#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))))))

;; ===================================================================
;; ========================== Number package =========================
;; ===================================================================

(define (install-scheme-number-package)
  (define (tag x)
    (attach-tag 'scheme-number x))
  (put 'egu? '(scheme-number scheme-number) 
       (lambda (x y) (= x y))) ;Problem 2.79
  (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)))
  ;problem 2.80
  (put '=zero? '(scheme-number)
    (lambda (a) (= a 0)))
  'done)

(install-scheme-number-package)

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


;; ===================================================================
;; ======================== Rational package =========================
;; ===================================================================

(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))))

  ;; z1a/z1b = z2a/z2b  iff z1a*z2b - z2a*z1b = 0
  ;; equ? for problem 2.79
  (define (equ? z1 z2)
    (= (- (* (numer z1) (denom z2))
          (* (numer z2) (denom z1)))
        0))
  ;; interface to rest of the system
  (put 'equ? '(rational rational) equ?)
  (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))))
  ;problem 2.80
  (put '=zero? '(rational)
    (lambda (a) (= (numer a) 0)))
  'done)

(install-rational-package)

(define (make-rational n d)
  ((get 'make 'rational) n d))

;; ===================================================================
;; ================= 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 (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 (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))))

  (define (equ? z1 z2) ; for problem 2.79
    (and (= (real-part z1) (real-part z2)) 
         (= (imag-part z1) (imag-part z2))))
  ;; interface to rest of the system
  (put 'equ? '(complex complex) equ?)
  (put 'real-part '(complex) real-part) ; Changes from problem 2.77
  (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))))
  ;problem 2.80
  (put '=zero? '(complex)
    (lambda (z) (and (= (real-part z) 0) (= (imag-part z) 0))))
  'done)

(install-complex-package)

(define (=zero? a)
  (apply-generic '=zero? 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))
(define (equ? a b)
  (apply-generic 'equ? a b))

(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))
(define b (make-complex-from-real-imag 3 4))
(define c (make-rational 3 4))
(define d (make-rational 6 8))

(newline) (display "Testing for 2.79") (newline)

(display "(equ? (make-complex-from-real-imag 3 4)
      (make-complex-from-real-imag 3 4))") (newline)
(equ? a b)
(display "(equ? (make-rational 3 4)
      (make-rational 6 8))") (newline)
(equ? c d)
(display "(equ? (make-rational 3 4)
      (add (make-rational 3 4) (make-rational 6 8)))") (newline)
(equ? a (apply-generic 'add a b))