;; The length of list L
(define (length L)
    (if (eqv? L '())
        0
        (+ (length (cdr L)) 1)))

;; How do you do this tail-recursively?
(define (length L)
  ;; The length of list P plus the integer n.
  (define (length+ P n)
    (if (null? P)
        n
        (length+ (cdr P) (+ n 1))))
  (length+ L 0))

;; Assumes f is a two-argument function and L is a list.  If L is (x1 x2...xn),
;; the result applying f n-1 times to give (f (f (... (f x1 x2) x3) x4) ...).
;; If L is empty, returns f with no arguments. (Simply Scheme version).
(define (reduce f L)
    (define (reduce-tail so-far L)
      (if (null? L) so-far
          (reduce-tail (f so-far (car L)) (cdr L))))
    (if (null? L) (f) (reduce-tail (car L) (cdr L))))

(define (map1 f L)
  (define (map1-tail results rest)
    (if (null? L) (reverse results)
        (map1-tail (cons (f (car rest))) (cdr rest)))))

;;; Assumes f is a k-argument function and L is a list of equal-length
;;; lists, L1...Ln. Returns the list ((f x11 x21 ...) ... (f x1n ...)), where
;;; xij is item j of list i.
(define (map f . L)
  (define (map-tail results rest)
    (if (null? (car rest)) (reverse results)
        (map-tail (cons (apply f (map1 car L)) results)
                  (map1 cdr L))))
  (map-tail '() L))