynamic language is hard and generics are one of the places where that new suit of armor can really chafe the squishy flesh underneath.

This is a topic strangely near to my heart for another reason too. I’m on the Dart team and when Dart was announced, we were widely criticized for its type system. Generics are covariant in Dart, which is a mortal sin to many.

Now when any new type system comes out, my first thought is, “I wonder if it’s got covariant generics?” (My second thought is, “God, I need a hobby that doesn’t involve programming languages.”)

Some more caveats before I get going:

I literally spent five minutes poking at this, so I may have things wrong.

Compiling programs with a compiler that isn’t 1.0 yet and claiming that says something about the language specification is asking for trouble.

I, despite my current occupation, am surprisingly bad at reading language specs.

I am currently drinking a fairly strong beer.

OK, party time! After playing around with it a bit, as far as I can tell, TypeScript’s subtype relations are more permissive than I expected. This isn’t necessarily bad, just surprising. As a preamble, let’s define a supertype and subtype:

class Base {} class Derived extends Base {}

Now consider:

class Box < T > { constructor ( public value: T ) {} };

This is the simplest possible generic type.

var a : Box < Base > = new Box < Base > ( null ); var b : Box < Derived > = new Box < Derived > ( null );

These are both fine, as you would expect.

new Box < number > ( "not num" )

This gives:

/generics.ts(5,0): error TS2081: Supplied parameters do not match any signature of call target. /generics.ts(5,0): error TS2085: Could not select overload for 'new' expression.

Looks about right. Now let’s try covariance:

var c : Box < Base > = new Box < Derived > ( null );

No errors. Contravariance?

var d : Box < Derived > = new Box < Base > ( null );

Still no errors. This, I think, makes its type system looser than arrays in Java, and more permissive than Dart. Generics are bivariant in TypeScript.

var e : Box < number > = new Box < string > ( null );

As a sanity check, this does give an error.

/generics.ts(73,4): error TS2012: Cannot convert 'Box<string>' to 'Box<number>': Types of property 'value' of types 'Box<string>' and 'Box<number>' are incompatible.

So it doesn’t just ignore the type parameters, it really is bivariant: it will allow either a subtype or supertype relation for the type parameters, but not no relation at all.

Part of this may be because TypeScript’s type system is structural (neat!). For example:

class A { foo ( arg : Base ) {} } class B { foo ( arg : Derived ) {} }

Here we have two unrelated types that happen to have the same shape (method names and signatures). Perhaps surprisingly, there’s no error here:

var f : A = new B (); var g : B = new A ();

This is perhaps extra surprising because A and B don’t have the exact same signatures: their parameter types for arg are different. So the type system is both structural and allows either supertype or subtypes on parameters.

If the type system is structural, maybe the Box<T> examples only worked then because it had no methods (aside from the value property) that used the type parameter. What if we make sure T shows up in parameter and return positions?

class Box < T > { constructor ( public value: T ) {} takeParam ( arg: T ) {} returnType () : T { return null ; } };

Nope, this makes no difference. Still same behavior as before.

I believe the relevant bits of the spec are:

3.6.2.1 Type Arguments A type reference to a generic type G designates a type wherein all occurrences of G’s type parameters have been replaced with the actual type arguments supplied in the type reference.

I think this basically says that generics are structurally typed and the type relation is determined based on the expanded type where type arguments have been applied. In other words, generic types don’t have type relations, just generic type applications. For example:

class Generic < T > { method ( arg: T ) {} } class NotGeneric { method ( arg: number ) {} } var h : NotGeneric = new Generic < number > ();

This is fine in TypeScript unlike most nominally-typed languages. Pretty neat!

3.8.2 Subtypes and Supertypes S is a subtype of a type T, and T is a supertype of S, if one of the following is true: S’ and T are object types and, for each member M in T, one of the following is true: M is a non-specialized call or construct signature and S’ contains a call or construct signature N where, when substituting ‘Object’ for all type parameters declared by M and N (if any), for parameter positions that are present in both signatures, each parameter type in N is a subtype or supertype of the corresponding parameter type in M , the result type of M is Void, or the result type of N is a subtype of that of M … …

…

My emphasis added. I believe this basically says that to compare two types, you walk their members and compare their types. For method parameters, “subtype or supertype” means bivariance: types go both ways. This is looser than the normal function typing rule which is contravariance for parameters and covariance for returns.

All in all, I find this pretty interesting. TypeScript has both a structural and prototypal type system, so it’s already pretty fascinating from a language design perspective. Allowing bivariance of parameter types is a pretty bold extension of that.

Oh, if you’d like to see this for yourself, here’s how:

$ git clone https://git01.codeplex.com/typescript $ cd typescript $ git checkout develop $ jake local $ chmod +x bin/tsc