Implement till 2.86
parent
40a017043b
commit
d9676999ef
256
ex-2_77-97.scm
256
ex-2_77-97.scm
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@ -34,6 +34,12 @@
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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 (has-tag? datum)
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(cond
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((number? datum) #t)
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((pair? datum) #t)
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(else #f)))
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(define (contents datum)
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(cond
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((number? datum) datum)
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@ -49,33 +55,31 @@
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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-integer-package)
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(define (make-integer x)
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(if (integer? x)
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(tag x)
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(error "Not an integer -- MAKE-INTEGER " x)))
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(define (integer->rational x)
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(define (install-scheme-number-package)
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(define (tag x) x)
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(define (scheme->rational x)
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(make-rational x 1))
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(define (tag x)
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(attach-tag 'integer x))
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(put 'add '(integer integer)
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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 '(integer integer)
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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 '(integer integer)
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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 '(integer integer)
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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 'equ? '(integer integer)
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(put 'equ? '(scheme-number scheme-number)
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(lambda (x y) (= x y)))
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(put 'exp '(integer integer)
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(lambda (x y) (tag (expt x y)))) ; using primitive expt
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(put '=zero? '(integer)
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(put 'exp '(scheme-number scheme-number)
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(lambda (x y) (tag (expt x y))))
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(put '=zero? '(scheme-number)
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(lambda (x) (= x 0)))
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(put 'make 'integer
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(lambda (x) (make-integer x)))
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(put 'raise '(integer) integer->rational)
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(display "[install-integer-package]\n")
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(put 'make 'scheme-number
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(lambda (x) (tag x)))
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(put 'arctan '(scheme-number scheme-number)
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(lambda (x y) (atan x y)))
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(put 'square-root '(scheme-number) sqrt)
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(put 'raise 'scheme-number scheme->rational)
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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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@ -83,8 +87,10 @@
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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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(if (and (integer? n) (integer? d))
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(let ((g (gcd n d)))
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(cons (/ n g) (/ d g)))
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(cons n d)))
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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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@ -105,7 +111,9 @@
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(= (* (numer x) (denom y))
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(* (numer y) (denom x))))
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(define (rational->real x)
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(make-scheme-number (/ (numer x) (denom x))))
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(make-real (/ (numer x) (denom x))))
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(define (rational->scheme x)
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(make-scheme-number (inexact->exact (round (/ (numer x) (denom x))))))
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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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@ -121,51 +129,63 @@
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(put 'equ? '(rational rational) equ?)
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(put '=zero? '(rational)
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(lambda (x) (= (numer x) 0)))
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(define (arctan-rational x y)
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(atan (/ (numer x) (denom x))
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(/ (numer y) (denom y))))
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(put 'arctan '(rational rational) arctan-rational)
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(put 'square-root '(rational)
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(lambda (x) (sqrt (/ (numer x) (denom x)))))
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(put 'make 'rational
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(lambda (n d) (tag (make-rat n d))))
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(put 'raise '(rational) rational->real)
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(put 'raise 'rational rational->real)
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(put 'project 'rational rational->scheme)
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(display "[install-rational-package]\n")
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'done)
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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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(define (install-real-package)
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(define (make-real x) (tag x))
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(define (real->rational x)
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(make-rational x 1))
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(define (real->complex x)
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(make-complex-from-real-imag x 0))
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(put 'add '(scheme-number scheme-number)
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(define (tag x)
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(attach-tag 'real x))
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(put 'add '(real real)
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(lambda (x y) (tag (+ x y))))
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(put 'sub '(scheme-number scheme-number)
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(put 'sub '(real real)
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(lambda (x y) (tag (- x y))))
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(put 'mul '(scheme-number scheme-number)
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(put 'mul '(real real)
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(lambda (x y) (tag (* x y))))
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(put 'div '(scheme-number scheme-number)
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(put 'div '(real real)
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(lambda (x y) (tag (/ x y))))
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(put 'equ? '(scheme-number scheme-number)
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(put 'equ? '(real real)
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(lambda (x y) (= x y)))
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(put 'exp '(scheme-number scheme-number)
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(lambda (x y) (tag (expt x y)))) ; using primitive expt
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(put '=zero? '(scheme-number)
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(put 'exp '(real real)
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(lambda (x y) (tag (expt x y))))
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(put '=zero? '(real)
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(lambda (x) (= x 0)))
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(put 'make 'scheme-number
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(lambda (x) (tag x)))
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(put 'raise '(scheme-number) real->complex)
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(display "[install-scheme-number-package]\n")
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(put 'make 'real
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(lambda (x) (make-real x)))
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(put 'raise 'real real->complex)
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(put 'project 'real real->rational)
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(display "[install-real-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 (square x) (mul x x))
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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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(square-root (add (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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(arctan (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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(tag (cons (mul r (cos a)) (mul 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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@ -179,14 +199,15 @@
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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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(mul (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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(mul (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 (sqrt x) (mul x x))
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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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(tag (cons (sqrt (add (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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@ -213,20 +234,22 @@
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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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(make-from-real-imag (add (real-part z1) (real-part z2))
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(add (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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(make-from-real-imag (sub (real-part z1) (real-part z2))
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(sub (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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(make-from-mag-ang (mul (magnitude z1) (magnitude z2))
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(add (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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(define (equ? z1 z2)
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(and (= (magnitude z1) (magnitude z2))
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(= (angle z1) (angle z2))))
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(make-from-mag-ang (div (magnitude z1) (magnitude z2))
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(sub (angle z1) (angle z2))))
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(define (equ?-complex z1 z2)
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(and (equ? (magnitude z1) (magnitude z2))
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(equ? (angle z1) (angle z2))))
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(define (complex->real x)
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(make-real (real-part x)))
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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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@ -245,20 +268,21 @@
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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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(put 'equ? '(complex complex) equ?)
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(put 'equ? '(complex complex) equ?-complex)
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(put '=zero? '(complex) =zero?)
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(put 'project 'complex complex->real)
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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-integer n)
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((get 'make 'integer) n))
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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-scheme-number n)
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((get 'make 'scheme-number) n))
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(define (make-real n)
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((get 'make 'real) n))
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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 (equ? x y) (apply-generic 'equ? x y))
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(define (=zero? x) (apply-generic '=zero? x))
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(define (exp x y) (apply-generic 'exp x y))
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(define (raise x) (apply-generic 'raise x))
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(define (arctan x y) (apply-generic 'arctan x y))
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(define (square-root x) (apply-generic 'square-root x))
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(install-integer-package)
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(install-rational-package)
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(install-scheme-number-package)
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(install-rational-package)
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(install-real-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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@ -411,15 +436,18 @@
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(display (coerce-args 'rational (list (make-rational 1 3) 2 3))) (newline)
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(newline) (display "ex-2.83") (newline)
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(newline) (display "ex-2.83 - raise") (newline)
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; Our scheme-number package supports real numbers so we use that as our
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; real-number package without further changes. Additionally, we create an
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; integer package that only accepts integers in the constructor.
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(assert (sub (make-integer 3) (make-integer 1)) (make-integer 2))
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(define (raise x)
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((get 'raise (type-tag x)) (contents x)))
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(define i (make-integer 3))
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(assert (sub (make-scheme-number 3) (make-scheme-number 1)) (make-scheme-number 2))
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(define i (make-scheme-number 3))
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(display i) (newline)
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(display (raise i)) (newline)
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(display (raise (raise i))) (newline)
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@ -433,24 +461,90 @@
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(define (coerce-arg arg)
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(if (eq? (type-tag arg) target-type)
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arg
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(let ((proc (get 'raise (list (type-tag arg)))))
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(if (procedure? proc)
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(proc (contents arg))
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(let ((raise (get 'raise (type-tag arg))))
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(if (procedure? raise)
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(raise (contents arg))
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arg))))
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(let ((coerced-args (map coerce-arg args)))
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(if (equal? args coerced-args)
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coerced-args ; no more raising possible
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(coerce-args target-type coerced-args))))
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(assert (equ? (make-integer 3) (make-complex-from-real-imag 3 0)) #t)
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(assert (equ? (make-integer 3) (make-complex-from-real-imag 3 1)) #f)
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(assert (equ? (make-integer 3) (make-rational 3 1)) #t)
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(assert (add3 (make-rational 1 3) (make-integer 2) (make-rational 3 9)) (make-rational 8 3))
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;(display (coerce-args 'scheme-number (list (make-rational 1 3) 2 (make-rational 3 9))))
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(assert (equ? (make-scheme-number 3) (make-complex-from-real-imag 3 0)) #t)
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(assert (equ? (make-scheme-number 3) (make-complex-from-real-imag 3 1)) #f)
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(assert (equ? (make-scheme-number 3) (make-rational 3 1)) #t)
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(assert (add3 (make-rational 1 3) (make-scheme-number 2) (make-rational 3 9)) (make-rational 8 3))
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(newline) (display "ex-2.85 - drop it") (newline)
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(newline) (display "ex-2.86") (newline)
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(newline) (display "ex-2.85 - project and drop") (newline)
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; Do not implement project in terms of apply-generic as that will result in an
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; endless loop when trying to drop values later automatically within the
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; context of apply-generic.
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(define (project x)
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((get 'project (type-tag x)) (contents x)))
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(define c (make-complex-from-real-imag 4.2 1))
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(display c) (newline)
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(display (project c)) (newline)
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(display (project (project c))) (newline)
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(display (project (project (project c)))) (newline)
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; Implement drop to transform number to lowest possible representation
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(define (drop x)
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;(display "---------\ndrop ") (display x) (newline)
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(if (has-tag? x)
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(let ((project (get 'project (type-tag x))))
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(if (procedure? project)
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(let ((projected (project (contents x))))
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(if (equ? projected x)
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(drop projected)
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x))
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x))
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x))
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;(assert (drop 3) (make-scheme-number 3))
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;(assert (drop (make-complex-from-real-imag 3.2 0)) (drop (make-real (/ 16 5.))))
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;(assert (drop (make-complex-from-real-imag 3 0)) (make-scheme-number 3))
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(define (apply-generic op . args)
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;(display "-----\napply-generic ") (display op) (display " ") (display args) (newline)
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(define (try-args args-list)
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(if (null? args-list)
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(error "No method for these types" (list op (map type-tag args)))
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(let ((proc (get op (map type-tag (car args-list))))
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(args-contents (map contents (car args-list))))
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(if (procedure? proc)
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(drop (apply proc args-contents))
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(try-args (cdr args-list))))))
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(define (coerce-to-arg arg)
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(coerce-args (type-tag arg) args))
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(try-args (cons args (map coerce-to-arg args))))
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(assert (equ? (add (make-rational 1 3)
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(make-complex-from-real-imag 3 0))
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(make-rational 10 3)) #t)
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(assert (add (make-rational 6 3)
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(make-complex-from-real-imag 3 0))
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(make-scheme-number 5))
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(assert (add (make-rational 6 3)
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(make-complex-from-real-imag 3 0))
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5)
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(display "\nex-2.86 - generic complex numbers\n")
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; All the procedures that are used by the complex packages would also have to
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; use the generic procedures. For example, we cannot use *, -, /, +, and have
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; to replace them with their generic counter-part. We then also have to
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; implement sine and cosine. I have skipped sin and cos, but handle atan and
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; sqrt, so the following works.
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(define cr (make-complex-from-real-imag (make-rational 1 2)
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(make-rational 1 2)))
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(display (add cr cr)) (newline)
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(display (mul cr cr)) (newline)
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(display "\n\nexample - symbolic algebra\n")
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(display "\nex-2.87\n")
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