(define (assert a b)
  (cond ((equal? a b) (display "[ok]"))
    (else
      (display "[error] ")
      (display a)
      (display " != ")
      (display b)))
  (newline))

(define (gcd a b)
  (if (= b 0) (abs a) (gcd b (remainder a b))))

(define (average a b) (/ (+ a b) 2.0))
(define (id n) n)
(define identity id)
(define (inc n) (+ n 1))
(define nil '())
(define (divides? a b) (= (remainder b a) 0))
(define (cube n) (* n n n))
(define (even? n) (= (remainder n 2) 0))
(define (odd? n) (= (remainder n 2) 1))

; copied prime? from 1.21
(define (find-divisor n test-divisor)
  (cond ((> (square test-divisor) n) n)
        ((divides? test-divisor n) test-divisor)
        (else (find-divisor n (+ test-divisor 1)))))
(define (smallest-divisor n)
  (find-divisor n 2))
(define (prime? n) (if (= n 1) #f (= n (smallest-divisor n))))

; https://mitpress.mit.edu/sites/default/files/sicp/full-text/book/book-Z-H-15.html
(define (enumerate-interval low high)
  (if (> low high)
      nil
      (cons low (enumerate-interval (+ low 1) high))))

; Returns #t if there is no #f in xs, otherwise returns #f.
(define (all? xs)
  (cond ((null? xs) #t)
        ((eq? (car xs) #f) #f)
        (else (all? (cdr xs)))))

(define (all-eq? xs)
  (cond ((null? xs) #t)
        ((null? (cdr xs)) #t)
        ((eq? (car xs) (cadr xs)) (all-eq? (cdr xs)))
        (else #f)))

(define (fold-right op initial sequence) ; same as accumulate
  (if (null? sequence)
      initial
      (op (car sequence)
          (fold-right op initial (cdr sequence)))))