Function body for a function that consumes a compound data list of universities and produces the name of school with the lowest tuition. BSL RACKET

Hello everyone Im having trouble coding the body for a function that consumes a compound data list of universities and produces the name of the university with the lowest tuition.

The language is BSL Racket.

Compound Data Definition:

(define-struct uni (name tuition))

interp. a university name as a string and its tuition as a 
natural

(define UNI-1 (make-uni "UBC" 28500))
; example of compound data definition

The List Data Definition For The Universities:

ListOfUni is one of:
  - empty
  - (cons uni ListOfUni)
 interp. a list of unis

(cons (make-uni "SFU" 27797) (cons (make-uni "UVIC" 26000) 
    empty))

Function Introduced:

 (lowest? lou) 

This is a function that consumes list of unis and produces the 
name of school with the lowest tuition 

The Check-Expects:

(check-expect (lowest? empty) "none")
(check-expect (lowest? (cons (make-uni "UBC" 28500) empty)) 
"UBC")
(check-expect (lowest? (cons (make-uni "SFU" 27797) (cons (make- 
uni "UVIC" 26000) empty))) "UVIC")

Attempt at function body:

 (define (lowest? lou)
  (cond [(empty? lou) "none"]
        [(empty? (rest lou)) (uni-name (first lou))]
        [else (if  (<(uni-tuition (first lou)) (uni-tuition (lowest? (rest lou))))
                (uni-name (first lou))
                (lowest? (rest lou)))]))

Error Message Given:

1 of the 3 tests failed.

Check failures:
 check-expect encountered the following error instead of the 
expected value, "UVIC". 
   :: uni-tuition: expects an uni, given "UVIC"

I don't understand how to get around this error and still have the code be recursive.

Also Please excuse any formatting errors, this is my first post on StackOverFlow

When you're iterating over the list of universities, you have to return uni struct from each step, because you call uni-tuition on the result: (uni-tuition (lowest? (rest lou)))

But when lou has only one element, your function returns (uni-name (first lou)) and that is a string. That is the meaning of the error message: :: uni-tuition: expects an uni, given "UVIC"

There are probably more ways to solve this exercise, but given BSL limitations (no let, or and and work only for #true and #false values), I had to come up with helper function and "none" university created with (make-uni "none" 0):

(define-struct uni (name tuition))

(define (lowest-helper lou)
  (cond [(empty? lou) (make-uni "none" 0)]
        [(empty? (rest lou)) (first lou)]
        [(< (uni-tuition (first lou))
            (uni-tuition (lowest-helper (rest lou))))
         (first lou)]
        [else
         (lowest-helper (rest lou))]))

(define (lowest? lou)
  (uni-name (lowest-helper lou)))

(check-expect (lowest? empty) "none")
(check-expect (lowest? (cons (make-uni "UBC" 28500) empty)) 
"UBC")
(check-expect (lowest? (cons (make-uni "SFU" 27797)
                             (cons (make-uni "UVIC" 26000) empty))) "UVIC")

Or you can return either "none" or uni struct and add a new function to differentiate between them:

(define (get-name result)
  (if (string? result)
      result
      (uni-name result)))

(define (lowest? lou)
  (get-name (lowest-helper lou)))