Recursion with Scheme

recursion.scm

;; (maximum '(1 2 5 4)) -> 5
;; (maximum '()) -> ERROR: maximum of empty list!
(define maximum
  (lambda (xs)
    (cond
      ((null? xs) (error "maximum of empty list!"))
      ((null? (cdr xs)) (car xs))
      (else
        (let ((x (car xs)) (y (maximum (cdr xs))))
          (if (> x y) x y))))))

;; (replicate 3 'a) -> (a a a)
;; (replicate 0 'b) -> ()
(define replicate
  (lambda (n x)
    (cond
      ((<= n 0) '())
      (else (cons x (replicate (- n 1) x))))))

;; (take 3 '(1 1 1 1 1 1)) -> (1 1 1)
;; (take 0 '(a b c)) -> ()
(define take
  (lambda (n l)
    (cond
      ((= n 0) '())
      ((null? l) '())
      (else (cons (car l) (take (- n 1) (cdr l)))))))

;; (reverse '(1 2 3 4 5)) -> (5 4 3 2 1)
;; (reverse '()) -> ()
(define reverse
  (lambda (l)
    (if (null? l)
      '()
      (append (reverse (cdr l)) (list (car l))))))

;; infility 
;; How to use it in scheme ?
(define repeat
  (lambda (n)
    (cons n (repeat n))))

;; (zip '(1 2 3) '(4 5 6)) -> ((1 4) (2 5) (3 6))
;; (zip '(a b c) '(d)) -> ((a d))
(define zip
  (lambda (x y)
    (cond
      ((null? x) '())
      ((null? y) '())
      (else
        (cons (cons (car x) (list (car y)))
              (zip (cdr x) (cdr y)))))))

;; (elem 2 '(1 2 3 4 5)) -> #t
;; (elem 1 '(3 4 5)) -> #f
;; (elem 3 '()) -> #f
(define elem
  (lambda (x l)
    (cond
      ((null? l) #f)
      ((eq? x (car l)) #t)
      (else (elem x (cdr l))))))

;; (filter <= 3 '(1 2 3 4 5)) -> (1 2 3)
;; (filter > 10 '(5 4 3)) -> ()
(define filter
  (lambda (f x l)
    (if (null? l)
      '()
      (let
        ((frst (car l)) (rest (cdr l)))
        (if (f frst x)
          (cons frst (filter f x rest))
          (filter f x rest))))))

;; (quicksort '(1 29 10 23 35 92 22 11)) -> (1 10 11 22 23 29 35 92)
;; (quicksort '()) -> ()
(define quicksort
  (lambda (l)
    (cond
      ((null? l) '())
      (else
        (let
          ((pivt (car l)) (rest (cdr l)))
          (append (quicksort (filter <= pivt rest))
                  (list pivt)
                  (quicksort (filter > pivt rest))))))))