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arithmetic-generic.rkt
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#lang racket
(provide add sub mul div)
(require "numerical.rkt")
(require "getput.rkt")
(require "generic.rkt")
(require "tagged-obj.rkt")
(require racket/trace)
(define (add x y) (apply-generic 'add x y))
(define (sub x y) (apply-generic 'sub x y))
(define (mul x y) (apply-generic 'mul x y))
(define (div x y) (apply-generic 'div x y))
(define (equ? x y) (if (eq? (type-tag x) (type-tag y))
(apply-generic 'equ? x y)
false))
(define (=zero? x) (apply-generic '=zero? x))
(define (exp x y) (apply-generic 'exp x y))
(define (install-scheme-number-package)
(define (tag x) (attach-tag 'scheme-number x))
(put 'add '(scheme-number scheme-number)
(lambda (x y) (tag (+ x y))))
(put 'sub '(scheme-number scheme-number)
(lambda (x y) (tag (- x y))))
(put 'mul '(scheme-number scheme-number)
(lambda (x y) (tag (* x y))))
(put 'div '(scheme-number scheme-number)
(lambda (x y) (tag (/ x y))))
(put 'equ? '(scheme-number scheme-number)
(lambda (x y) (= x y)))
(put 'exp '(scheme-number scheme-number)
(lambda (x y) (tag (expt x y))))
(put '=zero? '(scheme-number) (lambda (x) (= x 0)))
(put 'make 'scheme-number (lambda (x) (tag x)))
'done)
(define (make-scheme-number n)
((get 'make 'scheme-number) n))
(define (install-rational-package)
(define (numer x) (car x))
(define (denom x) (cdr x))
(define (make-rat n d)
(let ((g (gcd n d)))
(cons (/ n g) (/ d g))))
(define (add-rat x y)
(make-rat (+ (* (numer x) (denom y))
(* (numer y) (denom x)))
(* (denom x) (denom y))))
(define (sub-rat x y)
(make-rat (- (* (numer x) (denom y))
(* (numer y) (denom x)))
(* (denom x) (denom y))))
(define (mul-rat x y)
(make-rat (* (numer x) (numer y))
(* (denom x) (denom y))))
(define (div-rat x y)
(make-rat (* (numer x) (denom y))
(* (denom x) (numer y))))
(define (equ? x y)
(= (* (numer x) (denom y))
(* (numer y) (denom x))))
(define (=zero? x) (= (numer x) 0))
(define (tag x) (attach-tag 'rational x))
(put 'add '(rational rational)
(lambda (x y) (tag (add-rat x y))))
(put 'sub '(rational rational)
(lambda (x y) (tag (sub-rat x y))))
(put 'mul '(rational rational)
(lambda (x y) (tag (mul-rat x y))))
(put 'div '(rational rational)
(lambda (x y) (tag (div-rat x y))))
(put 'equ? '(rational rational) equ?)
(put '=zero? '(rational) =zero?)
(put 'make 'rational
(lambda (n d) (tag (make-rat n d))))
'done)
(define (make-rational n d)
((get 'make 'rational) n d))
(define (install-complex-package)
(define (install-rect-package)
(define (real-part z) (car z))
(define (imag-part z) (cdr z))
(define (make-from-real-imag x y) (cons x y))
(define (magnitude z)
(sqrt (+ (square (real-part z))
(square (imag-part z)))))
(define (angle z)
(atan (imag-part z) (real-part z)))
(define (make-from-mag-ang r a)
(cons (* r (cons a)) (* r (sin a))))
(define (equ? x y) (equal? x y))
(define (=zero? x) (and (= 0 (real-part x))
(= 0 (imag-part x))))
(define (tag x) (attach-tag 'rect x))
(put 'real-part '(rect) real-part)
(put 'imag-part '(rect) imag-part)
(put 'magnitude '(rect) magnitude)
(put 'angle '(rect) angle)
(put 'make-from-real-imag 'rect (lambda (x y) (tag (make-from-real-imag x y))))
(put 'make-from-mag-ang 'rect (lambda (r a) (tag (make-from-mag-ang r a))))
(put 'equ? '(rect rect) equ?)
(put '=zero? '(rect) =zero?)
'done)
(define (install-polar-package)
(define (magnitude z) (car z))
(define (angle z) (cdr z))
(define (make-from-mag-ang r a) (cons r a))
(define (real-part z) (* (magnitude z) (cos (angle z))))
(define (imag-part z) (* (magnitude z) (sin (angle z))))
(define (make-from-real-imag x y)
(cons (sqrt (+ (square x) (square y)))
(atan y x)))
(define (equ? x y) (equal? x y))
(define (=zero? x) (= 0 (magnitude x)))
(define (tag x) (attach-tag 'polar x))
(put 'real-part '(polar) real-part)
(put 'imag-part '(polar) imag-part)
(put 'magnitude '(polar) magnitude)
(put 'angle '(polar) angle)
(put 'make-from-real-imag 'polar (lambda (x y) (tag (make-from-real-imag x y))))
(put 'make-from-mag-ang 'polar (lambda (r a) (tag (make-from-mag-ang r a))))
(put 'equ? '(polar polar) equ?)
(put '=zero? '(polar) =zero?)
'done)
(install-rect-package)
(install-polar-package)
(define (real-part z) (apply-generic 'real-part z))
(define (imag-part z) (apply-generic 'imag-part z))
(define (magnitude z) (apply-generic 'magnitude z))
(define (angle z) (apply-generic 'angle z))
(define (equ? x y) (and (= (real-part x) (real-part y))
(= (imag-part x) (imag-part y))))
(define (=zero? x) (apply-generic '=zero? x))
(define (make-from-real-imag x y)
((get 'make-from-real-imag 'rect) x y))
(define (make-from-mag-ang r a)
((get 'make-from-mag-ang 'polar) r a))
(define (add-complex z1 z2)
(make-from-real-imag (+ (real-part z1) (real-part z2))
(+ (imag-part z1) (imag-part z2))))
(define (sub-complex z1 z2)
(make-from-real-imag (- (real-part z1) (real-part z2))
(- (imag-part z1) (imag-part z2))))
(define (mul-complex z1 z2)
(make-from-mag-ang (* (magnitude z1) (magnitude z2))
(+ (angle z1) (angle z2))))
(define (div-complex z1 z2)
(make-from-mag-ang (/ (magnitude z1) (magnitude z2))
(- (angle z1) (angle z2))))
(define (tag z) (attach-tag 'complex z))
(put 'add '(complex complex)
(lambda (z1 z2) (tag (add-complex z1 z2))))
(put 'sub '(complex complex)
(lambda (z1 z2) (tag (sub-complex z1 z2))))
(put 'mul '(complex complex)
(lambda (z1 z2) (tag (mul-complex z1 z2))))
(put 'div '(complex complex)
(lambda (z1 z2) (tag (div-complex z1 z2))))
(put 'make-from-real-imag 'complex
(lambda (x y) (tag (make-from-real-imag x y))))
(put 'make-from-mag-ang 'complex
(lambda (r a) (tag (make-from-mag-ang r a))))
(put 'real-part '(complex) real-part)
(put 'imag-part '(complex) imag-part)
(put 'magnitude '(complex) magnitude)
(put 'angle '(complex) angle)
(put 'equ? '(complex complex) equ?)
(put '=zero? '(complex) =zero?)
'done)
(define (make-complex-from-real-imag x y)
((get 'make-from-real-imag 'complex) x y))
(define (make-complex-from-mag-ang r a)
((get 'make-from-mag-ang 'complex) r a))
(define (real-part z) (apply-generic 'real-part z))
(define (imag-part z) (apply-generic 'imag-part z))
(define (magnitude z) (apply-generic 'magnitude z))
(define (angle z) (apply-generic 'angle z))
(for-each (lambda (x) (x)) (list install-scheme-number-package install-rational-package install-complex-package))
(magnitude (make-complex-from-real-imag 3 4))
(add 4 5)
(equ? 4 4)
(sub (make-complex-from-real-imag 3 4) (make-complex-from-real-imag 4 5))
(equ? (make-rational 3 4) (make-rational 6 8))
(equ? (make-complex-from-real-imag 3 4) (make-complex-from-real-imag 3 4))
(equ? (make-complex-from-real-imag 3 4) (make-complex-from-real-imag 4 3))
(equ? (make-complex-from-mag-ang 3 4) (make-complex-from-real-imag 4 3))
(=zero? 4)
(=zero? 0)
(=zero? (make-rational 0 4))
(=zero? (make-rational 1 4))
(=zero? (make-complex-from-real-imag 3 4))
(=zero? (make-complex-from-real-imag 0 0))
(=zero? (make-complex-from-mag-ang 0 10))
(=zero? (make-complex-from-mag-ang 10 10))
(exp 4 5)