bawp.scm

;; Square something
(define (square x) (* x x))

;; Sum of squares
(define (sum-of-squares x y ) (+ (square x) (square y)))

;; Absolute value using cond
(define (abs x)
  (cond ((> x 0) x)
        ((= x 0) 0)
        ((< x 0) (- x))))

;; Another way to eval absolute value
(define (abs2 x)
  (cond ((< x 0) (- x))
        (else x)))

;; Absolute value with if expression
(define (abs3 x)
  (if (< x 0)
      (- x)
      x))

;; A cond that can be undefined
;; With values 1, or less than 0
(define (uncond x)
  (cond ((> x 1) x)
        ((= x 0) 0)))

;; Example of or/not
(define (>= x y)
  (or (> x y) (= x y)))
;; alternatively: (not (< x y))

;; START Exercise 1.1 ;;
10 ; a

(+ 5 3 4) ; b

(- 9 1) ; c

(/ 6 2) ; d

(+ (* 2 4) (- 4 6)) ; e

(define a 3) ; f

(define b (+ a 1)) ; g

(+ a b (* a b)) ; h

(= a b) ; i

(if (and (> b a) (< b (* a b))) ; j
    b
    a)

(cond ((= a 4) 6)
      ((= b 4) (+ 6  7 a))
      (else 25)) ; k

(+ 2 (if (> b a) b a)); l

(* (cond ((> a b) a)
         ((< a b) b)
         (else -1))
   (+ a 1))
;; END Exercise 1.1 ;;

;; START Exercise 1.2 ;;
(/ (+ 5 4 (- 2 (- 3 (+ 6 (/ 4 5)))))
   (* 3 (- 6 2) (- 2 7)))
;; END Exercise 1.2 ;;

;; START Exercise 1.3 ;;
(define (sum-largest-2 x y z)
  (sum-of-squares (or (and (> x y) x) y)
                  (or (and (> z x) z) x)))
;; END Exercise 1.3 ;;

;; Square root by Newton's method
(define (sqrt-iter guess x)
  (if (good-enough? guess x)
      guess
      (sqrt-iter (improve guess x)
                 x)))

;; A guess is improved by avging it with the quotient of the radicand
;; and the old gues
(define (improve guess x)
  (average guess (/ x guess)))

;; Where
(define (average x y)
  (/ (+ x y) 2))

;; By good-enough? we mean we are close enough:
;; the square differs from the radicand by less than predetermined tolerence
(define (good-enough? guess x)
  (< (abs (- (square guess) x)) 0.001))

;; Finally we can always guess that the sqrt is 1
(define (sqrt x)
  (sqrt-iter 1.0 x))