As I am not familiar with TS, I am gonna use F# as an example:

    let sort (iterator: 'b -> 'a list) (collector: 'a list -> 'c) (comparator: 'a -> 'a -> bool)  (collection: 'b) -> 'c =
        ...

I added the type annotations to, hopefully make it clear. The iterator is a helper to convert some arbitrary collection to a list, with the collector turning it back into a collection type again (not necessarily the same.)

For example, the iterator could map from a tree to a list, and the collector then to an array. Or if you already have a list and want a list back, you could pass in the identity function for those.

One call could be the following:

    sort id id (>) somelist

Hope it isn't too unreadable.

Edit: Adjusted the order of the arguments, as the original order wouldn't work too well with partial application.