Thursday's Exercise Solutions

Exercise 2:

+
;Valid, value is primitive procedure for addition
2 * 3
;Kinda valid, it's really 3 expressions
(2 * 3)
;Invalid, first subexpression must be a procedure
;error: 2 is not applicable
(* 2 3)
;Valid, value is 6
((* 2 3))
;Invalid, (* 2 3) evaluates to 6, which is not a procedure for the
; outer combination
-3
;Valid, value is -3
- 3
;Kinda valid, it's two expressions
(- 3)
;Valid, value is -3 (subtraction procedure applied to one argument)
(define x 3)
;Valid, value is unspecified
(define x 4 5 6)
;Invalid, more than one value-exp provided
(define x * 1 2)
;Invalid, more than one value-exp provided

Exercise 3:

plan: takes in two numbers, x and y
      keep subtracting y from x until x is less than y
      what's left over is the remainder

(define remainder
  (lambda (x y)
    (if (< x y)
        x
        (remainder (- x y) y))))

Exercise 4:

plan: use remainder
      if y divides x with no remainder, x is divisible by y.

(define divisible?
  (lambda (x y)
    (= (remainder x y) 0)))