1.3.4 Procedures as Returned Values

タイトル修正。
lambda

前準備

(define tolerance 0.00001)

(define (fixed-point f first-guess)
  (define (close-enough? v1 v2)
    (< (abs (- v1 v2)) tolerance))
  (define (try guess)
    (let ((next (f guess)))
      (if (close-enough? guess next)
        next
        (try next))))
  (try first-guess))

(define (deriv g)
  (lambda (x)
    (/ (- (g (+ x dx)) (g x))
       dx)))

(define dx 0.00001)

(define (newton-transform g)
  (lambda (x)
    (- x (/ (g x) ((deriv g) x)))))

(define (newtons-method g guess)
  (fixed-point (newton-transform g) guess))

(define (average-damp f)
  (lambda (x) (average x (f x))))

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

1.40

(define (cubic a b c)
  (lambda (x) (+ (* x x x)
                 (* a x x)
                 (* b x)
                 c)))

1.41 (関数を2回適用する関数を返す関数)

(define (double proc)
  (lambda (arg)
    (proc (proc arg))))

1.42 (compose)

(define (compose f g)
  (lambda (x)
    (f (g x))))

1.43

(define (repeated f n)
  (if (= n 0)
    (lambda (x) x)
    (compose f (repeated f (- n 1)))))

1.44

(define (smooth f)
  (lambda (x)
    (/ (+ (f (- x dx))
          (f x)
          (f (+ x dx)))
       3)))

(define (smoothed f n)
  ((repeated smooth n) f))

1.45

(define (nth-root x n m)
  (fixed-point ((repeated average-damp m) (lambda (y) (/ x (expt y (- n 1)))))
               1.0))

1.46 (最後の抽象化)

(define (iterative-improve good-enough? improve-guess)
  (define (guess-until-good-enough guess)
    (if (good-enough? guess)
      guess
      (guess-until-good-enough (improve-guess guess))))
  guess-until-good-enough)

(define (sqrt x)
  ((iterative-improve (lambda (guess) (< (abs (- (* guess guess) x)) 0.001))
                      (lambda (guess) (average guess (/ x guess))))
   1.0))

(define (fixed-point f first-guess)
  ((iterative-improve (lambda (guess) (< (abs (- guess (f guess))) 0.00001))
                      f)
   first-guess))

抽象化完了。