Making my own helper function

[JJ C]

I am in a course where I have to use beginning student with list abbreviation in Racket to do assignments. 

Below is my code for unique-right, which is supposed to return a list which has only the right most occurrences of the elements of list. 

The restriction in doing the asisngment is that I cannot use any of the built-in functions such as append or member. 

I'd need to re name a function and define it as I was doing below. For example, in the place where I need to use member? I renamed it as mymember.

Now what I am trying to do is define the helper function mymember. I know that that bold part is incorrect but I have no idea at the moment how to make the code correct. 

; unique-right

; List<Any> -> List<Any>

; returns a list which has only the right most occurrences of the elements of lst

(define (unique-right lst)

  (cond

    [(empty? lst) lst]

    [else (if (mymember? (first lst) (rest lst)) (unique-right (rest lst)) (cons (first lst) (unique-right (rest lst))))]))

; mymember

; List<Any> -> List<Any>

; returns a list that has all of the elements of lst plus a non-occurring elt

(define (mymember elt lst)

  (cond

    [(empty? lst) lst]

    [else (if (equal? elt (first lst))

              lst

              (cons (mymember elt (rest lst)))]))

             

[Averell Aquino]

Creating examples will show you what you need to do. Check the examples below if I understood your intention.

; unique-right

; List<Any> -> List<Any>

; returns a list which has only the right most occurrences of the elements of lst

(check-expect (unique-right '()) '())

(check-expect (unique-right (list "a")) (list "a"))

(check-expect (unique-right (list "a" "b" "a")) (list "b" "a"))

(check-expect (unique-right (list "a" "b" "a" "c" "d" "c")) (list "b" "a" "d" "c"))

(define (unique-right lst)

  (cond

    [(empty? lst) '()]

    [else (if (mymember? (first lst) (rest lst))

              (unique-right (rest lst))

              (cons (first lst) (unique-right (rest lst))))]))

; mymember

; Any List<Any> -> Boolean

; is elt in list

(check-expect (mymember? "a" '()) #false)

(check-expect (mymember? "a" (list "a")) #true)

(check-expect (mymember? "c" (list "a" "b" "a")) #false)

(define (mymember? elt lst)

  (cond

    [(empty? lst) #false]

    [else (or (equal? elt (first lst))

              (mymember? elt (rest lst)))]))