1 665c255d 2023-08-04 jrmu ;; Exercise 2.83. Suppose you are designing a generic arithmetic system for dealing with the tower of types shown in figure 2.25: integer, rational, real, complex. For each type (except complex), design a procedure that raises objects of that type one level in the tower. Show how to install a generic raise operation that will work for each type (except complex).
3 665c255d 2023-08-04 jrmu ;; we have to modify our packages so that we have 4 types: integer, rational, real, and complex
5 665c255d 2023-08-04 jrmu (define (attach-tag type-tag contents)
6 665c255d 2023-08-04 jrmu (if (or (eq? type-tag 'integer)
7 665c255d 2023-08-04 jrmu (eq? type-tag 'real))
9 665c255d 2023-08-04 jrmu (cons type-tag contents)))
10 665c255d 2023-08-04 jrmu (define (type-tag datum)
11 665c255d 2023-08-04 jrmu (cond ((pair? datum) (car datum))
12 665c255d 2023-08-04 jrmu ((exact? datum) 'integer)
13 665c255d 2023-08-04 jrmu ((number? datum) 'real)
14 665c255d 2023-08-04 jrmu ((error "error -- invalid datum" datum))))
15 665c255d 2023-08-04 jrmu (define (contents datum)
16 665c255d 2023-08-04 jrmu (cond ((pair? datum) (cdr datum))
17 665c255d 2023-08-04 jrmu ((exact? datum) datum)
18 665c255d 2023-08-04 jrmu ((number? datum) (exact->inexact datum))
19 665c255d 2023-08-04 jrmu ((error "error -- invalid datum" datum))))
21 665c255d 2023-08-04 jrmu (define (make-table)
22 665c255d 2023-08-04 jrmu (define (assoc key records)
23 665c255d 2023-08-04 jrmu (cond ((null? records) false)
24 665c255d 2023-08-04 jrmu ((equal? key (caar records)) (car records))
25 665c255d 2023-08-04 jrmu (else (assoc key (cdr records)))))
26 665c255d 2023-08-04 jrmu (let ((local-table (list '*table*)))
27 665c255d 2023-08-04 jrmu (define (lookup key-1 key-2)
28 665c255d 2023-08-04 jrmu (let ((subtable (assoc key-1 (cdr local-table))))
29 665c255d 2023-08-04 jrmu (if subtable
30 665c255d 2023-08-04 jrmu (let ((record (assoc key-2 (cdr subtable))))
32 665c255d 2023-08-04 jrmu (cdr record)
35 665c255d 2023-08-04 jrmu (define (insert! key-1 key-2 value)
36 665c255d 2023-08-04 jrmu (let ((subtable (assoc key-1 (cdr local-table))))
37 665c255d 2023-08-04 jrmu (if subtable
38 665c255d 2023-08-04 jrmu (let ((record (assoc key-2 (cdr subtable))))
40 665c255d 2023-08-04 jrmu (set-cdr! record value)
41 665c255d 2023-08-04 jrmu (set-cdr! subtable
42 665c255d 2023-08-04 jrmu (cons (cons key-2 value)
43 665c255d 2023-08-04 jrmu (cdr subtable)))))
44 665c255d 2023-08-04 jrmu (set-cdr! local-table
45 665c255d 2023-08-04 jrmu (cons (list key-1
46 665c255d 2023-08-04 jrmu (cons key-2 value))
47 665c255d 2023-08-04 jrmu (cdr local-table)))))
49 665c255d 2023-08-04 jrmu (define (dispatch m)
50 665c255d 2023-08-04 jrmu (cond ((eq? m 'lookup-proc) lookup)
51 665c255d 2023-08-04 jrmu ((eq? m 'insert-proc!) insert!)
52 665c255d 2023-08-04 jrmu (else (error "Unknown operation -- TABLE" m))))
55 665c255d 2023-08-04 jrmu (define operation-table (make-table))
56 665c255d 2023-08-04 jrmu (define get (operation-table 'lookup-proc))
57 665c255d 2023-08-04 jrmu (define put (operation-table 'insert-proc!))
58 665c255d 2023-08-04 jrmu (define coercion-table (make-table))
59 665c255d 2023-08-04 jrmu (define get-coercion (coercion-table 'lookup-proc))
60 665c255d 2023-08-04 jrmu (define put-coercion (coercion-table 'insert-proc!))
62 665c255d 2023-08-04 jrmu (define (add x y) (apply-generic 'add x y))
63 665c255d 2023-08-04 jrmu (define (sub x y) (apply-generic 'sub x y))
64 665c255d 2023-08-04 jrmu (define (mul x y) (apply-generic 'mul x y))
65 665c255d 2023-08-04 jrmu (define (div x y) (apply-generic 'div x y))
66 665c255d 2023-08-04 jrmu (define (equ? x y) (apply-generic 'equ? x y))
67 665c255d 2023-08-04 jrmu (define (=zero? x) (apply-generic '=zero? x))
68 665c255d 2023-08-04 jrmu (define (raise x) (apply-generic 'raise x))
70 665c255d 2023-08-04 jrmu (define (install-integer-package)
71 665c255d 2023-08-04 jrmu (define (tag x) (attach-tag 'integer x))
72 665c255d 2023-08-04 jrmu (put 'add '(integer integer)
73 665c255d 2023-08-04 jrmu (lambda (x y) (tag (+ x y))))
74 665c255d 2023-08-04 jrmu (put 'sub '(integer integer)
75 665c255d 2023-08-04 jrmu (lambda (x y) (tag (- x y))))
76 665c255d 2023-08-04 jrmu (put 'mul '(integer integer)
77 665c255d 2023-08-04 jrmu (lambda (x y) (tag (* x y))))
78 665c255d 2023-08-04 jrmu (put 'div '(integer integer)
79 665c255d 2023-08-04 jrmu (lambda (x y) (tag (quotient x y))))
80 665c255d 2023-08-04 jrmu ;; (if (integer? (/ x y))
81 665c255d 2023-08-04 jrmu ;; (tag (/ x y))
82 665c255d 2023-08-04 jrmu ;; (div (raise (tag x))
83 665c255d 2023-08-04 jrmu ;; (raise (tag y))))))
84 665c255d 2023-08-04 jrmu ;; ;; we avoided calling make-rational to avoid dependencies
85 665c255d 2023-08-04 jrmu (put 'equ? '(integer integer) =)
86 665c255d 2023-08-04 jrmu (put '=zero? '(integer) zero?)
87 665c255d 2023-08-04 jrmu (put 'make 'integer
89 665c255d 2023-08-04 jrmu (if (exact? n)
91 665c255d 2023-08-04 jrmu (error "Not an exact integer" n))))
92 665c255d 2023-08-04 jrmu (put 'raise '(integer)
93 665c255d 2023-08-04 jrmu (lambda (x) (make-rational x 1)))
96 665c255d 2023-08-04 jrmu (define (install-rational-package)
97 665c255d 2023-08-04 jrmu (define (gcd a b)
100 665c255d 2023-08-04 jrmu (gcd b (remainder a b))))
101 665c255d 2023-08-04 jrmu (define (numer x) (car x))
102 665c255d 2023-08-04 jrmu (define (denom x) (cdr x))
103 665c255d 2023-08-04 jrmu (define (make-rat n d)
104 665c255d 2023-08-04 jrmu (if (not (and (integer? n) (integer? d)))
105 665c255d 2023-08-04 jrmu (error "Both numerator and denominator must be integers"
106 665c255d 2023-08-04 jrmu (list n d))
107 665c255d 2023-08-04 jrmu (let ((g (gcd n d)))
108 665c255d 2023-08-04 jrmu (cons (/ n g) (/ d g)))))
109 665c255d 2023-08-04 jrmu (define (add-rat x y)
110 665c255d 2023-08-04 jrmu (make-rat (+ (* (numer x) (denom y))
111 665c255d 2023-08-04 jrmu (* (numer y) (denom x)))
112 665c255d 2023-08-04 jrmu (* (denom x) (denom y))))
113 665c255d 2023-08-04 jrmu (define (sub-rat x y)
114 665c255d 2023-08-04 jrmu (make-rat (- (* (numer x) (denom y))
115 665c255d 2023-08-04 jrmu (* (numer y) (denom x)))
116 665c255d 2023-08-04 jrmu (* (denom x) (denom y))))
117 665c255d 2023-08-04 jrmu (define (mul-rat x y)
118 665c255d 2023-08-04 jrmu (make-rat (* (numer x) (numer y))
119 665c255d 2023-08-04 jrmu (* (denom x) (denom y))))
120 665c255d 2023-08-04 jrmu (define (div-rat x y)
121 665c255d 2023-08-04 jrmu (make-rat (* (numer x) (denom y))
122 665c255d 2023-08-04 jrmu (* (denom x) (numer y))))
123 665c255d 2023-08-04 jrmu (define (equ-rat? x y)
124 665c255d 2023-08-04 jrmu (and (= (numer x) (numer y))
125 665c255d 2023-08-04 jrmu (= (denom x) (denom y))))
126 665c255d 2023-08-04 jrmu (define (=zero-rat? x) (= (numer x) 0))
127 665c255d 2023-08-04 jrmu (define (tag x) (attach-tag 'rational x))
128 665c255d 2023-08-04 jrmu (put 'add '(rational rational)
129 665c255d 2023-08-04 jrmu (lambda (x y) (tag (add-rat x y))))
130 665c255d 2023-08-04 jrmu (put 'sub '(rational rational)
131 665c255d 2023-08-04 jrmu (lambda (x y) (tag (sub-rat x y))))
132 665c255d 2023-08-04 jrmu (put 'mul '(rational rational)
133 665c255d 2023-08-04 jrmu (lambda (x y) (tag (mul-rat x y))))
134 665c255d 2023-08-04 jrmu (put 'div '(rational rational)
135 665c255d 2023-08-04 jrmu (lambda (x y) (tag (div-rat x y))))
136 665c255d 2023-08-04 jrmu (put 'equ? '(rational rational) equ-rat?)
137 665c255d 2023-08-04 jrmu (put '=zero? '(rational) =zero-rat?)
138 665c255d 2023-08-04 jrmu (put 'make 'rational
139 665c255d 2023-08-04 jrmu (lambda (n d) (tag (make-rat n d))))
140 665c255d 2023-08-04 jrmu (put 'raise '(rational)
141 665c255d 2023-08-04 jrmu (lambda (x) (make-real (/ (numer x) (denom x)))))
145 665c255d 2023-08-04 jrmu (define (install-real-package)
146 665c255d 2023-08-04 jrmu (define (tag x) (attach-tag 'real x))
147 665c255d 2023-08-04 jrmu (put 'add '(real real)
148 665c255d 2023-08-04 jrmu (lambda (x y) (tag (+ x y))))
149 665c255d 2023-08-04 jrmu (put 'sub '(real real)
150 665c255d 2023-08-04 jrmu (lambda (x y) (tag (- x y))))
151 665c255d 2023-08-04 jrmu (put 'mul '(real real)
152 665c255d 2023-08-04 jrmu (lambda (x y) (tag (* x y))))
153 665c255d 2023-08-04 jrmu (put 'div '(real real)
154 665c255d 2023-08-04 jrmu (lambda (x y) (tag (/ x y))))
155 665c255d 2023-08-04 jrmu (put 'equ? '(real real) =)
156 665c255d 2023-08-04 jrmu (put '=zero? '(real) zero?)
157 665c255d 2023-08-04 jrmu (put 'make 'real
158 665c255d 2023-08-04 jrmu (lambda (n)
159 665c255d 2023-08-04 jrmu (if (rational? n)
160 665c255d 2023-08-04 jrmu (tag (exact->inexact n))
162 665c255d 2023-08-04 jrmu (put 'raise '(real)
163 665c255d 2023-08-04 jrmu (lambda (x) (make-complex-from-real-imag x 0)))
167 665c255d 2023-08-04 jrmu (define (install-complex-package)
168 665c255d 2023-08-04 jrmu (define (make-from-real-imag x y)
169 665c255d 2023-08-04 jrmu ((get 'make-from-real-imag 'rectangular) x y))
170 665c255d 2023-08-04 jrmu (define (make-from-mag-ang r a)
171 665c255d 2023-08-04 jrmu ((get 'make-from-mag-ang 'polar) r a))
173 665c255d 2023-08-04 jrmu (define (real-part z) (apply-generic 'real-part z))
174 665c255d 2023-08-04 jrmu (define (imag-part z) (apply-generic 'imag-part z))
175 665c255d 2023-08-04 jrmu (define (magnitude z) (apply-generic 'magnitude z))
176 665c255d 2023-08-04 jrmu (define (angle z) (apply-generic 'angle z))
178 665c255d 2023-08-04 jrmu ;; rectangular and polar representations...
180 665c255d 2023-08-04 jrmu (define (install-complex-rectangular)
181 665c255d 2023-08-04 jrmu (define (make-from-real-imag-rectangular x y)
182 665c255d 2023-08-04 jrmu (cons x y))
183 665c255d 2023-08-04 jrmu (define (make-from-mag-ang-rectangular r a)
184 665c255d 2023-08-04 jrmu (cons (* r (cos a)) (* r (sin a))))
185 665c255d 2023-08-04 jrmu (define (real-part z) (car z))
186 665c255d 2023-08-04 jrmu (define (imag-part z) (cdr z))
187 665c255d 2023-08-04 jrmu (define (magnitude z)
188 665c255d 2023-08-04 jrmu (sqrt (+ (square (real-part z))
189 665c255d 2023-08-04 jrmu (square (imag-part z)))))
190 665c255d 2023-08-04 jrmu (define (angle z) (atan (imag-part z) (real-part z)))
191 665c255d 2023-08-04 jrmu (define (tag x) (attach-tag 'rectangular x))
192 665c255d 2023-08-04 jrmu (put 'real-part '(rectangular) real-part)
193 665c255d 2023-08-04 jrmu (put 'imag-part '(rectangular) imag-part)
194 665c255d 2023-08-04 jrmu (put 'magnitude '(rectangular) magnitude)
195 665c255d 2023-08-04 jrmu (put 'angle '(rectangular) angle)
196 665c255d 2023-08-04 jrmu (put 'make-from-real-imag 'rectangular
197 665c255d 2023-08-04 jrmu (lambda (x y) (tag (make-from-real-imag-rectangular x y))))
198 665c255d 2023-08-04 jrmu (put 'make-from-mag-ang 'rectangular
199 665c255d 2023-08-04 jrmu (lambda (r a) (tag (make-from-mag-ang-rectangular r a))))
201 665c255d 2023-08-04 jrmu (define (install-complex-polar)
202 665c255d 2023-08-04 jrmu (define (make-from-real-imag-polar x y)
203 665c255d 2023-08-04 jrmu (cons (sqrt (+ (square x) (square y)))
204 665c255d 2023-08-04 jrmu (atan y x)))
205 665c255d 2023-08-04 jrmu (define (make-from-mag-ang-polar r a)
206 665c255d 2023-08-04 jrmu (cons r a))
207 665c255d 2023-08-04 jrmu (define (real-part z) (* (magnitude z) (cos (angle z))))
208 665c255d 2023-08-04 jrmu (define (imag-part z) (* (magnitude z) (sin (angle z))))
209 665c255d 2023-08-04 jrmu (define (magnitude z) (car z))
210 665c255d 2023-08-04 jrmu (define (angle z) (cdr z))
211 665c255d 2023-08-04 jrmu (define (tag x) (attach-tag 'polar x))
212 665c255d 2023-08-04 jrmu (put 'real-part '(polar) real-part)
213 665c255d 2023-08-04 jrmu (put 'imag-part '(polar) imag-part)
214 665c255d 2023-08-04 jrmu (put 'magnitude '(polar) magnitude)
215 665c255d 2023-08-04 jrmu (put 'angle '(polar) angle)
216 665c255d 2023-08-04 jrmu (put 'make-from-real-imag 'polar
217 665c255d 2023-08-04 jrmu (lambda (x y) (tag (make-from-real-imag-polar x y))))
218 665c255d 2023-08-04 jrmu (put 'make-from-mag-ang 'polar
219 665c255d 2023-08-04 jrmu (lambda (r a) (tag (make-from-mag-ang-polar r a))))
221 665c255d 2023-08-04 jrmu (install-complex-rectangular)
222 665c255d 2023-08-04 jrmu (install-complex-polar)
223 665c255d 2023-08-04 jrmu ;; end rectangular and polar representations
225 665c255d 2023-08-04 jrmu (define (add-complex z1 z2)
226 665c255d 2023-08-04 jrmu (make-from-real-imag (+ (real-part z1) (real-part z2))
227 665c255d 2023-08-04 jrmu (+ (imag-part z1) (imag-part z2))))
228 665c255d 2023-08-04 jrmu (define (sub-complex z1 z2)
229 665c255d 2023-08-04 jrmu (make-from-real-imag (- (real-part z1) (real-part z2))
230 665c255d 2023-08-04 jrmu (- (imag-part z1) (imag-part z2))))
231 665c255d 2023-08-04 jrmu (define (mul-complex z1 z2)
232 665c255d 2023-08-04 jrmu (make-from-mag-ang (* (magnitude z1) (magnitude z2))
233 665c255d 2023-08-04 jrmu (+ (angle z1) (angle z2))))
234 665c255d 2023-08-04 jrmu (define (div-complex z1 z2)
235 665c255d 2023-08-04 jrmu (make-from-mag-ang (/ (magnitude z1) (magnitude z2))
236 665c255d 2023-08-04 jrmu (- (angle z1) (angle z2))))
237 665c255d 2023-08-04 jrmu (define (equ-complex? z1 z2)
238 665c255d 2023-08-04 jrmu (or (and (= (real-part z1) (real-part z2))
239 665c255d 2023-08-04 jrmu (= (imag-part z1) (imag-part z2))) ;; in case of rounding error
240 665c255d 2023-08-04 jrmu (and (= (magnitude z1) (magnitude z2))
241 665c255d 2023-08-04 jrmu (= (angle z1) (angle z2)))))
242 665c255d 2023-08-04 jrmu (define (=zero-complex? z)
243 665c255d 2023-08-04 jrmu (and (= (real-part z) 0)
244 665c255d 2023-08-04 jrmu (= (imag-part z) 0)))
246 665c255d 2023-08-04 jrmu (define (tag x) (attach-tag 'complex x))
247 665c255d 2023-08-04 jrmu (put 'add '(complex complex)
248 665c255d 2023-08-04 jrmu (lambda (z1 z2) (tag (add-complex z1 z2))))
249 665c255d 2023-08-04 jrmu (put 'sub '(complex complex)
250 665c255d 2023-08-04 jrmu (lambda (z1 z2) (tag (sub-complex z1 z2))))
251 665c255d 2023-08-04 jrmu (put 'mul '(complex complex)
252 665c255d 2023-08-04 jrmu (lambda (z1 z2) (tag (mul-complex z1 z2))))
253 665c255d 2023-08-04 jrmu (put 'div '(complex complex)
254 665c255d 2023-08-04 jrmu (lambda (z1 z2) (tag (div-complex z1 z2))))
255 665c255d 2023-08-04 jrmu (put 'equ? '(complex complex) equ-complex?)
256 665c255d 2023-08-04 jrmu (put '=zero? '(complex) =zero-complex?)
257 665c255d 2023-08-04 jrmu (put 'make-from-real-imag 'complex
258 665c255d 2023-08-04 jrmu (lambda (x y) (tag (make-from-real-imag x y))))
259 665c255d 2023-08-04 jrmu (put 'make-from-mag-ang 'complex
260 665c255d 2023-08-04 jrmu (lambda (r a) (tag (make-from-mag-ang r a))))
263 665c255d 2023-08-04 jrmu (define (make-integer n)
264 665c255d 2023-08-04 jrmu ((get 'make 'integer) n))
265 665c255d 2023-08-04 jrmu (define (make-rational n d)
266 665c255d 2023-08-04 jrmu ((get 'make 'rational) n d))
267 665c255d 2023-08-04 jrmu (define (make-real n)
268 665c255d 2023-08-04 jrmu ((get 'make 'real) n))
269 665c255d 2023-08-04 jrmu (define (make-complex-from-real-imag x y)
270 665c255d 2023-08-04 jrmu ((get 'make-from-real-imag 'complex) x y))
271 665c255d 2023-08-04 jrmu (define (make-complex-from-mag-ang r a)
272 665c255d 2023-08-04 jrmu ((get 'make-from-mag-ang 'complex) r a))
274 665c255d 2023-08-04 jrmu (define (apply-generic op . args)
275 665c255d 2023-08-04 jrmu (let ((type-tags (map type-tag args)))
276 665c255d 2023-08-04 jrmu (let ((proc (get op type-tags)))
278 665c255d 2023-08-04 jrmu (apply proc (map contents args))
279 665c255d 2023-08-04 jrmu (if (= (length args) 2)
280 665c255d 2023-08-04 jrmu (let ((type1 (car type-tags))
281 665c255d 2023-08-04 jrmu (type2 (cadr type-tags))
282 665c255d 2023-08-04 jrmu (a1 (car args))
283 665c255d 2023-08-04 jrmu (a2 (cadr args)))
284 665c255d 2023-08-04 jrmu (let ((t1->t2 (get-coercion type1 type2))
285 665c255d 2023-08-04 jrmu (t2->t1 (get-coercion type2 type1)))
286 665c255d 2023-08-04 jrmu (cond (t1->t2
287 665c255d 2023-08-04 jrmu (apply-generic op (t1->t2 a1) a2))
289 665c255d 2023-08-04 jrmu (apply-generic op a1 (t2->t1 a2)))
291 665c255d 2023-08-04 jrmu (error "No method for these types"
292 665c255d 2023-08-04 jrmu (list op type-tags))))))
293 665c255d 2023-08-04 jrmu (error "No method for these types"
294 665c255d 2023-08-04 jrmu (list op type-tags)))))))
296 665c255d 2023-08-04 jrmu ;; install number packages
298 665c255d 2023-08-04 jrmu (install-integer-package)
299 665c255d 2023-08-04 jrmu (install-rational-package)
300 665c255d 2023-08-04 jrmu (install-real-package)
301 665c255d 2023-08-04 jrmu (install-complex-package)
304 665c255d 2023-08-04 jrmu (define (test-case actual expected)
306 665c255d 2023-08-04 jrmu (display "Actual: ")
307 665c255d 2023-08-04 jrmu (display actual)
309 665c255d 2023-08-04 jrmu (display "Expected: ")
310 665c255d 2023-08-04 jrmu (display expected)
313 665c255d 2023-08-04 jrmu (test-case (equ? (add (make-integer 3) (make-integer 4))
314 665c255d 2023-08-04 jrmu (sub (make-integer 12) (make-integer 5))) #t)
315 665c255d 2023-08-04 jrmu (test-case (equ? (div (make-integer 24) (make-integer 4))
316 665c255d 2023-08-04 jrmu (mul (make-integer 2) (make-integer 3))) #t)
317 665c255d 2023-08-04 jrmu (test-case (equ? (add (make-integer 3) (make-integer 3))
318 665c255d 2023-08-04 jrmu (sub (make-integer 12) (make-integer 5))) #f)
319 665c255d 2023-08-04 jrmu (test-case (equ? (div (make-integer 24) (make-integer 4))
320 665c255d 2023-08-04 jrmu (mul (make-integer 2) (make-integer 2))) #f)
321 665c255d 2023-08-04 jrmu (test-case (=zero? (sub (div (make-integer 24) (make-integer 4))
322 665c255d 2023-08-04 jrmu (mul (make-integer 2) (make-integer 3)))) #t)
323 665c255d 2023-08-04 jrmu (test-case (=zero? (sub (div (make-integer 24) (make-integer 4))
324 665c255d 2023-08-04 jrmu (mul (make-integer 2) (make-integer 4)))) #f)
325 665c255d 2023-08-04 jrmu (test-case (make-integer 5) 5)
326 665c255d 2023-08-04 jrmu (test-case (type-tag (make-integer 5)) 'integer)
327 665c255d 2023-08-04 jrmu (test-case (type-tag (make-real 5)) 'real)
328 665c255d 2023-08-04 jrmu (test-case (make-real 1.66667) 1.66667)
329 665c255d 2023-08-04 jrmu (test-case (make-real (/ 5 3)) 1.66667)
330 665c255d 2023-08-04 jrmu (test-case (type-tag (make-real (/ 5 3))) 'real)
332 665c255d 2023-08-04 jrmu (test-case (div (make-integer 3) (make-integer 4)) 0)
333 665c255d 2023-08-04 jrmu (test-case (=zero? (sub (make-rational 4 1)
334 665c255d 2023-08-04 jrmu (div (add (make-rational 1 2)
335 665c255d 2023-08-04 jrmu (make-rational 3 2))
336 665c255d 2023-08-04 jrmu (mul (make-rational 3 2)
337 665c255d 2023-08-04 jrmu (make-rational 2 6))))) #t)
338 665c255d 2023-08-04 jrmu (test-case (=zero? (sub (make-rational 4 1)
339 665c255d 2023-08-04 jrmu (div (add (make-rational 1 2)
340 665c255d 2023-08-04 jrmu (make-rational 3 2))
341 665c255d 2023-08-04 jrmu (mul (make-rational 3 2)
342 665c255d 2023-08-04 jrmu (make-rational 2 5))))) #f)
343 665c255d 2023-08-04 jrmu (test-case (equ? (add (make-rational 7 2)
344 665c255d 2023-08-04 jrmu (make-rational 2 4))
345 665c255d 2023-08-04 jrmu (div (add (make-rational 1 2)
346 665c255d 2023-08-04 jrmu (make-rational 3 2))
347 665c255d 2023-08-04 jrmu (mul (make-rational 3 2)
348 665c255d 2023-08-04 jrmu (make-rational 2 6)))) #t)
349 665c255d 2023-08-04 jrmu (test-case (equ? (add (make-rational 3 2)
350 665c255d 2023-08-04 jrmu (make-rational 2 4))
351 665c255d 2023-08-04 jrmu (div (add (make-rational 1 2)
352 665c255d 2023-08-04 jrmu (make-rational 3 2))
353 665c255d 2023-08-04 jrmu (mul (make-rational 3 2)
354 665c255d 2023-08-04 jrmu (make-rational 1 6)))) #f)
355 665c255d 2023-08-04 jrmu (test-case (equ? (div (make-rational 4 2)
356 665c255d 2023-08-04 jrmu (make-rational 1 3))
357 665c255d 2023-08-04 jrmu (sub (make-rational 9 1)
358 665c255d 2023-08-04 jrmu (mul (make-rational 4 1)
359 665c255d 2023-08-04 jrmu (make-rational 3 4)))) #t)
360 665c255d 2023-08-04 jrmu (test-case (equ? (div (make-rational 4 2)
361 665c255d 2023-08-04 jrmu (make-rational 1 3))
362 665c255d 2023-08-04 jrmu (sub (make-rational 9 1)
363 665c255d 2023-08-04 jrmu (mul (make-rational 4 1)
364 665c255d 2023-08-04 jrmu (make-rational 3 5)))) #f)
365 665c255d 2023-08-04 jrmu (test-case (equ? (add (make-complex-from-real-imag 3 4)
366 665c255d 2023-08-04 jrmu (make-complex-from-real-imag -5 -3))
367 665c255d 2023-08-04 jrmu '(complex rectangular -2 . 1))
369 665c255d 2023-08-04 jrmu (test-case (equ? (add (make-complex-from-real-imag 3 4.5)
370 665c255d 2023-08-04 jrmu (make-complex-from-real-imag -5 -3))
371 665c255d 2023-08-04 jrmu '(complex rectangular -2 . 1))
373 665c255d 2023-08-04 jrmu (test-case (=zero? (sub (add (make-complex-from-real-imag 3 4)
374 665c255d 2023-08-04 jrmu (make-complex-from-real-imag -5 -3))
375 665c255d 2023-08-04 jrmu '(complex rectangular -2 . 1)))
378 665c255d 2023-08-04 jrmu (test-case (=zero? (sub (add (make-complex-from-real-imag 3 5)
379 665c255d 2023-08-04 jrmu (make-complex-from-real-imag -5 -3))
380 665c255d 2023-08-04 jrmu '(complex rectangular -2 . 1)))
384 665c255d 2023-08-04 jrmu (test-case (raise (make-integer 5)) '(rational 5 . 1))
385 665c255d 2023-08-04 jrmu (test-case (raise (raise (make-integer 5))) 5.)
386 665c255d 2023-08-04 jrmu (test-case (raise (raise (raise (make-integer 5)))) '(complex rectangular 5. . 0))
388 665c255d 2023-08-04 jrmu (test-case (raise (make-rational 5 3)) 1.666667)
389 665c255d 2023-08-04 jrmu (test-case (raise (raise (make-rational 5 3))) '(complex rectangular 1.666667 . 0))
