Existential type?

[dead-claudia]

Here's a case where I need a few existentials. It's for a definition file, where I need to have parameters for Binding and Scheduler, but it doesn't matter to me what they are. All I care about is that they're internally correct (and any doesn't cover this), and I'd rather not simulate it by making the constructor unnecessarily generic.

The alternative for me is to be able to declare additional constructor-specific type parameters that don't carry to other methods, but existentials would make it easier.

export interface Scheduler<Frame, Idle> {
 nextFrame(func: () => any): Frame;
 cancelFrame(frame: Frame): void;
 nextIdle(func: () => any): Idle;
 cancelIdle(frame: Idle): void;
 nextTick(func: () => any): void;
}

export interface Binding<E> extends Component {
 binding: E;

 patchEnd?(): void;

 patchAdd?(
 prev: string | E | void,
 next: string | E | void,
 pos: number,
 ): void;

 patchRemove?(
 prev: string | E | void,
 next: string | E | void,
 pos: number
 ): void;

 patchChange?(
 oldPrev: string | E | void,
 newPrev: string | E | void,
 oldNext: string | E | void,
 newNext: string | E | void,
 oldPos: number,
 newPos: number
 ): void;
}

export class Subtree {
 constructor(
 onError?: (err: Error) => any,
 scheduler?: type<F, I> Scheduler<F, I>
 );

 // ...
}

export class Root extends Subtree {
 constructor(
 component: type<E> Binding<E>,
 onError?: (err: Error) => any,
 scheduler?: type<F, I> Scheduler<F, I>
 );

 // ...
}

[rotemdan]

Hi again :),

I'll try my best to clarify what this means (hopefully my understanding isn't flawed - at least I hope). I took a simple example as a starting point: of a generic type, and a non-generic container type. The container contains a property content which accepts a value matching any instantiation of the generic type, as long as it follows its internal "shape":

interface MyType<T> {
	a: T;
	b: T[];
}

interface Container {
	content<E>: MyType<E>
}

Of course the above doesn't currently compile, but it demonstrates another approach to a possible syntax.

The idea is that the affected property or variable is "modified" by a type parameter, which is always inferred (for the 'write' direction it is conceptually similar to a generic setter method setContent<E>(newContent: MyType<E>) where E is always inferred when called). That type parameter can be passed to any secondary generic type, or even be used to define an anonymous generic type:

interface Container {
	content<E>: {
		a: E;
		b: E[];
	}
}

One thing to note is that if no constraint is imposed over E. It can always be matched with any, meaning that perhaps surprisingly, the following might work:

const c: Container = {
	content: {
		a: 12,
		b: ["a", 6, "c"]
	}
}

Since E can be substituted with any, any type with properties a and b and where b is an array can satisfy MyType<E>.

Even if E was constrained:

interface Container {
	content<E extends number | string>: MyType<E>
}

The above example can still be matched by E = number | string (Edit: or in practice technically also E = any as well, but I was just giving that as an illustration).

Maybe what we need is an "exclusive or" type constraint, that would constrain E to be either number or string, but not the possibility of both:

interface Container {
	content<E extends number ^ string>: MyType<E>
}

const c: Container = {
	content: {
		a: 12,
		b: ["a", 6, "c"]
	}
} // <- Error this time: can't match either `number` or `string` to unify with `MyType`

Another thing to note is that the resulting container type would probably be used mostly as an abstract one, to be inherited by classes or other interfaces, or maybe serve as a constraint for type arguments. When used on its own, trying to read content would return a value whose type always falls back to its existential types' constraints.

[dead-claudia]

Rotem Dan (@rotemdan) I see what you mean. That could work (provided it works for arguments, too). But how would something like this work? (My idea of type<T> Foo<T> similar to Haskell's forall a. Foo a has a similar potential issue, too.)

interface C {
 prop<T>: Array<T>;
}

let c: C = {prop: [2]}
let value = c.prop[0] // What type is this?

With the information provided, this is an opaque type AFAIK.

[rotemdan]

@isiahmeadows

My approach was just an intuitive instinct - a starting point. I can't say I'm an expert in this area but I thought it might be a meaningful contribution.

I felt it might look simple and aesthetically elegant to modify the identifier itself, though that approach still doesn't cover all possible use cases. It only covers:

Properties:

interface C {
 prop<E>: { a: E; b: E[] };
}

Variable declaration (const, let and var):

let c<E>: { a: E; b: E[] }

Function, method and constructor parameters:

function doSomething(c<E>: { a: E; b: E[] }, s: string);

interface I {
 doSomething(c<E>: { a: E; b: E[] }, s: string);
}

class C {
 constructor(c<E>: { a: E; b: E[] }, s: string);
}

This syntax doesn't provide a solution to introduce explicit existential-only type variables into other scopes like entire interfaces or classes, or functions. However since these scopes do allow for "universal" type parameters, these type parameters can be "wrapped" by existentials at the use site:

interface Example<T> {
 a: T;
}

let x<E>: Example<E>;

I'm reading about forall in Haskell (I don't think I understand it 100% at this point) and investigating the flexibility of an equivalent type <T> style syntax. I would be interested in seeing more examples for the scopes where type <T> can be used. Can it wrap arbitrary code blocks? can it wrap type aliases? entire constructors, getters and setters, etc?

[dead-claudia]

Rotem Dan (@rotemdan) I'd say the easiest way to understand existentials is through Haskell's version (Haskell/etc. normally leaves it implicit). Basically, it's a lot like Scheduler<any, any>, except it still validates you're implementing Scheduler with the right internal types.

As a special case, consider polymorphic functions as an existing common special case:

// TypeScript
type Flattener = <T>(arg: T[][]) => T[];
type Flattener = type<T> (arg: T[][]) => T[];

-- Haskell's equivalent
type Flattener = [[a]] -> [a]
type Flattener = forall a. [[a]] -> [a]

[rotemdan]

• In what code positions can type<T> be used? From your examples so far it seems like it could fit in variable declarations, properties, function and constructor parameters and type aliases. What about entire interfaces, methods, constructors?

• Since TypeScript has the any type and unions like number | string. How can the compiler decide whether a literal, say { a: 1, b: [1, "x", "y", 4] } is compatible with a polymorphic type, say type <E> { a: E, b: E[] } since E can always be unified with any? (or number | string etc).

Edit: instantiation -> literal

[rotemdan]

@isiahmeadows

I apologize I forgot to answer your question about:

interface C {
 prop<T>: Array<T>;
}

let c: C = {prop: [2]}
let value = c.prop[0] // What type is this?

When I mentioned that it is "mostly useful in the write direction" I meant that in general it improves type safety only when written to. When read from, the type falls back to a supertype based on the constraint for the existential type parameter (which here is not provided, so I guess can be assumed to be T extends any). So I believe the resulting type of c.prop[0] should be any, unfortunately, unless more sophisticated flow analysis is applied (which might be able to specialize the type only for the particular variable c).

Based on what I read about 'opaque' types so far, I believe this may qualify as one.

Edit: my personal feeling about this is that it is just one more example that demonstrates the 'flakiness' of mutable variables. If all TS variables and properties were immutable, the compiler could easily keep track on the 'internal' types held within an entity bound to an existential type, since once it is first inferred, it cannot be changed anymore. Due to this and many other reasons I'm personally making an effort to come up with a plan to try to move away from mutable variables in my own programming.. ASAP :) .

[rotemdan]

I'll try to demonstrate how this can work with type inference and flow analysis:

For the type:

interface C {
 prop<E>: {
 a: E;
 b: E[];
 }
}

An instance would provide a temporary instantiation, that would be determined by type inference and flow analysis, for example, when a literal is assigned:

let x: C = {
 prop: {
 a: 12,
 b: [1, 2, 3]
 }
}

The declared type of x would remain C but the actual one would be specialized to { prop: { a: number; b: number[] } } (I'm ignoring, for now, the issues with any inference I mentioned earlier).

Trying to assign:

x.prop.b[2] = "hi";

Should fail, however, reassigning x itself with a value implying a different instantiation might work, e.g.:

x = {
 prop: {
 a: "hello",
 b: ["world"]
 }
}

If x was declared with const then the "apparent" type of x would be permanently locked to { prop: { a: number; b: number[] } }.

This is at least how I imagine it could work.

Edit: fixed code examples

---

Edit 2:

After thinking about this for a while, I'm wondering whether prop should be allowed to be reassigned with a value representing a different instantiation as well, e.g.:

x.prop = {
 a: "hello",
 b: ["world"]
}

If that would be allowed (I mean, for both the cases where x was declared as let and const), then flow analysis might need to become more sophisticated as it would need to track the change of type for 'deep' properties in the object tree of x.

[zpdDG4gta8XKpMCd]

forgive my ignorance, isn't wrapping into a closure would be a commonly accepted answer to existential types problem?

[dead-claudia]

Not in the case of declaration files, where you almost never see that.

[cameron-martin]

@isiahmeadows Surely the type of c.prop[0] in your example would be type<T> T with your proposed syntax?

[dead-claudia]

Cameron Martin (@cameron-martin)

Surely the type of c.prop[0] in your example would be type<T> T with your proposed syntax?

That is the correct understanding, but it was Rotem Dan (@rotemdan)'s proposed syntax, not mine - I was just translating a type between the two. The main question I had was this: what is type<T> T equivalent to?

[cameron-martin]

@isiahmeadows possibly Object?