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TypeScript is a superset of JavaScript because any JavaScript program is also a Typescript program but not vice versa. There is no contradiction.

> TS as a language is a superset of JS language. TS as a spec is a rough subset of JS spec.

This does not make any sense. A spec which fully describes TypeScript including runtime behavior would include the JavaScript spec and therefore be a superset. The TypeScript spec itself is in no way a subset of the JS spec, sine it descries features and syntax which does not exist in vanilla JavaScript.

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This is how you should think about it: Spec > Language > Code.

Code is an instance of Language (and in structural typing land it can be compatible with multiple languages). Language is an instance (implementation) of Spec.

> sine it descries features and syntax which does not exist in vanilla JavaScript

That's exactly why TS spec is a subset. Take example from the article:

  type B = true extends boolean ? 1 : 0; // 1

Type B is a subset of boolean, meaning there are less objects in the world that satisfy type B.

There are less language implementations in the world that satisfy TS spec than JS spec. Every language that satisfies TS spec also satisfies JS spec. TS spec adds more constraints (requirements) to language implementation compared to JS spec, it is more strict, therefore it's a subset.

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So you are saying the implementation of the Typescript language are a subset of all JavaScript implementations? I guess that is true in a certain sense. But this does not contradict the fact that TypeScript as a language is a superset of JavaScript - rather it follows logically.

(Although in reality the Typescript implementation is a preprocessor, intended to use together with a regular JavaScript engine.)

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Kind of. The language gets confusing because we use subset and superset next to each other, but we put different meaning on them.

{foo: number, bar: string} as type is a subset of both {foo: number} and {bar: string}. It requires it's members to have both properties. You can construct this type using intersection:

  type Foo = {foo: number}
  type Bar = {bar: string}
  type FooBar = foo & bar

{foo: 1, bar: 'hello'} as object is a superset of {foo: 1} and {bar: 'hello'}. It contains both properties. We can construct this object using union (I use pipe instead of spread to illustrate the idea):

  let foo = {foo: 1}
  let bar = {bar: 'hello'}
  let foobar = foo | bar

When I'm saying TS is a superset of JS, I mean it in the object sense. It has all the properties of JS, and some more. All JS programs are also TS programs, but not vice versa. There's more JS programs in the world than TS programs.

When I'm saying TS spec is a subset of JS spec, I mean it in a type sense. Language is an instance of a spec. TS spec has all of the requirements of JS spec, and some more. All TS implementations (languages) will contain JS implementations, but not vice versa. There's more JS implementations in the world, than TS implementations (assuming you can build TS as compiler/interpreter instead of transpiler).

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> All JS programs are also TS programs, but not vice versa. There's more JS programs in the world than TS programs.

I think you are confusing terminology, because those two statements are contradictory.

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You're absolutely right, last statement should be inverted. I think meant to say something else, but at this point I don't remember what it was.

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In any case, the TS spec is a superset of the JS spec, since it incorporates the JS spec. If you don't consider the JS spec as part of the TS spec then they are disjoint sets. But the TS spec cannot be a subset of the JS spec since that would mean it removed some parts of the JS spec, which is not the case.