sicp exercise 2.80

;; Exercise 2.80.  Define a generic predicate =zero? that tests if its argument is zero, and install it in the generic arithmetic package. This operation should work for ordinary numbers, rational numbers, and complex numbers.


(define (square x) (* x x))
(define *op-table* (make-hash-table 10))
(define (put op type proc)
  (hash-set! *op-table* (list op type) proc))
(define (get op type)
  (hash-ref *op-table* (list op type) '()))

(define (apply-generic op . param)
  (let ((p (map type param)))
    (apply (get op p) (map contents param))))


(define (attach-tag tag oper)
  (if (number? oper) oper
      (list tag oper)))

(define (type data)
  (if (number? data) 'scheme-number
      (car data)))

(define (contents data)
  (if (number? data) data
      (cadr data)))

(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 (eq? x y) (apply-generic 'eq? x y))
(define (=zero? x) (apply-generic '=zero? x))

(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)))
  (put 'eq? '(scheme-number scheme-number)
       (lambda(x y)(= x y)))
  (put '=zero? '(scheme-number)
       (lambda(x)(= x 0)))
  'done)

(define (make-scheme-number n)
  ((get 'make 'scheme-number) n))

(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))))
  (define (eq? x y)
    (and (= (numer x) (numer y))
         (= (denom x) (denom y))))
  (define (=zero? x)
    (= (numer x) 0))
  ;; 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 'eq? '(rational rational) eq?)
  (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-rectangular-package)
  ;; internal procedures
  (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 (cos a)) (* r (sin a))))
  (define (eq? z1 z2)
    (and (= (real-part z1) (real-part z2))
         (= (imag-part z1) (imag-part z2))))
  (define (=zero? z)
    (and (= (real-part z) 0)
         (= (imag-part z) 0)))
  ;; interface to the rest of the system
  (define (tag x) (attach-tag 'rectangular x))
  (put 'real-part '(rectangular) real-part)
  (put 'imag-part '(rectangular) imag-part)
  (put 'magnitude '(rectangular) magnitude)
  (put 'angle '(rectangular) angle)
  (put 'make-from-real-imag 'rectangular
       (lambda (x y) (tag (make-from-real-imag x y))))
  (put 'make-from-mag-ang 'rectangular
       (lambda (r a) (tag (make-from-mag-ang r a))))
  (put 'eq?    '(rectangular rectangular) eq?)
  (put '=zero? '(rectangular) =zero?)
  'done)

(define (install-polar-package)
  ;; internal procedures
  (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 (eq? z1 z2)
    (and (= (magnitude z1) (magnitude z2))
         (= (angle z1) (angle z2))))
  (define (=zero? z)
    (= (magnitude z) 0))
  ;; interface to the rest of the system
  (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 'eq?   '(polar polar) eq?)
  (put '=zero? '(polar) =zero?)
  'done)
(define (magnitude z)
  (apply-generic 'magnitude z))

(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))
  ;; 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
  (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 'eq? '(complex complex) eq?)
  (put '=zero? '(complex) =zero?)

  (put 'real-part '(complex) real-part)
  (put 'imag-part '(complex) imag-part)
  (put 'magnitude '(complex) magnitude)
  (put 'angle '(complex) angle)

  'done)

(define (make-complex-from-real-imag x y)
  ((get 'make-from-real-imag 'complex) x y))


(install-scheme-number-package)
(install-rational-package)
(install-complex-package)
(install-rectangular-package)
(install-polar-package)

(define z1 (make-complex-from-real-imag 0 0))
(define z2 (make-complex-from-real-imag 4 3))
(display (=zero? z1)) (newline)
(display (=zero? z2)) (newline)
(display (=zero? (make-scheme-number 0))) (newline)
(display (=zero? (make-scheme-number 4))) (newline)
(display (=zero? (make-rational 0 6))) (newline)
(display (=zero? (make-rational 1 6))) (newline)