6.090 IAP '05 - Homework 2 Solutions

Problem 1:

#[compound-procedure 12]

11

4

2

;The object 5 is not applicable

122

10

;Unbound variable: yummy

Problem 2:

1. See Lecture 2 Solutions.

2.
(define minutes->days
  (lambda (mins)
    (/ (/ mins minutes-per-hour) hours-per-day)))

(define days->minutes
  (lambda (days)
    (* days hours-per-day minutes-per-hour)))

3.
(define pythagoras
  (lambda (a b)
    (sqrt (+ (square a) (square b)))))

(define square
  (lambda (x) (* x x)))

4.
(define xor
  (lambda (x y) 
    (if (boolean=? x y) 
        #f 
        #t)))

5.
(define censor
  (lambda (s)
    (if (substring? "scheme sucks" s)
	"BEEP"
	s)))


Problem 3:

1.

Plan:  0 * y = 0
       x * y = (x-1) * y + y

(define slow-mul
  (lambda (x y)
    (if (= x 0)
        0
        (+ y (slow-mul (- x 1) y)))))

2.

Plan:  n < 2 -> n is even if n=0
       even? n = even? n-2

(define even?
  (lambda (n)
    (if (< n 2)
        (= n 0)
        (even? (- n 2)))))