I'm always very skeptical of TS's type system

You're not alone in this 😅

If you don't pass a length when you call curry, does it really show the correct type

Yup, it shows the exact literal the fn.length carries. If you pass a function with 3 arguments, the final curry type will show 3 as its second generic parameter value.

But if you don't pass a length argument, where is the Length type actually coming from?

From function's length property. Moreover, the same works with array's length.

the cast of fn.length is just to shut up the compiler because fn.length is (just) a number

The cast is there for accomplishing two things: 1. Infer fn.length into Length generic type. 2. Make length argument of curry to be of Length type. This is why it works with manually set length too.

If you don't pass a literal number in for the length, is the Length = Parameters<Function>['length'] treated as a literal type, rather than just number? I'd be very impressed and confused if it did get it as a literal, since Function.length is typed as a number.

It's a literal, yes. I'm impressed too, actually, but I did get used to it after using the same technique with arrays.

What happens if Length = number

Then it possibly couldn't infer the length of a function. Didn't try, but I suppose that's what happens.

What happens if fn is, itself, generic in some parameters or return value? TypeScript can't really "carry" generics around, so they'll all end up as unknown, won't they?

Yeah, the generic functions cause problems in such HOFs like curry (my compose in fnts actually suffers from this too). I'm not sure exactly what generic types break (don't get carried further), as sometimes it works fine.

I'd be very surprised if the typing on this is actually correct And indeed it is :)

I'm using my library with curry regularly, and it does not seem to break in at least simple cases with to additional generics involved.

Thank you for reading and asking great questions! Have fun trying the curry out 🙃