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#lang sicp
;; Chapter 1
;; Building Abstractions with Procedures
;; 1.1
;; The Elements of Programming
#| 1.1 |#
#| 10 |#
#| 10 |#
#| (+ 5 3 4) |#
#| 12 |#
#| (- 9 1) |#
#| 8 |#
#| (/ 6 2) |#
#| 3 |#
#| (+ (* 2 4) (- 4 6)) |#
#| 6 |#
#| (define a 3) |#
#| () |#
#| (define b (+ a 1)) |#
#| () |#
#| (+ a b (* a b)) |#
#| 19 |#
#| (= a b) |#
#| #f |#
#| (if |#
#| (and (> b a) (< b (* a b))) |#
#| b |#
#| a) |#
#| 4 |#
#| (cond |#
#| ((= a 4) 6) |#
#| ((= b 4) (+ 6 7 a)) |#
#| (else 25)) |#
#| 16 |#
#| (+ 2 (if (> b a) b a)) |#
#| 6 |#
#| (* |#
#| (cond |#
#| ((> a b) a) |#
#| ((< a b) b) |#
#| (else -1)) |#
#| (+ a 1)) |#
#| 16 |#
#| 1.2 |#
(/
(+ 5 4 (- 2 (- 3 (+ 6 (/ 4 5)))))
(* 3 (- 6 2) (- 2 7)))
(#%provide square)
(define (square x) (* x x))
(define (sum-of-squares x y) (+ (square x) (square y)))
#| 1.3 |#
(#%provide sos-two-larger)
(define (sos-two-larger a b c)
(if (> a b)
(sum-of-squares a (if (> b c) b c))
(sum-of-squares b (if (> a c) a c))))
#| 1.4 |#
(#%provide a-plus-abs-b)
(define (a-plus-abs-b a b)
((if (> b 0) + -) a b))
#| 1.5 |#
(#%provide p)
(#%provide test)
(define (p) (p))
(define (test x y)
(if (= x 0)
0
y))
#| Applicative order: this will loop forever |#
#| Normal order: this will terminate after one call to test |#
#| (test 0 (p)) |#
(define (average x y)
(/ (+ x y) 2))
(#%provide sqrt-)
(define (sqrt- x)
(define (good-enough? guess)
(< (abs (- (square guess) x)) 0.001))
(define (improve guess)
(average guess (/ x guess)))
(define (sqrt-iter guess)
(if (good-enough? guess)
guess
(sqrt-iter (improve guess))))
(sqrt-iter 1.0))
#| 1.6 |#
(define (new-if pred then-clause else-clause)
(cond
(pred then-clause)
(else else-clause)))
(#%provide sqrt-new)
(define (sqrt-new x)
(define (good-enough? guess)
(< (abs (- (square guess) x)) 0.001))
(define (improve guess)
(average guess (/ x guess)))
(define (sqrt-iter guess)
(new-if (good-enough? guess)
guess
(sqrt-iter (improve guess))))
(sqrt-iter 1.0))
#| 1.7 |#
(#%provide sqrt-delt)
(define (sqrt-delt x)
(define (good-enough? last-guess guess)
(< (/ (abs (- last-guess guess)) x) 0.000000000001))
(define (improve guess)
(average guess (/ x guess)))
(define (sqrt-iter last-guess guess)
(if (good-enough? last-guess guess)
guess
(sqrt-iter guess (improve guess))))
(sqrt-iter 1.0 (improve 1.0)))
(square (sqrt-delt 479800023432748679))
(square (sqrt-delt 0.00000024353))
#| 1.8 |#
(#%provide cube)
(define (cube x) (* x x x))
(#%provide cbrt)
(define (cbrt x)
(define (good-enough? guess)
(< (abs (- (cube guess) x)) 0.001))
(define (improve y)
(/ (+ (/ x (square y)) (* 2 y)) 3))
(define (cbrt-iter guess)
(if (good-enough? guess)
guess
(cbrt-iter (improve guess))))
(cbrt-iter 1.0))
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