;;; (factorial n) returns n factorial, for n>=0.
(define (factorial n)
    (if (= n 0) 
        1
        (* n (factorial (- n 1)))))

;;; Same function using tail-recursion (= iteration)
(define (factorial n)
    (define (f n val)
        (if (= n 0) 
            val 
            (f (- n 1) (* val n))))
    (f n 1))

;;; (map f vals) returns the list resulting from
;;; applying function f to each value in the list values.
(define (map f vals)
    (if (null? vals)
        '()
        (cons (f (first vals)) (map f (rest vals)))))

;;; (deriv exp var) returns the result of differentiating
;;; the symbolic expression exp wrt the variable var.
(define (deriv exp var)
  (cond ((number? exp) 0)
        ((variable? exp)
         (if (same-variable? exp var) 1 0))
        ((sum? exp)     ; e.g., (+ 2 x (* 3 y))
         (make-sum (map (lambda (exp) (deriv exp var))
                        (summands exp))))
        ((product? exp) ; e.g., (* (+ x 1) (* (+ 2 y) 3))
         (make-sum
           (make-product (multiplier exp)
                         (deriv (multiplicand exp) var))
           (make-product (deriv (multiplier exp) var)
                         (multiplicand exp))))
        (else
         (error "unknown expression type -- DERIV" exp))))