(define (pop stack)
  (let ((var (car stack))
		(ret-stack (cdr stack)))
	(values var ret-stack)))

(define (push var stack)
  (append (list var) stack))

(define (dup stack)
  (let ((head (car stack)))
	(append (list head) stack)))

(define (fact x)
  (define (fact-iter n current)
	(if (= n 1)
	  current
	  (fact-iter (- n 1) (* n current))))
  (fact-iter x 1))

(define (rpn-func func args stack)
  (if (= args 1)
	(let-values (((var stack) (pop stack)))
	  (push (func var) stack))
	(let*-values (((var1 stack) (pop stack))
				  ((var2 stack) (pop stack)))
	  (push (func var1 var2) stack))))

(define (insert-into-alist key val alist)
  (let ((mem? (assq key alist)))
	(if mem?
	  (update-alist key val alist)
	  (append alist (list (cons key val))))))

(define (index-in-alist key alist)
  (let loop ((list (list-copy alist))
			 (index 0))
	(if (= (length list) 0)
	  #f
	  (let ((list-head-key (car (car list))))
		(if (eq? list-head-key key)
		  index
		  (loop (cdr list) (+ index 1)))))))

(define (update-alist key new-val alist)
  (let ((index (index-in-alist key alist)))
	(list-set! alist index (list (cons key new-val)))
	alist))

(define (run-func sym dict stack)
  (let ((func (assq sym dict)))
	(if func
	  ((cdr func) stack dict)
	  (begin
		(display "ERROR: symbol not in dictionary: ")
		(display sym)
		(newline)
		stack))))

(define (swap stack)
  (let ((a (car stack))
		 (b (cadr stack)))
	(append (list b) (list a) (cddr stack))))

(define init-dict 
  (list (cons '$ (lambda (stack dict)
				   (let-values (((var stack) (pop stack)))
					 (display var)
					 (newline)
					 stack)))
		(cons '+ (lambda (stack dict) (rpn-func + 2 stack)))
		(cons '- (lambda (stack dict) (rpn-func - 2 stack)))
		(cons '* (lambda (stack dict) (rpn-func * 2 stack)))
		(cons '/ (lambda (stack dict) (rpn-func / 2 stack)))
		(cons '% (lambda (stack dict) (rpn-func modulo 2 stack)))
		(cons '! (lambda (stack dict) (rpn-func fact 1 stack)))
		(cons 'dup (lambda (stack dict) (dup stack)))
		(cons 'swap (lambda (stack dict) (swap stack)))
		(cons 'sin (lambda (stack dict) (rpn-func sin 1 stack)))
		(cons 'cos (lambda (stack dict) (rpn-func cos 1 stack)))
		(cons 'tan (lambda (stack dict) (rpn-func tan 1 stack)))
		(cons 'trunc (lambda (stack dict) (rpn-func truncate 1 stack)))
		(cons 'ceil (lambda (stack dict) (rpn-func ceiling 1 stack)))
		(cons 'floor (lambda (stack dict) (rpn-func floor 1 stack)))))

(define (user-func-from-list func)
  (lambda (stack dict)
	(let loop ((func func)
			   (stack stack))
	  (if (= (length func) 1)
		(if (number? (car func))
		  (push (car func) stack)
		  (run-func (car func) dict stack))
		(if (number? (car func))
		  (loop (cdr func) (push (car func) stack))
		  (loop (cdr func) (run-func (car func) dict stack)))))))

(define (new-func list dictionary)
  (insert-into-alist (car list) (user-func-from-list (cdr list)) dictionary))

(let loop ((input (read)) 
		   (stack '())
		   (dict init-dict))
  (cond
   ((number? input) (loop (read) (push input stack) dict))
   ((list? input) (loop (read) stack (new-func input dict)))
   ((symbol? input) (loop (read) (run-func input dict stack) dict))
   (else (begin
		   (display "ERROR not valid input: ")
		   (display input)
		   (newline)
		   (loop (read) stack dict)))))