Can't you do this with a GADT? With a GADT, the type of the output can be specified by which branch of the GADT the input matches. Seems quite a similar idea.
Like, append: Vector n t -> Vector m t -> Vector (n+m) t. With GADTs you need to manually lift (+) to work on the types, and then provide proofs that it's compatible with the value-level.
Then you often need singletons for the cases that are more complex- if I have a set of integers, and an int x, and I want to constrain that the item is in the set and is also even, the GADT approach looks like:
doThing :: Singleton Int x -> Singleton (Set Int) s -> IsInSet x s -> IsEven x -> SomeOutput
Which looks reasonable, until you remember that the Singleton type has to have a representation which is convenient to prove things about, not a representation that is convenient/efficient to operate on, which means your proofs will be annoying or your function itself will hardly resemble a "naive" untyped implementation.
Dependent types fix this because your values are "just" values, so it would be something like
doThing :: (x : int) -> (s : set int) -> so (is_in s x) -> so (even x) -> SomeOutput
Here, x and s are just plain values, not a weird wrapper, and is_in and event are ordinary (and arbitrary) library functions.
OTOH you can do this in TypeScript easily without wrapping; it could return a union type `number | string`.
myFunc(x: true): number
myFunc(x: false): string
foo.ts:1:10 - error TS2393: Duplicate function implementation.https://www.typescriptlang.org/play/?#code/GYVwdgxgLglg9mABA...
It's a bit of a hack, though - if you incorrectly implement myFunc so that, say, it returns a string even when x is true, it can violate the overloading assertions without any error or warning.
Being able to use a function along those lines in a type safe manner is still pretty nifty, even if you can't write it with type safety.
The limitation is what comes later in the article - the dependent type can express the relationship between the argument and the returned type. But that's "out of scope" of the question of "typing a function that can return either a number or a string depending on the boolean argument". It only becomes a problem later on because to use the result you need to test the type (using `typeof`) even if you know you which boolean you passed in; that information doesn't end up tracked by the type system - although there actually are a couple of different ways to do this that satisfy this example in TypeScript, as suggested by some other comments.
Just using a union type in TypeScript isn't dissimilar to my suggestion of wrapping the result in an ADT; it's just that TypeScript makes this lightweight.
The union type (or the more or less equivalent Either ADT) don't give you type checking because you can take either (sic) branch no matter what your boolean value was. You're free to write a function that takes false and returns an int, and the type checker will accept that function as correct.
No matter how you twist and turn in GHC Haskell or TypeScript, you can't prevent that just by the type signature alone, so you have to "trust me bro" that the code does what the comment says.
For this example that's trivial and laughable, but being able to trust that code does what the compiler-enforced types say and nothing more is perhaps a step towards addressing supply chain attacks.