(load "util.scm") (display "\nexample - generic arithmetic operations\n") ;; Helpers for generic arithmetic operations (define (attach-tag type-tag contents) (cond ((eq? type-tag 'scheme-number) contents) (else (cons type-tag contents)))) (define (type-tag datum) (cond ((number? datum) 'scheme-number) ((pair? datum) (car datum)) (else (error "Bad tagged datum -- TYPE-TAG" datum)))) (define (contents datum) (cond ((number? datum) datum) ((pair? datum) (cdr datum)) (else (error "Bad tagged datum -- CONTENTS" datum)))) (define (apply-generic op . args) (let ((type-tags (map type-tag args))) (let ((proc (get op type-tags))) (if proc (apply proc (map contents args)) (error "No method for these types -- APPLY-GENERIC" (list op type-tags)))))) (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 'make 'scheme-number (lambda (x) (tag x))) (display "[install-scheme-number-package]\n") 'done) (define (install-rational-package) ;; internal procedures (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)))) ;; interface to rest of the system (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 'make 'rational (lambda (n d) (tag (make-rat n d)))) (display "[install-rational-package]\n") 'done) (define (install-rectangular-package) (define (real-part z) (car z)) (define (imag-part z) (cdr z)) (define (magnitude z) (sqrt (+ (square (real-part z)) (square (imag-part z))))) (define (angle z) (atan (imag-part z) (real-part z))) (define (tag z) (attach-tag 'rectangular z)) (define (make-from-real-imag x y) (tag (cons x y))) (define (make-from-mag-ang r a) (tag (cons (* r (cos a)) (* r (sin a))))) ; interface to the rest of the system (put 'real-part '(rectangular) real-part) (put 'imag-part '(rectangular) imag-part) (put 'magnitude '(rectangular) magnitude) (put 'angle '(rectangular) angle) (put 'make-from-mag-ang 'rectangular make-from-mag-ang) (put 'make-from-real-imag 'rectangular make-from-real-imag) (display "[install-rectangular-package]\n") 'done) (define (install-polar-package) (define (real-part z) (* (magnitude z) (cos (angle z)))) (define (imag-part z) (* (magnitude z) (sin (angle z)))) (define (magnitude z) (car z)) (define (angle z) (cdr z)) (define (tag z) (attach-tag 'polar z)) (define (make-from-real-imag x y) (tag (cons (sqrt (+ (square x) (square y))) (atan y x)))) (define (make-from-mag-ang r a) (tag (cons r a))) ; interface to rest of the system (put 'real-part '(polar) real-part) (put 'imag-part '(polar) imag-part) (put 'magnitude '(polar) magnitude) (put 'angle '(polar) angle) (put 'make-from-mag-ang 'polar make-from-mag-ang) (put 'make-from-real-imag 'polar make-from-real-imag) (display "[install-polar-package]\n") 'done) (define (install-complex-package) ;; imported procedures from rectangular and polar packages (define (make-from-real-imag x y) ((get 'make-from-real-imag 'rectangular) x y)) (define (make-from-mag-ang r a) ((get 'make-from-mag-ang 'polar) r a)) ;; getters (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)) ;; internal procedures (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)))) ;; interface to rest of the system (put 'real-part '(complex) real-part) (put 'imag-part '(complex) imag-part) (put 'magnitude '(complex) magnitude) (put 'angle '(complex) angle) (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)))) (display "[install-complex-package]\n") 'done) ;; constructors (define (make-scheme-number n) ((get 'make 'scheme-number) n)) (define (make-rational n d) ((get 'make 'rational) n d)) (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)) ;; generic operations (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)) (install-scheme-number-package) (install-rational-package) (install-rectangular-package) (install-polar-package) (install-complex-package) (assert (add (make-scheme-number 10) (make-scheme-number 20)) (make-scheme-number 30)) (define p1 (make-complex-from-mag-ang 14.142 0.7853)) (define e1 (make-complex-from-real-imag 10 10)) (assert (add e1 e1) (make-complex-from-real-imag 20 20)) (newline) (display "ex-2.77 - see comments") (newline) ; real-part (and all other selectors are implemented via calls to apply ; generic. The first call to apply generic has the type 'magnitude '(complex). ; By adding the code from Alyssa that call gets dispatched a second time which ; results in a call to apply generic with 'magnitude '(rectangular). This calls ; the actual magnitude function from the rectangular package. (newline) (display "ex-2.78 - simplify scheme number") (newline) ; Solution at the beginning of this file. (assert (add 5 3) 8) (newline) (display "ex-2.79 - equ?") (newline) (newline) (display "ex-2.80 - =zero?") (newline)