Permutations in Racket

(define (lst-without-first-occurrence-of lst element)
  (cond
    [(empty? lst) empty]
    [(= (first lst) element) (rest lst) ]
    [else (cons (first lst) (lst-without-first-occurrence-of (rest lst) element))]))

(define ( len lst)
  (cond
    [(empty? lst) 0]
    [else (+ 1 (len (rest lst)))]))

(define (last lst)
  (cond
   [(empty? lst)0]
   [(= (len lst) 1) (first lst)]
   [else (last (rest lst))]))


(define (swap lst)
  (cond
    [(empty? lst)0]
    [else(cons (last lst)(lst-without-first-occurrence-of lst (last lst)))]))

(define (factorial n)
  ( if ( = n 0 ) 1 ( * n ( factorial ( - n 1 ) ) ) ) )
(define (is-there? accu-list elementlst)
  (cond
  [(empty? accu-list)#f]
  [(and(empty? accu-list)(empty? elementlst)) #f]
  [(equal? (first accu-list) (list elementlst))#t]
  [else (is-there? (rest accu-list) elementlst)]))

(define (all-permutations-helper lst accu)
  (local
    ((define (all-permutations-helper-accu lst-helper prefix accu)
       (cond
         [(and (empty? lst-helper)(empty? prefix))(all-permutations (swap lst accu))]
         [[empty? prefix] (all-permutations-helper-accu (rest lst-helper) (list (first lst-helper)) accu) ]
         [(is-there? accu prefix) (all-permutations-helper-accu (swap (rest lst-helper)) (first prefix)  accu)]
         [(empty? lst-helper) (all-permutations prefix ( append (list prefix) accu))]
         [(= (len lst-helper)1) (all-permutations-helper-accu (rest lst-helper) (append (list (first lst-helper)) prefix)  accu)]
         [else (all-permutations-helper-accu (swap (rest lst-helper)) (append (list (first lst-helper)) prefix)  accu)])))
   (all-permutations-helper-accu lst empty accu)))

(define (all-permutations lst accu)
  (cond
    [(empty? lst) #f]
    [(= (len accu)(factorial(len lst))) accu]
    [else (all-permutations-helper lst accu)]
  ))

(all-permutations (list 1 2 3) empty)