0415.scm

(define (attach-tag type-tag contents)
  (if (eq? type-tag 'scheme-number)
    contents
    (cons type-tag contents)))

(define (type-tag datum)
  (if (pair? datum)
    (car datum)
    'scheme-number))

(define (contents datum)
  (if (pair? datum)
    (cdr datum)
    datum))

(define (square x) (* x x))
(define (install-rectangular-package)
  ; internal procedure
  (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))))

  ; public interface
  (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 x y))))
  'done)

(define (install-polar-package)
  ; internal procedure
  (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 (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 x y))))
  'done)


(define (apply-generic op . args)
  (print 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-table)
  (let ((local-table (list '*table*)))
    (define (lookup key-1 key-2)
      (let ((subtable (assoc key-1 (cdr local-table))))
        (if subtable
          (let ((record (assoc key-2 (cdr subtable))))
            (if record
              (cdr record)
              false))
          false)))
    (define (insert! key-1 key-2 value)
      (let ((subtable (assoc key-1 (cdr local-table))))
        (if subtable
          (let ((record (assoc key-2 (cdr subtable))))
            (if record
              (set-cdr! record value)
              (set-cdr! subtable
                        (cons (cons key-2 value)
                              (cdr subtable)))))
          (set-cdr! local-table
                    (cons (list key-1
                                (cons key-2 value))
                          (cdr local-table)))))
      'ok)
    (define (dispatch m)
      (cond ((eq? m 'lookup-proc) lookup)
            ((eq? m 'insert-proc!) insert!)
            (else (error "Unknown operation --TABLE" m))))
    dispatch))
(define operation-table (make-table))
(define get (operation-table 'lookup-proc))
(define put (operation-table 'insert-proc!))

(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 (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 'nega '(scheme-number)
       (lambda (x) (tag (- x))))
  'done)

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

(define (install-rational-package)
  (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))))

  ;; interface to reset 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))))
  'done)

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


(define (install-complex-package)
  (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))))

  'done)

(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 (add-complex-to-schemenum z x)
  (make-from-real-imag (+ (real-part z) x)
                       (imag-part z)))

(put 'add '(complex scheme-number)
     (lambda (z x) (tag (add-complex-to-schemenum z x))))

(define (scheme-number->complex n)
  (make-complex-from-real-imag (contents n) 0))

(define coercion-table (make-table))
(define get-coercion (coercion-table 'lookup-proc))
(define put-coercion (coercion-table 'insert-proc!))

(put-coercion 'scheme-number 'complex scheme-number->complex)

(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))
        (if (= (length args) 2)
          (let ((type1 (car type-tags))
                (type2 (cadr type-tags))
                (a1 (car args))
                (a2 (cadr args)))
            (let ((t1->t2 (get-coercion type1 type2))
                  (t2->t1 (get-coercion type2 type1)))
              (cond (t1->t2
                      (apply-generic op (t1->t2 a1) a2))
                    (t2->t1
                      (apply-generic op a1 (t2->t1 a2)))
                    (else
                      (error "No method for these types"
                             (list op type-tags))))))
          (error "No method for these types"
                 (list op type-tags)))))))

(define (variable? x) (symbol? x))

(define (same-variable? v1 v2)
  (and (variable? v1) (variable? v2) (eq? v1 v2)))
(define (install-polynomial-package)
  (define (make-poly variable term-list)
    (cons variable term-list))
  (define (variable p) (car p))
  (define (term-list p) (cdr p))
  (define (=zero?-poly p)
    (=zero?-terms (term-list p)))
  (define (=zero?-terms L)
    (or (empty-termlist? L)
        (and (=zero? (cadr (first-term L))) (=zero?-terms (rest-terms L)))))

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

  (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 (sub-poly p1 p2)
    (if (same-variable? (variable p1) (variable p2))
      (add-poly p1 (nega-poly p2))
      (error "Polys not in same var -- SUB-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 (div-poly p1 p2)
    (if (same-variable? (variable p1) (variable p2))
      (let ((answer ((div-terms (term-list p1)
                                (term-list p2)))))
        (make-poly (variable p1) (car answer)))
      (error "Polys not in same var -- DIV-POLY"
             (list p1 p2))))

  (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-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)))))))))


  (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))))))


  (define (nega-poly p)
    (define nega-term-list (map nega-term (term-list p)))
    (cons (variable p) nega-term-list))

  (define (nega-term term)
    (make-term (order term)
               (nega (coeff term))))

  (define (tag p) (attach-tag 'polynomial p))

  (put 'add '(polynomial polynomial)
       (lambda (p1 p2) (tag (add-poly p1 p2))))
  (put 'sub '(polynomial polynomial)
       (lambda (p1 p2) (tag (sub-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))))
  (put '=zero? '(polynomial)
       (lambda (p) (=zero?-poly p)))
  (put 'nega '(polynomial)
       (lambda (p) (tag (nega-poly p))))
  'done)

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

(define (install-=zero?-package)
  (define (=zero?-scheme-number n)
    (eq? n 0))
  (define (=zero?-rational x)
    (eq? (car x) 0))
  (define (=zero?-complex x)
    (eq? (magnitude x) 0))

  (put '=zero? '(scheme-number)
       (lambda (x) (=zero?-scheme-number x)))
  (put '=zero? '(rational)
       (lambda (x) (=zero?-rational x)))
  (put '=zero? '(complex)
       (lambda (x) (=zero?-complex x)))
  'done)

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

(define (install-nega-package)
  (define (nega-scheme-number n)
    (- n))
  (put 'nega '(scheme-number)
       (lambda (x) (nega-scheme-number x)))
  'done)
(define (nega x) (apply-generic 'nega x))

(install-polynomial-package)
(install-scheme-number-package)
(install-=zero?-package)

(define p1 (make-polynomial 'x '((5 1) (0 -1))))
(define p2 (make-polynomial 'x '((2 1) (0 -1))))
(define q1 (make-polynomial 'y `((1 ,p1) (0 ,p2))))
(define q2 (make-polynomial 'y `((1 ,p2) (0 ,p1))))

(print (nega p1))
(print (sub p1 p2))
(print (sub q1 q2))


(define (install-dense-polynomial-package)
  (define (make-poly variable term-list)
    (cons variable term-list))
  (define (variable p) (car p))
  (define (term-list p) (cdr p))
  (define (=zero?-poly p)
    (=zero?-terms (term-list p)))
  (define (=zero?-terms L)
    (or (empty-termlist? L)
        (and (=zero? (cadr (first-term L))) (=zero?-terms (rest-terms L)))))

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

  (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 (sub-poly p1 p2)
    (if (same-variable? (variable p1) (variable p2))
      (add-poly p1 (nega-poly p2))
      (error "Polys not in same var -- SUB-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 (div-poly p1 p2)
    (if (same-variable? (variable p1) (variable p2))
      (let ((answer ((div-terms (term-list p1)
                                (term-list p2)))))
        (make-poly (variable p1) (car answer)))
      (error "Polys not in same var -- DIV-POLY"
             (list p1 p2))))

  (define (rev-termlist-empty) '())
  (define (rev-termlist-empty? term-list) (null? term-list))
  (define (rev-termlist-mul-ax L1 a)
    (cons 0 (rev-termlist-scale L1 a)))
  (define (rev-termlist-scale L1 a)
    (map (lambda (coeff) (mul a coeff)) L1))

  (define (rev-termlist-add r1 r2)
    ;(prove "add-lhs:" r1)
    ;(prove "add-rhs:" r2)
    (prove "return" (cond ((rev-termlist-empty? r1) r2)
                          ((rev-termlist-empty? r2) r1)
                          (else (cons (add (car r1) (car r2))
                                      (rev-termlist-add (cdr r1) (cdr r2)))))))
  (define (rev-termlist-mul r1 r2)
    ;(prove "mul-lhs:" r1)
    ;(prove "mul-rhs:" r2)
    (prove "return:" (cond ((rev-termlist-empty? r1) (rev-termlist-empty))
                           ((rev-termlist-empty? r2) (rev-termlist-empty))
                           (else (rev-termlist-add (rev-termlist-scale r1 (car r2))
                                                   (rev-termlist-mul-ax (rev-termlist-mul r1 (cdr r2)) 1))))))

  (define (prove name x)
    ;(print name x)
    x)

  (define (add-terms L1 L2)
    (reverse (rev-termlist-add (reverse L1) (reverse L2))))

  (define (mul-terms L1 L2)
    (reverse (rev-termlist-mul (reverse L1) (reverse L2))))

  (define (nega-poly p)
    (make-poly (variable p)
               ;本当は reverse する必要ない
               (reverse (rev-termlist-scale (reverse (term-list p)) -1))))

  (define (tag p) (attach-tag 'dense-polynomial p))

  (put 'add '(dense-polynomial dense-polynomial)
       (lambda (p1 p2) (tag (add-poly p1 p2))))
  (put 'sub '(dense-polynomial dense-polynomial)
       (lambda (p1 p2) (tag (sub-poly p1 p2))))
  (put 'mul '(dense-polynomial dense-polynomial)
       (lambda (p1 p2) (tag (mul-poly p1 p2))))
  (put 'make 'dense-polynomial
       (lambda (var terms) (tag (make-poly var terms))))
  (put '=zero? '(dense-polynomial)
       (lambda (p) (=zero?-poly p)))
  (put 'nega '(dense-polynomial)
       (lambda (p) (tag (nega-poly p))))
  'done)

(install-dense-polynomial-package)


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

(define p1 (make-dense-polynomial 'x '(1 2 3)))
(define p2 (make-dense-polynomial 'x '(3 4 5)))

(print p1)
(print p2)
(print (add p1 p2))
(print (mul p1 p2))
(print (sub p1 p2))