223 lines
7.4 KiB
Scheme
223 lines
7.4 KiB
Scheme
(load "util.scm")
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(display "\nexample - generic arithmetic operations\n")
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;; Helpers for generic arithmetic operations
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(define (attach-tag type-tag contents)
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(cond
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((eq? type-tag 'scheme-number) contents)
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(else (cons type-tag contents))))
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(define (type-tag datum)
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(cond
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((number? datum) 'scheme-number)
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((pair? datum) (car datum))
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(else (error "Bad tagged datum -- TYPE-TAG" datum))))
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(define (contents datum)
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(cond
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((number? datum) datum)
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((pair? datum) (cdr datum))
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(else (error "Bad tagged datum -- CONTENTS" datum))))
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(define (apply-generic op . args)
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(let ((type-tags (map type-tag args)))
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(let ((proc (get op type-tags)))
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(if proc
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(apply proc (map contents args))
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(error
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"No method for these types -- APPLY-GENERIC"
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(list op type-tags))))))
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(define (install-scheme-number-package)
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(define (tag x)
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(attach-tag 'scheme-number x))
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(put 'add '(scheme-number scheme-number)
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(lambda (x y) (tag (+ x y))))
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(put 'sub '(scheme-number scheme-number)
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(lambda (x y) (tag (- x y))))
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(put 'mul '(scheme-number scheme-number)
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(lambda (x y) (tag (* x y))))
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(put 'div '(scheme-number scheme-number)
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(lambda (x y) (tag (/ x y))))
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(put 'make 'scheme-number
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(lambda (x) (tag x)))
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(display "[install-scheme-number-package]\n")
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'done)
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(define (install-rational-package)
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;; internal procedures
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(define (numer x) (car x))
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(define (denom x) (cdr x))
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(define (make-rat n d)
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(let ((g (gcd n d)))
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(cons (/ n g) (/ d g))))
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(define (add-rat x y)
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(make-rat (+ (* (numer x) (denom y))
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(* (numer y) (denom x)))
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(* (denom x) (denom y))))
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(define (sub-rat x y)
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(make-rat (- (* (numer x) (denom y))
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(* (numer y) (denom x)))
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(* (denom x) (denom y))))
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(define (mul-rat x y)
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(make-rat (* (numer x) (numer y))
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(* (denom x) (denom y))))
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(define (div-rat x y)
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(make-rat (* (numer x) (denom y))
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(* (denom x) (numer y))))
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;; interface to rest of the system
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(define (tag x) (attach-tag 'rational x))
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(put 'add '(rational rational)
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(lambda (x y) (tag (add-rat x y))))
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(put 'sub '(rational rational)
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(lambda (x y) (tag (sub-rat x y))))
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(put 'mul '(rational rational)
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(lambda (x y) (tag (mul-rat x y))))
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(put 'div '(rational rational)
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(lambda (x y) (tag (div-rat x y))))
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(put 'make 'rational
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(lambda (n d) (tag (make-rat n d))))
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(display "[install-rational-package]\n")
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'done)
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(define (install-rectangular-package)
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(define (real-part z) (car z))
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(define (imag-part z) (cdr z))
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(define (magnitude z)
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(sqrt (+ (square (real-part z))
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(square (imag-part z)))))
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(define (angle z)
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(atan (imag-part z)
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(real-part z)))
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(define (tag z) (attach-tag 'rectangular z))
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(define (make-from-real-imag x y)
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(tag (cons x y)))
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(define (make-from-mag-ang r a)
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(tag (cons (* r (cos a)) (* r (sin a)))))
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; interface to the rest of the system
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(put 'real-part '(rectangular) real-part)
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(put 'imag-part '(rectangular) imag-part)
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(put 'magnitude '(rectangular) magnitude)
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(put 'angle '(rectangular) angle)
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(put 'make-from-mag-ang 'rectangular make-from-mag-ang)
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(put 'make-from-real-imag 'rectangular make-from-real-imag)
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(display "[install-rectangular-package]\n")
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'done)
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(define (install-polar-package)
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(define (real-part z)
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(* (magnitude z) (cos (angle z))))
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(define (imag-part z)
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(* (magnitude z) (sin (angle z))))
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(define (magnitude z) (car z))
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(define (angle z) (cdr z))
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(define (tag z) (attach-tag 'polar z))
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(define (make-from-real-imag x y)
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(tag (cons (sqrt (+ (square x) (square y)))
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(atan y x))))
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(define (make-from-mag-ang r a) (tag (cons r a)))
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; interface to rest of the system
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(put 'real-part '(polar) real-part)
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(put 'imag-part '(polar) imag-part)
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(put 'magnitude '(polar) magnitude)
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(put 'angle '(polar) angle)
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(put 'make-from-mag-ang 'polar make-from-mag-ang)
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(put 'make-from-real-imag 'polar make-from-real-imag)
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(display "[install-polar-package]\n")
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'done)
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(define (install-complex-package)
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;; imported procedures from rectangular and polar packages
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(define (make-from-real-imag x y)
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((get 'make-from-real-imag 'rectangular) x y))
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(define (make-from-mag-ang r a)
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((get 'make-from-mag-ang 'polar) r a))
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;; getters
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(define (real-part z) (apply-generic 'real-part z))
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(define (imag-part z) (apply-generic 'imag-part z))
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(define (magnitude z) (apply-generic 'magnitude z))
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(define (angle z) (apply-generic 'angle z))
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;; internal procedures
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(define (add-complex z1 z2)
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(make-from-real-imag (+ (real-part z1) (real-part z2))
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(+ (imag-part z1) (imag-part z2))))
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(define (sub-complex z1 z2)
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(make-from-real-imag (- (real-part z1) (real-part z2))
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(- (imag-part z1) (imag-part z2))))
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(define (mul-complex z1 z2)
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(make-from-mag-ang (* (magnitude z1) (magnitude z2))
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(+ (angle z1) (angle z2))))
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(define (div-complex z1 z2)
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(make-from-mag-ang (/ (magnitude z1) (magnitude z2))
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(- (angle z1) (angle z2))))
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;; interface to rest of the system
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(put 'real-part '(complex) real-part)
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(put 'imag-part '(complex) imag-part)
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(put 'magnitude '(complex) magnitude)
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(put 'angle '(complex) angle)
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(define (tag z) (attach-tag 'complex z))
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(put 'add '(complex complex)
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(lambda (z1 z2) (tag (add-complex z1 z2))))
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(put 'sub '(complex complex)
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(lambda (z1 z2) (tag (sub-complex z1 z2))))
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(put 'mul '(complex complex)
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(lambda (z1 z2) (tag (mul-complex z1 z2))))
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(put 'div '(complex complex)
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(lambda (z1 z2) (tag (div-complex z1 z2))))
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(put 'make-from-real-imag 'complex
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(lambda (x y) (tag (make-from-real-imag x y))))
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(put 'make-from-mag-ang 'complex
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(lambda (r a) (tag (make-from-mag-ang r a))))
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(display "[install-complex-package]\n")
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'done)
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;; constructors
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(define (make-scheme-number n)
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((get 'make 'scheme-number) n))
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(define (make-rational n d)
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((get 'make 'rational) n d))
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(define (make-complex-from-real-imag x y)
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((get 'make-from-real-imag 'complex) x y))
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(define (make-complex-from-mag-ang r a)
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((get 'make-from-mag-ang 'complex) r a))
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;; generic operations
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(define (add x y) (apply-generic 'add x y))
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(define (sub x y) (apply-generic 'sub x y))
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(define (mul x y) (apply-generic 'mul x y))
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(define (div x y) (apply-generic 'div x y))
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(install-scheme-number-package)
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(install-rational-package)
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(install-rectangular-package)
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(install-polar-package)
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(install-complex-package)
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(assert (add (make-scheme-number 10) (make-scheme-number 20)) (make-scheme-number 30))
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(define p1 (make-complex-from-mag-ang 14.142 0.7853))
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(define e1 (make-complex-from-real-imag 10 10))
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(assert (add e1 e1) (make-complex-from-real-imag 20 20))
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(newline) (display "ex-2.77 - see comments") (newline)
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; real-part (and all other selectors are implemented via calls to apply
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; generic. The first call to apply generic has the type 'magnitude '(complex).
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; By adding the code from Alyssa that call gets dispatched a second time which
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; results in a call to apply generic with 'magnitude '(rectangular). This calls
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; the actual magnitude function from the rectangular package.
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(newline) (display "ex-2.78 - simplify scheme number") (newline)
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; Solution at the beginning of this file.
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(assert (add 5 3) 8)
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(newline) (display "ex-2.79 - equ?") (newline)
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(newline) (display "ex-2.80 - =zero?") (newline)
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