;; A Queue is a
;;   (list Listof[SchemeValue] Listof[SchemeValue])
;;
;; interpretation: 
;; A Queue (F R) is the sequence (append F (reverse R))
;;
;; INVARIANT: for any Queue (F R), F is null only if R is null.

;; empty : -> Queue
(define empty (lambda ()  (list '() '())))

;; snoc : Queue SchemeValue -> Queue
(define snoc
  (lambda (q v)
    (cond ;; question: why do we know the first clause below is okay?
     ((null? (car q)) (list (list v) '())) 
     (else (list (car q) (cons v (cadr q)))))))

;; isEmpty: Queue -> Boolean
(define isEmpty (lambda (q) (and (null? (car q)) (null? (cadr q)))))

;; head : Queue -> SchemeValue
(define head (lambda (q) (car (car q))))

;; tail : Queue -> Queue
(define tail 
  (lambda (q) 
    (cond 
     ((null? (cdr (car q))) (list (reverse (cadr q)) '()))
     (else (list (cdr (car q)) (cadr q))))))