Function typing in TypedRacket

Is it possible to write something similar to C++'s

template <typename... T> std::string dup(int n, std::string s, T... tail) {
  std::string result;
  for (int i = 0; i < n; ++i) {
      result += s;
  }
  if constexpr (sizeof...(tail) == 0) {
    return result;
  } else {
    return result + dup(tail...);
  }
}


std::cout << dup(1, std::string("abc"), 2, std::string("xyz"), 3, std::string("a")) << std::endl; // abcxyzxyzaaa

I tried to write the following function in TypedRacket

#lang typed/racket

(: repeat-string (-> Integer String String))
(define (repeat-string n str)
  (apply string-append (build-list n (λ (_) str))))

(: dup (All (T ...) (-> Integer String T ... T String)))
(define (dup n s . tail)
  (define result (repeat-string n s))
  (cond [(empty? tail) result]
        [else (string-append result (apply dup tail))])
  )

but i have typecheck error: Type Checker: Bad arguments to function in 'apply': Domain: Integer String T ... T Arguments: (List T ... T) in: (apply dup tail)

Honestly, i dont understand why arguments are (List T ... T) but not (T ... T). Moreover, the function is correct, untyped Racket produces the correct results

The key to doing this with proper type safety is to specify the type of your function using ->* with a #:rest-star keyword:

#lang typed/racket

;; Version that avoids building an intermediate list
(: repeat-string : Integer String -> String)
(define (repeat-string n s)
  (define len (string-length s))
  (build-string (* n len) (lambda (i) (string-ref s (remainder i len)))))


(: dup (->* (Integer String) #:rest-star (Integer String) String))
(define (dup n s . rest)
  (if (null? rest)
      (repeat-string n s)
      (string-append (repeat-string n s) (apply dup rest))))

(dup 1 "abc" 2 "xyz" 3 "a") ; "abcxyzxyzaaa"

If your function takes a list directly, you can use Rec and List* to create the type signature. You can also then define dup in terms of it:

(: dup* : (Rec IntStrRepeated (U Null (List* Integer String IntStrRepeated))) -> String)
(define (dup* pairs)
  (if (null? pairs)
      ""
      (string-append (repeat-string (car pairs) (cadr pairs)) (dup* (cddr pairs)))))

(: dup (->* (Integer String) #:rest-star (Integer String) String))
(define (dup n s . rest)
  (dup* (list* n s rest)))


(dup* '(1 "abc" 2 "xyz" 3 "a")) ; "abcxyzxyzaaa"