1 ;; The first three lines of this file were inserted by DrScheme. They record metadata
2 ;; about the language level of this file in a form that our tools can easily process.
3 #reader(lib "htdp-intermediate-reader.ss" "lang")((modname 21.2.1) (read-case-sensitive #t) (teachpacks ((lib "draw.ss" "teachpack" "htdp"))) (htdp-settings #(#t constructor repeating-decimal #f #t none #f ((lib "draw.ss" "teachpack" "htdp")))))
4 (local ((define (f x) x))
5   (build-list 4 f))
6 
7 (local ((define (f x) (+ 1 x)))
8   (build-list 4 f))
9 
10 (local ((define (f x)
11           (expt 10 (* -1 
12                       (+ x 1)))))
13   (build-list 4 f))
14 
15 ;evens : N [>=0] -> (listof N [>=0])
16 ;Given n, evens creates a list of the first n even numbers.
17 
18 (define (evens n)
19   (local ((define (evens n)
20             (build-list n f))
21           (define (f n)
22             (* 2
23                (+ 1 n))))
24     (evens n)))
25 
26 #|
27 
28 (define (tabulate op n)
29   (cond
30     [(= n 0) (list (op 0))]
31     [else (cons (op n)
32                 (tabulate op (sub1 n)))]))
33 
34 |#
35 
36 ;tabulate : (number -> X) number -> (listof X)
37 ;Given op and n, tabulate a list of (f x) from x = n to x = 0.
38 
39 (define (tabulate op n)
40   (reverse (build-list (+ n 1) op)))
41 
42 ;diagonal : N [>=0] -> (listof (listof number))
43 ;Creates a list of list of numbers representing a square identity matrix of width and height n with 1's where the row index equals the column index and 0's elsewhere.  Do this by building a list of length n with 1 in the n-th position and 0's elsewhere.  Then, append this list to the previously formed diagonal with a column of 0's appended to it.
44 
45 ;first-row : N [>=0] -> (listof number)
46 ;Given n, create the first row of the n-by-n identity matrix.
47 
48 ;add-col-zero : (listof (listof number)) -> (listof (listof number))
49 ;Given a-diag, add a new column of zeros to the left side of a-diag.
50 
51 (define (diagonal n)
52   (local ((define (diagonal n) 
53             (cond
54               [(zero? n) empty]
55               [else (append (list (build-list n first-row))
56                             (add-col-zero (diagonal (sub1 n))))]))
57           (define (first-row n)
58             (cond
59               [(= n 0) 1]
60               [else 0]))
61           (define (add-col-zero a-diag)
62             (cond
63               [(empty? a-diag) empty]
64               [else (cons (cons 0 (first a-diag))
65                           (add-col-zero (rest a-diag)))])))
66     (diagonal n)))
67 
68 #|
69 
70 ;f : N[>=0] N[>=0] -> (listof number)
71 ;Creates a (listof number) with length l with 1 at the n-th position (the first position has an index of zero) and 0's elsewhere.
72 
73 (define (f n l)
74   (cond
75     [(zero? l) empty]
76     [else ... (sub1 l) ...]))
77 
78 
79         (list 
80          (list 1 0 0)
81          (list 0 1 0)
82          (list 0 0 1)))
83 
84 
85         (list 
86          (list 1 0)
87          (list 0 1)))
88 
89 |#
90 
91 #|
92 Exercise 21.2.1.   Use build-list
93 
94 to define tabulate from exercise 21.1.1; and
95 
96 to define diagonal, which consumes a natural number n and creates a list of lists of 0 and 1. 
97 Example:
98 
99 (equal? (diagonal 3)
100         (list 
101          (list 1 0 0)
102          (list 0 1 0)
103          (list 0 0 1)))
104 Use local if function definitions require auxiliary functions.    Solution
105 
106 ;; build-list : N (N  ->  X)  ->  (listof X)
107 ;; to construct (list (f 0) ... (f (- n 1)))
108 (define (build-list n f) ...)
109 
110 |#