sicp-define.md

準備

SICPを読むためにやっておくと便利かもしれないこと

http://qiita.com/da1/items/02f7d2f157c7145d58f2

http://yoshiko.hatenablog.jp/entry/2014/04/10/%E6%95%B0%E5%AD%A6%E3%83%BB%E6%83%85%E5%A0%B1%E7%B3%BB%E3%82%92%E5%B0%82%E6%94%BB%E3%81%97%E3%81%A6%E3%81%AA%E3%81%84Web%E3%82%A8%E3%83%B3%E3%82%B8%E3%83%8B%E3%82%A2%E3%81%8CSICP%E3%82%92%E8%AA%AD

defineなど

(define (sqrt-iter guess x) (if (good-enough? guess x) guess (sqrt-iter (improve guess x) x)))

(define (improve guess x) (average guess (/ x guess)))

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

(define (abs x) (cond ((< x 0) (- x)) (else x)))

(define (good-enough? guess x) (< (abs (- (square guess) x)) 0.001))

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

(define (sqrt-iter guess x) (new-if (good-enough? guess x) guess (sqrt-iter (improve guess x) x)))

condによる評価のsqrt-iter

(define (sqrt-iter guess x) (cond ((good-enough? guess x) guess) (else (sqrt-iter (improve guess x) x)) ))

tempoary

(define (new-if predicate then-clause else-clause) (cond (predicate then-clause) (else else-clause)))

(sqrt-iter 1.0 3)

201000000000000

(sqrt-iter 1.0 8000000000000)

立方根のよりよい近似値

(define (improve-cubert guess x) (/ (+ (/ x (square guess)) (* 2 guess) ) 3) )

(define (crt-iter guess x) (if (good-enough-cubert? guess x) guess (crt-iter (improve-cubert guess x) x)))

(define (good-enough-cubert? guess x) (< (abs (- 1 (/ guess (improve-cubert guess x)))) 0.000000001))