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-advanced-reader.ss" "lang")((modname |31.3|) (read-case-sensitive #t) (teachpacks ((lib "draw.ss" "teachpack" "htdp") (lib "arrow.ss" "teachpack" "htdp") (lib "gui.ss" "teachpack" "htdp"))) (htdp-settings #(#t constructor repeating-decimal #t #t none #f ((lib "draw.ss" "teachpack" "htdp") (lib "arrow.ss" "teachpack" "htdp") (lib "gui.ss" "teachpack" "htdp")))))
4 ;product : (listof numbers) -> numbers
5 ;Computes the product of alon0.
6 
7 (define (product alon0)
8   (local ;; the accumulator represents the product of all the numbers preceding alon1 in alon0,
9     ;; ie, it represents the product of (alon1,alon0]
10     ((define (product-accu alon1 accumulator)
11        (cond
12          [(empty? alon1) accumulator]
13          [else (product-accu (rest alon1) (* (first alon1) accumulator))])))
14     (product-accu alon0 1)))
15 
16 (equal? (product '(1 2 3 4 5 6)) 720)
17 
18 ;how-many : (listof X) -> number
19 ;Determines how many items there are in alox0.
20 
21 (define (how-many alox0)
22   (local ;;the accumulator represents the number of items preceding alox1 in alox0
23     ((define (how-many-accu alox1 accumulator)
24        (cond
25          [(empty? alox1) accumulator]
26          [else (how-many-accu (rest alox1) (+ 1 accumulator))])))
27     (how-many-accu alox0 0)))
28 
29 (equal? (how-many '(5 hey joe 5 1 0 true true false)) 9)
30 
31 ;add-to-pi : N -> number
32 ;Adds pi to n.
33 
34 (define (add-to-pi n0)
35   (local ;; the accumulator represents n0-n1+pi.
36     ((define (add-to-pi-accu n1 accumulator)
37        (cond
38          [(zero? n1) accumulator]
39          [else (add-to-pi-accu (sub1 n1) (add1 accumulator))])))
40     (add-to-pi-accu n0 pi)))
41 
42 ;add-to-x : N -> number
43 ;Adds x to n.
44 
45 (define (add-to-x n0 x)
46   (local ;; the accumulator represents n0-n1+x.
47     ((define (add-to-x-accu n1 accumulator)
48        (cond
49          [(zero? n1) accumulator]
50          [else (add-to-x-accu (sub1 n1) (add1 accumulator))])))
51     (add-to-x-accu n0 x)))
52 
53 (equal? (add-to-x 5 6) 11)
54 
55 ;make-palindrome : (listof X) -> (listof X)
56 ;Creates a palindrome from alox (non-empty list).
57 
58 (define (make-palindrome alox0)
59   (local ;The accumulator represents the items in alox0 preceding alox1
60          ;in reverse order as in alox0.
61     ((define (make-palindrome-accu alox1 accumulator)
62        (cond
63          [(empty? alox1) empty]
64          [(empty? (rest alox1)) (cons (first alox1) accumulator)]
65          [else (cons (first alox1)
66                      (make-palindrome-accu (rest alox1) (cons (first alox1) accumulator)))])))
67     (make-palindrome-accu alox0 empty)))
68 
69 (make-palindrome '(a b c 1 5 3))
70 
71 ;is-prime? : N -> boolean
72 ;Determines if n is a prime number.
73 
74 (define (is-prime? n0)
75   (local ;;accumulator i represents the numbers tested from [2,i) in order to
76          ;;determine if n1 is prime
77     ((define (is-prime?-accu n1 i)
78        (cond
79          [(= n1 i) true]
80          [(= (remainder n1 i) 0) false]
81          [else (is-prime?-accu n1 (add1 i))])))
82     (is-prime?-accu n0 2)))
83 
84 (and (is-prime? 2)
85      (is-prime? 3)
86      (not (is-prime? 4))
87      (is-prime? 5)
88      (not (is-prime? 6))
89      (is-prime? 7))