After some reflection, here is how I think you should proceed:
#lang typed/racket
(: 1+ (Nonnegative-Integer -> Positive-Integer))
(define (1+ n)
(+ n 1))
;; entirely unnecessary but helped me read
(define-type (Maybe α) (U False α))
(define-type NI Nonnegative-Integer)
(define-type LNI (Listof NI))
(define-type VNI (Vectorof NI))
(define-type LVNI (Listof VNI))
(let* ((given : LVNI '(#(1 2) #(3 4) #(5 6)))
(length : NI (1+ (apply max (map (lambda ({x : VNI}) (vector-ref x 0))
given))))
(result : [Vectorof [Maybe NI]] (make-vector length #f)))
(for ((q : VNI (in-list given)))
(vector-set! result (vector-ref q 0) (vector-ref q 1)))
result)
The above -- minus types -- is how I would probably write the code in Racket,
following the style guide. (I would use three defines instead of let* but let's
ignore this point.) I would use
-- given as a parameter (I am guessing here)
-- length to tell the reader that this is the new length of the vector
-- result to spell out what this vector is about
The for-loop would use a single line because it is short and brings across the
idea.
If I were to move this code to Typed Racket, I'd add a type declaration to each
identifier just like in any other (explicitly, statically) typed programming
language. That's what I did, and there was no problem checking and running your
code.
-- Matthias
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