1 12687dd9 2023-08-04 jrmu ;; The first three lines of this file were inserted by DrScheme. They record metadata
 2 12687dd9 2023-08-04 jrmu ;; about the language level of this file in a form that our tools can easily process.
 3 12687dd9 2023-08-04 jrmu #reader(lib "htdp-beginner-reader.ss" "lang")((modname 11.2.3) (read-case-sensitive #t) (teachpacks ((lib "draw.ss" "teachpack" "htdp") (lib "arrow.ss" "teachpack" "htdp"))) (htdp-settings #(#t constructor repeating-decimal #f #t none #f ((lib "draw.ss" "teachpack" "htdp") (lib "arrow.ss" "teachpack" "htdp")))))
 4 12687dd9 2023-08-04 jrmu ;A natural-number is
 5 12687dd9 2023-08-04 jrmu ;1. 0 or
 6 12687dd9 2023-08-04 jrmu ;2. (add1 n) where n is a natural-number.
 7 12687dd9 2023-08-04 jrmu ;
 8 12687dd9 2023-08-04 jrmu ;A list-of-symbols is
 9 12687dd9 2023-08-04 jrmu ;1. an empty list or
10 12687dd9 2023-08-04 jrmu ;2. (cons s los) where s is a symbol and
11 12687dd9 2023-08-04 jrmu ;los is a list-of-symbols.
12 12687dd9 2023-08-04 jrmu ;
13 12687dd9 2023-08-04 jrmu ;repeat : natural-number symbol -> list-of-symbols
14 12687dd9 2023-08-04 jrmu ;Given a natural-number n, returns word n times
15 12687dd9 2023-08-04 jrmu ;as a list-of-symbols.
16 12687dd9 2023-08-04 jrmu ;
17 12687dd9 2023-08-04 jrmu ;Template
18 12687dd9 2023-08-04 jrmu ;(define (repeat n word)
19 12687dd9 2023-08-04 jrmu ;  (cond
20 12687dd9 2023-08-04 jrmu ;    [(zero? n) ...]
21 12687dd9 2023-08-04 jrmu ;    [else ... (repeat (sub1 n)) ...]))
22 12687dd9 2023-08-04 jrmu 
23 12687dd9 2023-08-04 jrmu (define (repeat n word)
24 12687dd9 2023-08-04 jrmu   (cond
25 12687dd9 2023-08-04 jrmu     [(zero? n) empty]
26 12687dd9 2023-08-04 jrmu     [else (cons word (repeat (sub1 n) word))]))
27 12687dd9 2023-08-04 jrmu 
28 12687dd9 2023-08-04 jrmu ;; f : number  ->  number
29 12687dd9 2023-08-04 jrmu (define (f x)
30 12687dd9 2023-08-04 jrmu   (+ (* 3 (* x x)) 
31 12687dd9 2023-08-04 jrmu      (+ (* -6 x)
32 12687dd9 2023-08-04 jrmu         -1)))
33 12687dd9 2023-08-04 jrmu ;
34 12687dd9 2023-08-04 jrmu ;A list-of-posns is either
35 12687dd9 2023-08-04 jrmu ;1. an empty list or
36 12687dd9 2023-08-04 jrmu ;2. (cons p lop) where p is a posn and lop is a list-of-posns.
37 12687dd9 2023-08-04 jrmu ;tabulate-f : natural-number -> list-of-posns
38 12687dd9 2023-08-04 jrmu ;Creates a "table".  Returns a list of n posns of the form
39 12687dd9 2023-08-04 jrmu ;(cons (make-posn (f n) n) (cons (make-posn (f (- n 1) (- n 1)))...
40 12687dd9 2023-08-04 jrmu 
41 12687dd9 2023-08-04 jrmu (define (tabulate-f n)
42 12687dd9 2023-08-04 jrmu   (cond
43 12687dd9 2023-08-04 jrmu     [(zero? n) empty]
44 12687dd9 2023-08-04 jrmu     [else (cons (make-posn (f n) n) (tabulate-f (sub1 n)))]))