#lang sicp

(define (square x) (* x x))
;; ===================================================================
;; =========================== generic ops ===========================
;; ===================================================================
(define operation-table '())

(define (assoc key records)
  (cond ((null? records) #f)
        ((equal? key (caar records)) (car records))
        (else (assoc key (cdr records)))))

(define (assoc-op key records)
   (cond ((null? records) #f)
         ((equal? key (caar records)) (car records))
         (else (assoc-op key (cdr records)))))

(define (put op type-tags proc)
  (let ((op-list-entry (assoc-op op operation-table)))
    (if op-list-entry
        (let ((proc-list (cadr op-list-entry)))
           (let ((proc-pair-entry (assoc type-tags proc-list)))
             (if proc-pair-entry
                 (set-cdr! proc-pair-entry proc)
                 (set-car! (cdr op-list-entry)
                           (cons (cons type-tags proc) proc-list)))))
        (set! operation-table
              (cons (list op (list (cons type-tags proc)))
                    operation-table)))))

(define (get op type-tags)
  (let ((op-list-entry (assoc-op op operation-table)))
    (if op-list-entry
        (let ((proc-list (cadr op-list-entry)))
          (let ((proc-pair-entry (assoc type-tags proc-list)))
            (if proc-pair-entry
                (cdr proc-pair-entry)
                #f)))
        #f)))

;; Modified for ex2-78. 
(define (attach-tag type-tag contents)
  (if (equal? type-tag 'scheme-number) 
      contents
      (cons type-tag contents)))
(define (type-tag datum)
  (cond ((pair? datum) (car datum))
        ((number? datum) 'scheme-number)
        (else (error "Bad tagged datum: TYPE-TAG" datum))))
(define (contents datum)
  (cond ((pair? datum) (cdr datum))
        ((number? datum) 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))))))

;; ===================================================================
;; ================= Complex polar and rectangular ===================
;; ===================================================================

(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)))
  ;; 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))))
  'done)
(install-polar-package)

(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))))
  ;; 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))))
  'done)
(install-rectangular-package)


;; ===================================================================
;; ========================= Complex package =========================
;; ===================================================================

(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))
  ;; 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))))

  (put 'real-part '(complex) real-part)
  (put 'imag-part '(complex) imag-part)
  (put 'magnitude '(complex) magnitude)
  (put 'angle '(complex) angle)
  ;; 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 'make-from-mag-ang 'complex
       (lambda (r a) 
         (tag (make-from-mag-ang r a))))
  'done)

(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))

(install-complex-package)

(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 a (make-complex-from-real-imag 3 4))
(magnitude a)
(display a)