some solutions for MIT Press's "structure and interpretation of computer programs", I guess
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(define (square x) (* x x))
(define (average x y)
(/ (+ x y) 2))
(define (improve guess x)
(average guess (/ x guess)))
(define (good-enough? guess x)
(< (abs (- (square guess) x)) 0.001))
(define (sqrt-iter guess x)
(if (good-enough? guess x)
(sqrt-iter (improve guess x) x)))
(define (sqrt x)
(sqrt-iter 1.0 x))
;;; this is where things begin fucking up
;;; it doesn't work because if is a special case
;;; that uses lazy evaluation, thus it doesn't have to
;;; evaluate its parameters.
;;; when testing, i found that in guile, it caused a stack overflow;
;;; whereas in chicken, it caused an infinite loop (maybe).
(define (new-if predicate then-clause else-clause)
(cond (predicate then-clause)
(else else-clause)))
(define (new-sqrt-iter guess x)
(new-if (good-enough? guess x)
(new-sqrt-iter (improve guess x) x)))
(display (sqrt 3))
;;(display (new-sqrt-iter 1.0 2))