A magical demonstration implements rational number data type in a few codes, showing the succinctness of fp. That’s why i love it always.
I reproduced the code. It runs nearly perfectly under revo. One issue is that revo doesn’t treat fractions good. Although revo has built-in fraction type, as specified in R5RS, it doesn’t deal with the condition of downcasting a fraction back to an integer. For example, (/ (/ 1 2) (/ 1 2)) will result in 1/1, which is not what I expected. The issued was submitted to the revo github repository, issue #1. I’d fix this later.
Besides, revo doesn’t have built-in fraction number syntax. All’d to write now is (/ 1 2), while what I want is to write 1/2 directly. reported as issue #2. Fixation of this issue could involve lexical scanner and syntax parser. I’d work on it later as well.
The exercise left to the readers is:
Exercise 2.1: Define a better version of
make-ratthat handles both positive and negative arguments.make-ratshould normalize the sign so that if the rational number is positive, both the numerator and denominator are positive, and if the rational number is negative, only the numerator is negative.SICP - Page 125 (chinese version: page 58)
Keep working on it.
Just found an incompleteness in revo. It doesn’t cope with negations normally. Since neither syntactic -1 nor functional (- 1) work properly. It was not bug but a requiring function. Reported as issue #3.
My solution is: {% codeblock solution to exercise 2.1 lang:scheme https://github.com/shouya/sicp-exercise/blob/master/2.1.ss#L29 view on github %} (define (make-rat n d) (let* ((xor (lambda (x y) (or (and x (not y)) (and y (not x))))) (neg? (xor (negative? n) (negative? d))) (abs-n (abs n)) (abs-d (abs d)) (g (gcd abs-n abs-d)) (new-n (/ abs-n g)) (new-d (/ abs-d g)) (signed-n (if neg? (- new-n) new-n))) (cons signed-n new-d)))
(define (neg-rat x) (make-rat (- (numer x)) (denom x))) {% endcodeblock %}
Test cases:
(print-rat (add-rat one-half one-third)) ;=> 5/6
(print-rat (add-rat one-third one-third)) ;=> 2/3
(print-rat (add-rat (neg-rat one-half)
one-third)) ;=> -1/6
(print-rat (mul-rat (neg-rat one-third)
(neg-rat one-third))) ;=> 1/9It works as expectation, great.
All right. My feeling to write scheme code was still ambivalent. On one hand I feel quite comfortable to code in scheme, and enjoy the beauty of it. On the other I still can’t write very mature code to dominate scheme as so to ruby. Okay, it’s well yet; just keep going and practice more.