hello everybody,                                  well, it's me again. i know what are you thinking, this newbie is really totally brain-less. but i have spent my 6 months of financial-sums to order HtDP from USA and i want to solve 100% of exercises given in the book at any cost even if i need to spend 8 hrs. in front my AMD64. Also Mr. Matthias is very helpful regarding problems faced by newbies. anyway here is the original exercise from the book: --- Exercise 11.4.6.   In exercises <a href="http://htdp.org/2003-09-26/Book/curriculum-Z-H-15.html#node_thm_11.2.2">11.2.2</a>, <a href="http://htdp.org/2003-09-26/Book/curriculum-Z-H-15.html#node_thm_11.4.4">11.4.4</a>, and <a href="http://htdp.org/2003-09-26/Book/curriculum-Z-H-15.html#node_thm_11.4.5">11.4.5</a>, we developed functions that tabulate the mathematical function <code class="scheme">f</code> in various ranges. In both cases, the final function produced a list of <code class="scheme">posn</code>s that was ordered in descending order. That is, an expression like <code class="scheme">(tabulate-f 3)</code> yields the list <div align="left"><pre class="scheme">(cons (make-posn 3 2.4) (cons ( make-posn 2 3.4) (cons (make-posn 1 3.6) (cons (make-posn 0 3.0) empty)))) </pre> </div> If we prefer a list of <code class="scheme">posn</code>s in ascending order, we must look at a different data collection, natural numbers up to a certain point in the chain: A natural number <code class="scheme">[<= 20]</code> (<code class="scheme">N[<=20]</code>) is either <ol><li><code class="scheme">20</code> or </li><li><code class="scheme">(sub1 n)</code> if <code class="scheme">n</code> is a natural number <code class="scheme">[ <= 20]</code>. </li></ol> Of course, in high school, we refer to <code class="scheme">N[<=-1]</code> as the negative integers. Develop the function <a name="node_idx_974"></a> <div align="left"><pre class="scheme">;; <code class="scheme">tabulate-f-up-to-20 : N [<= 20]  <tt>-></tt>  N</code> (define (tabulate-f-up-to-20 n-below-20) ...) </pre></div> which tabulates the values of <code class="scheme">f</code> for natural numbers less than <code class="scheme">20</code>. Specifically, it consumes a natural number <code class="scheme">n</code> less than or equal to <code class="scheme">20</code> and produces a list of <code class="scheme">posn</code>s, each of which has the shape <code class="scheme">(make-posn n (f n))</code> for some <code class="scheme"> n</code> between <code class="scheme">0</code> and <code class="scheme">n</code> (inclusively). ---- i have developed the solution but according to the data-definition it is wrong (i know it) but i am not able to solve it, even i have solved all the previous problems of sec-11. may you help me out? ------------------------ start ---------------------------------------------------------- ;; A natural number [<=20] is either: ;;               1. 20, or ;;               2. (sub1 n) where nis a natural number[<=20] ;; in this case natural numbers end upto 0, because beyond zero starts the series of -ve integers.. ;; which we do not refer to as natural numbers in this case. ;; tabulate-f-upto-20 : N[<=20] -> list ;; to pruduce a list of posns in ascending order which has shape (make-posn n (f n)) for N[<=20] and upto n only. ;; (define (tabulate-f-upto-20 n)..) #| TEMPLATE (define (tabulate-f-upto-20 n)   (cond     [(= n 20)...]                    [else....(tabulate-f-upto-20 (add1 n))...])) ;; (= n 20) it is because we want the list in ascending order ;; 2nd it exactly matches the data-definition (tabulate-f-upto-20 20) ;; expected answer empty (tabulate-f20 5) ;; expected answer (cons (make-posn 0 (f 0))       (cons (make-posn 1 (f 1))             (cons (make-posn 2 (f 2))                   (cons (make-posn 3 (f 3))                         (cons (make-posn 4 (f 4)) (cons (make-posn 5 (f 5)) empty)))))) |# (define (tabulate-f-upto-20 n)   (cond     [(= n 20) empty]                    [else (cons (make-posn n (f n)) (tabulate-f-upto-20 (add1 n)))])) (define (f x)   (+ (* 3 (* x x))      (+ (* -6 x)         -1))) ;; tests (tabulate-f-upto-20 20) ;; expected answer 'empty (tabulate-f-upto-20 5) ;; expected answer (cons (make-posn 0 (f 0))       (cons (make-posn 1 (f 1))             (cons (make-posn 2 (f 2))                   (cons (make-posn 3 (f 3))                         (cons (make-posn 4 (f 4)) (cons (make-posn 5 (f 5)) empty)))))) --------------------------- end ------------------------------------------------------- OUPUT it produces: 'empty -- in 2nd test-case it produces all posn from 5-20 not from 0-5 as problem wants.-- -- "the great intellectuals"