SICP/ex-2_77-97.scm

(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)