#lang sicp

(define pi 3.14159)
(define (square x) (* x x))
(define (accumulate op initial sequence)
  (if (null? sequence)
      initial
      (op (car sequence)
          (accumulate op
                      initial
                      (cdr sequence)))))
;; get and put definitions
(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 '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 '=zero? '(scheme-number)
       (lambda (x) (= x 0)))
  (put 'negate '(scheme-number)
       (lambda (x) (- x)))
  '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)
    (cons n d))
  (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 (=zero? x) (apply-generic '=zero? x))
  (define (negate x) (apply-generic 'negate x))
  (define (add-rat x y)
    (make-rat (add (mul (numer x) (denom y))
                 (mul (numer y) (denom x)))
              (mul (denom x) (denom y))))
  (define (sub-rat x y)
    (make-rat (sub (mul (numer x) (denom y))
                 (mul (numer y) (denom x)))
              (mul (denom x) (denom y))))
  (define (mul-rat x y)
    (make-rat (mul (numer x) (numer y))
              (mul (denom x) (denom y))))
  (define (div-rat x y)
    (make-rat (mul (numer x) (denom y))
              (mul (denom x) (numer y))))

  ;; z1a/z1b = z2a/z2b  iff z1amulz2b - z2amulz1b = 0
  ;; equ? for problem 2.79
  (define (equ? z1 z2)
    (=zero? (sub (mul (numer z1) (denom z2))
          (mul (numer z2) (denom z1)))))
  ;; 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) (=zero? (numer a))))
  (put 'negate '(rational)
       (lambda (r) (tag (make-rat (negate (numer r)) (denom r)))))
  'done)

(install-rational-package)

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

(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 (mul a b)
  (apply-generic 'mul a b))
(define (add a b)
  (apply-generic 'add a b))
(define (sub a b)
  (apply-generic 'sub a b))
(define (equ? a b)
  (apply-generic 'equ? a b))


(define (install-polynomial-package)
  ;; internal procedures
  ;; representation of poly
  (define (make-poly variable term-list)
    (cons variable term-list))
  (define (variable p) (car p))
  (define (term-list p) (cdr p))

  (define (variable? x) (symbol? x))
  (define (same-variable? v1 v2)
    (and (variable? v1)
         (variable? v2)
         (eq? v1 v2)))

  (define (mul-terms L1 L2)
    (if (empty-termlist? L1)
      (the-empty-termlist)
      (add-terms
       (mul-term-by-all-terms
        (first-term L1) L2)
       (mul-terms (rest-terms L1) L2))))

  (define (mul-term-by-all-terms t1 L)
    (if (empty-termlist? L)
      (the-empty-termlist)
      (let ((t2 (first-term L)))
        (adjoin-term
         (make-term
          (+ (order t1) (order t2))
          (mul (coeff t1) (coeff t2)))
         (mul-term-by-all-terms
          t1
          (rest-terms L))))))


  ;; representation of terms and term lists
  (define (adjoin-term term term-list)
    (if (=zero? (coeff term))
      term-list
      (cons term term-list)))
  (define (the-empty-termlist) '())
  (define (first-term term-list) (car term-list))
  (define (rest-terms term-list) (cdr term-list))
  (define (empty-termlist? term-list)
    (null? term-list))
  (define (make-term order coeff)
    (list order coeff))
  (define (order term) (car term))
  (define (coeff term) (cadr term))


  (define (add-poly p1 p2)
    (if (same-variable? (variable p1)
                        (variable p2))
      (make-poly
       (variable p1)
       (add-terms (term-list p1)
                  (term-list p2)))
      (error "Polys not in same var:
             ADD-POLY"
             (list p1 p2))))

  (define (mul-poly p1 p2)
    (if (same-variable? (variable p1)
                        (variable p2))
      (make-poly
       (variable p1)
       (mul-terms (term-list p1)
                  (term-list p2)))
      (error "Polys not in same var:
             MUL-POLY"
             (list p1 p2))))

  (define (add-terms L1 L2)
    (cond ((empty-termlist? L1) L2)
      ((empty-termlist? L2) L1)
      (else
       (let ((t1 (first-term L1))
             (t2 (first-term L2)))
         (cond ((> (order t1) (order t2))
                (adjoin-term
                 t1
                 (add-terms (rest-terms L1)
                            L2)))
           ((< (order t1) (order t2))
            (adjoin-term
             t2
             (add-terms
              L1
              (rest-terms L2))))
           (else
            (adjoin-term
             (make-term
              (order t1)
              (add (coeff t1)
                   (coeff t2)))
             (add-terms
              (rest-terms L1)
              (rest-terms L2)))))))))
  ;; During construction, we don't check whether coefficients are zero
  ;; So now, we have to check all coefficients.
  (define (=zero?-poly poly)
    (accumulate (lambda (x y) (and y (=zero? (coeff x))))
                #t
                (term-list poly)))
  ;; Make sure to install the function
  (put '=zero? '(polynomial) =zero?-poly)

  ;; Exercise 2-88
  (define (negate-terms L) 
    (if (empty-termlist? L)
      L
      (let ((t (first-term L)) (r (rest-terms L)))
        (adjoin-term (make-term (order t) (apply-generic 'negate (coeff t)))
                     (negate-terms r)))))
  (define (sub-terms L1 L2)
    (add-terms L1 (negate-terms L2)))
  (define (sub-poly p1 p2)
    (if (same-variable? (variable p1)
                        (variable p2))
      (make-poly
       (variable p1)
       (sub-terms (term-list p1)
                  (term-list p2)))
      (error "Polys not in same var:
             SUB-POLY"
             (list p1 p2))))
  (put 'sub '(polynomial polynomial)
       (lambda (p1 p2) 
         (tag (sub-poly p1 p2))))
  (put 'negate '(polynomial)
       (lambda (p) 
         (tag (make-poly (variable p) (negate-terms (term-list p))))))
  ;; interface to rest of the system
  (define (tag p) (attach-tag 'polynomial p))
  (put 'add '(polynomial polynomial)
       (lambda (p1 p2) 
         (tag (add-poly p1 p2))))
  (put 'mul '(polynomial polynomial)
       (lambda (p1 p2) 
         (tag (mul-poly p1 p2))))
  (put 'make 'polynomial
       (lambda (var terms) 
         (tag (make-poly var terms))))
  'done)

(install-polynomial-package)

(define (make-polynomial var terms)
  ((get 'make 'polynomial) var terms))

(define p1 (make-polynomial 'x '((2 1) (0 1))))
(define p2 (make-polynomial 'x '((3 1) (0 1))))
(define rf (make-rational p2 p1))
rf
(apply-generic 'add rf rf)