It kind of is a type error, in that the error comes from the programmer incorrectly thinking that the function has type t => r, when it actually has type (t, s) => r. It's not a type error from TypeScript's point of view, because according to TypeScript's rules, both t => r and (t, s) => r are subtypes of (t, s, u) => r. The point of type systems is to detect cases where the programmer is wrong about the types of some value they're using, so it is a limitation of TypeScript that it wasn't able to detect the error in this case (I'm not sure if there's a good way to allow it to detect this particular error while also maintaining compatibility with JavaScript, but it is a cost that's being paid for that compatibility).
TS is taking on an impossible challenge in trying to add a robust type system on top of JS without harming compatibility. Its designers have chosen to favour compatibility where the two can’t be reconciled, and that is a reasonable, pragmatic choice. Better a new language that offers some improvements and lots of people actually use than a new language that offers somewhat more improvements that hardly anyone uses?
Unfortunately, this does mean TypeScript’s type system can’t be entirely sound. A classic situation that is also legal according to the rules of TS but “ought” to fail type checking is something like this:
Now arr_num[0] is null, clearly violating the intended type constraint.
This problem could be fixed by making it an error to alias arr_opt to arr_num. However, that might also cause a lot of extra work for anyone trying to migrate an existing JS code base, particularly if the types involved are not of their choosing but instead determined by code written elsewhere.
For example, if you called a library function that returned an Array<number> and you passed that into another library function that required an Array<number | null> and wasn’t going to modify that array, enforcing the constraint could mean that working code was broken for no real benefit.
Then you get into deeper questions about enforcing immutability using the type system, and finding that again you’re building on sand because you still have JS underneath. IMHO, it’s hard to blame the TS designers for not wanting to go down these kinds of rabbit holes.
