Allow object types to have property-like associated types

Edit: Add static Type variant for classes, make abstractness a little clearer, clarify things.

This has probably already been asked before, but a quick search didn't turn up anything.

This is similar, and partially inspired by, Swift's/Rust's associated types and Scala's abstract types.

Rationale

• In complex structures like in virtual DOM components/nodes and in graphs, where there are numerous constraints to check, but they would get cumbersome in a hurry to force off onto the user.
• In dynamic imports, where you never have the module namespace itself until runtime, yet you still want to be able to use types defined within it. Edit: Already addressed elsewhere.
• In types where there's a lot of optional parameters, it'd be easier and more flexible to label which ones you're defining as part of the type.
• In types where you want to specify a single optional parameter, and the required ordering requires you to specify some that you don't want to specify, that would get boilerplatey in a hurry. I've experienced this personally on multiple occasions.
• It would allow fully typing namespaces and named module imports without hard-coded compiler handling.

Proposed Syntax/Semantics

• Each interface and object type may have a number of associated types within it.
• Associated types are checked for assignability like any other usual property, except they live in a different "namespace" from properties. In particular, the type must be assignable to the target's type.
• To access an associated type, you use TypeName.Type, where Type is the name of an associated type.
  • For sugar and namespace compatibility, object.Type is equivalent to (typeof object).Type
• To expect an interface with an associated type, you use Foo & {type Type: Value} or Foo with <Type: Value>.
• To expect an object with an associated type, you use {type Type: Value}.
• To declare an abstract associated type, you use type Type: * within the interface or object type.
• To declare a non-abstract associated type, you use type Type: Default within the interface or object type.
• To constrain an abstract associated type, you use type Type: * extends Super.
• Associated types may be inherited from other interfaces and/or object types.
• Namespaces' types are modified to include the exported types as associated types.
• Classes may also define associated types, optionally with visibility modifiers.
• Associated types may have defaults, in case they aren't defined or further constrained later.
  • Constraining an associated type with an existing default removes the default if and only if the existing constraint is not assignable to the new constraint. For example, {type Foo: string | number = string} & {type Foo: string | number} is assignable to {type Foo: string}, but {type Foo: string | number = string} & {type Foo: number} is not.

Here's what that would look like in syntax:

// Interfaces
interface Foo {
    type Type: *; // abstract
    type Sub: * extends Type; // abstract, constrained
    type Type: Default;
    type Type: * extends Type = Default; // late-bound default
}

// Objects
type Foo = {
    type Type: Foo,
}

// Classes
abstract class Foo {
    // Note: outer class *must* be abstract for these, and the keyword is required.
    abstract type Type: *; // abstract
    private abstract type Sub: * extends Type; // abstract, constrained
    protected abstract type Type: * extends Type = Default, // late-bound default

    // Note: outer class *may* be not abstract for these.
    type Type: Default;
    private type Type: Default;

    // Declare an associated type in the class
    // Note: type must not be abstract.
    static Type: Foo;
}

Emit

This has no effect on the JavaScript emit as it is purely type-level.

Compatibility

• This is purely additive, making no observably incompatible changes beyond possibly different error messages.
• This has no impact on any existing JavaScript-related proposal.

Other

• It may slow down the type checker a little initially when namespaces are unified, but two optimization points are available, which would recover most of the perf hit, if not all:
  • Associated types could be stored in a per-interface type map.
  • The list of associated types could be initially stored as undefined to avoid generating a large number of empty arrays.
• It should have little effect on editor tooling.

The issue names no files, tests, or entry points, so begin by locating the parser and type-checker code for interfaces, object types, classes, namespaces, and type queries. Read the relevant compiler tests before proposing an implementation. Done means the proposed associated-type syntax and semantics are implemented, checked across the listed cases, and confirmed to have no JavaScript emit changes.