#lang sicp

; Building on top of exercise 2.79

;;;
;;;
;;; Setup for the exercise
;;;
;;;

(define (square x) (* x x))

; Dispatch table: list of rows, structure below:
; one row: (op-tag . (... one cell) (...) (...))
; one cell: ((list of type tags) . procedure)
; essentially, the whole table is an alist of alists
; (list of type tags) is a list of length n for n-ary op
; a unary op can be called with a symbol instead of a list of symbols for a type
; tag, but this will be converted to a length-1 list while searching the table
(define *dispatch-table* '())

;;;
;;; Dispatch table
;;;

; finds member in alist based on tag, which is the car of the row
(define (search-in-list tag list)
  (if (null? list)
      nil
      (let* ((current-member (car list))
             (member-tag (car current-member)))
        (if (equal? member-tag tag)
            current-member ; we don't strip the key when returning
            (search-in-list tag (cdr list))))))

(define (get op-tag init-type-tags)
  (let* ((type-tags (if (symbol? init-type-tags)
                        (list init-type-tags)
                        init-type-tags))
         ; wrap type-tags in a list if it's supplied as a symbol
         (row-1 (search-in-list op-tag *dispatch-table*))
         (row (if (null? row-1) nil (cdr row-1))) ; we strip the name of the row
         (procedure-1 (search-in-list type-tags row))
         (procedure (if (null? procedure-1) nil (cdr procedure-1))))
    (if (null? procedure)
        (error "Procedure not found in dispatch table:" op-tag type-tags)
        procedure)))

(define (add-pair! alist tag value)
  (set! alist (cons (cons tag value)
                    alist)))

(define (put op-tag init-type-tags procedure)
  (let* ((type-tags (if (symbol? init-type-tags)
                        (list init-type-tags)
                        init-type-tags))
         (search-row (search-in-list op-tag *dispatch-table*))
         ; here we don't strip the key from search-in-list
         (row (if (null? search-row)
                  (begin (set! *dispatch-table* (cons (cons op-tag nil)
                                                      *dispatch-table*))
                         (car *dispatch-table*))
                  search-row))
         (search-cell (search-in-list type-tags (cdr row))))
    (if (null? search-cell)
        (set-cdr! row (cons (cons type-tags procedure)
                            (cdr row)))
        ; attaching new pair to row
        (set-cdr! search-cell procedure))))

;;;
;;; Auxillary functions for type tags
;;;

; The actual exercise 2.78
(define (attach-tag type-tag contents)
  (if (eq? type-tag 'scheme-number)
      contents
      (cons type-tag contents)))
(define (type-tag datum)
  (cond ((pair? datum) (car datum))
        ((number? datum) 'scheme-number)
        (error "Bad tagged datum: TYPE-TAG" datum)))
(define (contents datum)
  (cond ((pair? datum) (cdr datum))
        ((number? datum) datum)
        (error "Bad tagged datum: CONTENTS" datum)))

;;;
;;; Complex packages
;;;

(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)

(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-rectangular-package)
(install-polar-package)

;;;
;;; Apply generic and complex function definitions
;;;


(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 (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))


;;;
;;; Generic function definition
;;;

(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))

;;;
;;; Scheme number package
;;;

(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)))
  ; part of exercise 2.79
  (put 'equ? '(scheme-number scheme-number) =)
  ; part of exercise 2.80
  (put '=zero? '(scheme-number) (lambda (x) (zero? x)))
  'done)
(install-scheme-number-package)

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

;;;
;;; Rational number package
;;;

(define (install-rational-package)
  ;; internal procedures
  (define (numer x) (car x))
  (define (denom x) (cdr x))
  ; Modified to make exercise 2.79 easier to implement
  (define (make-rat n d)
    (let ((g (gcd n d))
          (sign-flip (if (< d 0) -1 1)))
      (cons (/ n g sign-flip) (/ d g sign-flip))))
  (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))))
  ; part of exercise 2.79
  (put 'equ? '(rational rational)
       (lambda (x y) (and (= (numer x) (numer y))
                          (= (denom x) (denom y)))))
  ; part of exercise 2.80
  (put '=zero? '(rational)
       (lambda (x) (= (numer x) 0)))
  'done)
(install-rational-package)
(define (make-rational n d)
  ((get 'make 'rational) n d))

;;;
;;; Complex number 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))))
  ;; 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))))
  
  ; Code added as fix in the exercise 2.77
  (put 'real-part '(complex) real-part)
  (put 'imag-part '(complex) imag-part)
  (put 'magnitude '(complex) magnitude)
  (put 'angle '(complex) angle)
  ; Code added as fix in the exercise
  
  ; part of exercise 2.79
  (put 'equ? '(complex complex)
       (lambda (z1 z2) (and (= (real-part z1) (real-part z2))
                            (= (imag-part z1) (imag-part z2)))))
  ; part of exercise 2.80
  (put '=zero? '(complex)
       (lambda (z) (= (magnitude z) 0)))
  'done)
(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))


;;;
;;;
;;; The actual exercise is dispersed through the packages, but clearly marked
;;;
;;;

; I believe that in this exercise, we are only expected to define equ? to
; compare numbers of the same type, not on different types, since this matter
; is more fully addressed in the following subsection of the book.
(define (equ? x y) (apply-generic 'equ? x y))
(define (=zero? x) (apply-generic '=zero? x))