317 lines
No EOL
11 KiB
Scheme
317 lines
No EOL
11 KiB
Scheme
#lang sicp
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;;;
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;;;
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;;; Setup for the exercise
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;;;
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;;;
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(define (square x) (* x x))
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; Dispatch table: list of rows, structure below:
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; one row: (op-tag . (... one cell) (...) (...))
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; one cell: ((list of type tags) . procedure)
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; essentially, the whole table is an alist of alists
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; (list of type tags) is a list of length n for n-ary op
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; a unary op can be called with a symbol instead of a list of symbols for a type
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; tag, but this will be converted to a length-1 list while searching the table
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(define *dispatch-table* '())
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;;;
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;;; Dispatch table
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;;;
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; finds member in alist based on tag, which is the car of the row
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(define (search-in-list tag list)
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(if (null? list)
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nil
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(let* ((current-member (car list))
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(member-tag (car current-member)))
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(if (equal? member-tag tag)
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current-member ; we don't strip the key when returning
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(search-in-list tag (cdr list))))))
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(define (get op-tag init-type-tags)
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(let* ((type-tags (if (symbol? init-type-tags)
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(list init-type-tags)
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init-type-tags))
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; wrap type-tags in a list if it's supplied as a symbol
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(row-1 (search-in-list op-tag *dispatch-table*))
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(row (if (null? row-1) nil (cdr row-1))) ; we strip the name of the row
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(procedure-1 (search-in-list type-tags row))
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(procedure (if (null? procedure-1) nil (cdr procedure-1))))
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(if (null? procedure)
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(error "Procedure not found in dispatch table:" op-tag type-tags)
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procedure)))
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(define (add-pair! alist tag value)
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(set! alist (cons (cons tag value)
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alist)))
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(define (put op-tag init-type-tags procedure)
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(let* ((type-tags (if (symbol? init-type-tags)
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(list init-type-tags)
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init-type-tags))
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(search-row (search-in-list op-tag *dispatch-table*))
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; here we don't strip the key from search-in-list
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(row (if (null? search-row)
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(begin (set! *dispatch-table* (cons (cons op-tag nil)
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*dispatch-table*))
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(car *dispatch-table*))
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search-row))
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(search-cell (search-in-list type-tags (cdr row))))
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(if (null? search-cell)
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(set-cdr! row (cons (cons type-tags procedure)
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(cdr row)))
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; attaching new pair to row
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(set-cdr! search-cell procedure))))
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;;;
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;;; Auxillary functions for type tags
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;;;
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(define (attach-tag type-tag contents)
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(cons type-tag contents))
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(define (type-tag datum)
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(if (pair? datum)
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(car datum)
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(error "Bad tagged datum: TYPE-TAG" datum)))
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(define (contents datum)
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(if (pair? datum)
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(cdr datum)
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(error "Bad tagged datum: CONTENTS" datum)))
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;;;
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;;; Complex packages
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;;;
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(define (install-rectangular-package)
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;; internal procedures
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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 (make-from-real-imag x y) (cons x y))
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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) (real-part z)))
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(define (make-from-mag-ang r a)
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(cons (* r (cos a)) (* r (sin a))))
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;; interface to the rest of the system
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(define (tag x) (attach-tag 'rectangular x))
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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-real-imag 'rectangular
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(lambda (x y) (tag (make-from-real-imag x y))))
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(put 'make-from-mag-ang 'rectangular
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(lambda (r a) (tag (make-from-mag-ang r a))))
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'done)
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(define (install-polar-package)
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;; internal procedures
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(define (magnitude z) (car z))
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(define (angle z) (cdr z))
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(define (make-from-mag-ang r a) (cons r a))
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(define (real-part z) (* (magnitude z) (cos (angle z))))
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(define (imag-part z) (* (magnitude z) (sin (angle z))))
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(define (make-from-real-imag x y)
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(cons (sqrt (+ (square x) (square y)))
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(atan y x)))
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;; interface to the rest of the system
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(define (tag x) (attach-tag 'polar x))
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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-real-imag 'polar
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(lambda (x y) (tag (make-from-real-imag x y))))
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(put 'make-from-mag-ang 'polar
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(lambda (r a) (tag (make-from-mag-ang r a))))
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'done)
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(install-rectangular-package)
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(install-polar-package)
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;;;
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;;; Apply generic and complex function definitions
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;;;
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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 "No method for these types: APPLY-GENERIC"
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(list op type-tags))))))
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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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(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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;;;
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;;; Generic function definition
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;;;
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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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;;;
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;;; Scheme number package
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;;;
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(define (install-scheme-number-package)
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(define (tag x) (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 (lambda (x) (tag x)))
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'done)
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(install-scheme-number-package)
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(define (make-scheme-number n)
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((get 'make 'scheme-number) n))
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;;;
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;;; Rational number package
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;;;
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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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'done)
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(install-rational-package)
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(define (make-rational n d)
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((get 'make 'rational) n d))
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;;;
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;;; Complex number package
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;;;
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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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;; 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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(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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; Code added as fix in the exercise 2.77
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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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; Code added as fix in the exercise
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'done)
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(install-complex-package)
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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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;;;
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;;;
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;;; The actual exercise
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;;;
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;;;
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; The explanation:
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; When magnitude is invoked on the object '(complex rectangular 3 . 4), the call
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; sequence will look roughly like so (represented in the substitution model:
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; (magnitude '(complex rectangular 3 . 4))
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; (apply-generic 'magnitude '(complex rectangular 3 . 4))
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; (let ((type-tags (map type-tag args))) <- this will be '(complex)
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; (let ((proc (get op type-tags))) <- this will return the exact same
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; magnitude procedure again
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; (if #<proc:magnitude> <- this will not be #f
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; (apply #<proc:magnitude> (map contents '((complex rectangular 3 . 4))))
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; (error "No method for these types: APPLY-GENERIC"
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; (list op type-tags))))))
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; (apply #<procedure:magnitude> (map contents '((complex rectangular 3 . 4))))
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; (apply #<procedure:magnitude> '((rectangular 3 . 4)))
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; (#<procedure:magnitude> '(rectangular 3 . 4))
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; (apply-generic 'magnitude '(rectangular 3 . 4)) <- apply-generic expands again
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; but we'll skip that
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; (#<proc:magnitude-from-rectangular package> '(3 . 4))
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; (sqrt (+ (square (real-part '(3 . 4)))
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; (square (imag-part '(3 . 4)))))
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; (sqrt (+ (square 3) (square 4)))
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; 5
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; In other words, the magnitude procedure, which calls apply-generic, will strip
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; the outer tag 'complex, and then pass the stripped object back to itself
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; (magnitude), which will, again, call apply-generic, which will then strip the
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; second tag 'rectangular, and finally pass the object to magnitude and
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; sub-procedures in the rectangular package. So apply-generic gets called twice. |