382 lines
14 KiB
Scheme
382 lines
14 KiB
Scheme
(load "util.scm")
|
|
|
|
(display "\nexample - generic arithmetic operations\n")
|
|
|
|
; (define (display x) ())
|
|
; (define (newline) ())
|
|
; can be used to import stuff silently
|
|
|
|
; Put and get functions. We could have implemented this via a list of
|
|
; three-tuples, but I don't know how to create global variables yet so we just
|
|
; use this code from SO. Doesn't look too complicated.
|
|
; https://stackoverflow.com/questions/5499005/how-do-i-get-the-functions-put-and-get-in-sicp-scheme-exercise-2-78-and-on
|
|
(define *op-table* (make-hash-table))
|
|
(define (put op type proc)
|
|
(hash-table/put! *op-table* (list op type) proc))
|
|
(define (get op type)
|
|
(hash-table/get *op-table* (list op type) #f))
|
|
|
|
(define *coercion-table* (make-hash-table))
|
|
(define (put-coercion type1 type2 proc)
|
|
(hash-table/put! *coercion-table* (list type1 type2) proc))
|
|
(define (get-coercion type1 type2)
|
|
(hash-table/get *coercion-table* (list type1 type2) #f))
|
|
|
|
;; Helpers for generic arithmetic operations
|
|
(define (attach-tag type-tag contents)
|
|
(cond
|
|
((eq? type-tag 'scheme-number) contents)
|
|
(else (cons type-tag contents))))
|
|
|
|
(define (type-tag datum)
|
|
(cond
|
|
((number? datum) 'scheme-number)
|
|
((pair? datum) (car datum))
|
|
(else (error "Bad tagged datum -- TYPE-TAG" datum))))
|
|
|
|
(define (contents datum)
|
|
(cond
|
|
((number? datum) datum)
|
|
((pair? datum) (cdr 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))))))
|
|
|
|
(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 'equ? '(scheme-number scheme-number)
|
|
(lambda (x y) (= x y)))
|
|
(put 'exp '(scheme-number scheme-number)
|
|
(lambda (x y) (tag (expt x y)))) ; using primitive expt
|
|
(put '=zero? '(scheme-number)
|
|
(lambda (x) (= x 0)))
|
|
(put 'make 'scheme-number
|
|
(lambda (x) (tag x)))
|
|
(display "[install-scheme-number-package]\n")
|
|
'done)
|
|
|
|
(define (install-rational-package)
|
|
;; internal procedures
|
|
(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))))
|
|
(define (add3-rat x y z)
|
|
(add-rat (add-rat x y) z))
|
|
(define (equ? x y)
|
|
(= (* (numer x) (denom y))
|
|
(* (numer y) (denom x))))
|
|
;; interface to rest of the system
|
|
(define (tag x) (attach-tag 'rational x))
|
|
(put 'add '(rational rational)
|
|
(lambda (x y) (tag (add-rat x y))))
|
|
(put 'add3 '(rational rational rational)
|
|
(lambda (x y z) (tag (add3-rat x y z))))
|
|
(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 'equ? '(rational rational) equ?)
|
|
(put '=zero? '(rational)
|
|
(lambda (x) (= (numer x) 0)))
|
|
(put 'make 'rational
|
|
(lambda (n d) (tag (make-rat n d))))
|
|
(display "[install-rational-package]\n")
|
|
'done)
|
|
|
|
(define (install-rectangular-package)
|
|
(define (real-part z) (car z))
|
|
(define (imag-part z) (cdr z))
|
|
(define (magnitude z)
|
|
(sqrt (+ (square (real-part z))
|
|
(square (imag-part z)))))
|
|
(define (angle z)
|
|
(atan (imag-part z)
|
|
(real-part z)))
|
|
(define (tag z) (attach-tag 'rectangular z))
|
|
(define (make-from-real-imag x y)
|
|
(tag (cons x y)))
|
|
(define (make-from-mag-ang r a)
|
|
(tag (cons (* r (cos a)) (* r (sin a)))))
|
|
; interface to the rest of the system
|
|
(put 'real-part '(rectangular) real-part)
|
|
(put 'imag-part '(rectangular) imag-part)
|
|
(put 'magnitude '(rectangular) magnitude)
|
|
(put 'angle '(rectangular) angle)
|
|
(put '=zero? '(rectangular) (lambda (z) (= (real-part z) (imag-part z) 0)))
|
|
(put 'make-from-mag-ang 'rectangular make-from-mag-ang)
|
|
(put 'make-from-real-imag 'rectangular make-from-real-imag)
|
|
(display "[install-rectangular-package]\n")
|
|
'done)
|
|
|
|
(define (install-polar-package)
|
|
(define (real-part z)
|
|
(* (magnitude z) (cos (angle z))))
|
|
(define (imag-part z)
|
|
(* (magnitude z) (sin (angle z))))
|
|
(define (magnitude z) (car z))
|
|
(define (angle z) (cdr z))
|
|
(define (tag z) (attach-tag 'polar z))
|
|
(define (make-from-real-imag x y)
|
|
(tag (cons (sqrt (+ (square x) (square y)))
|
|
(atan y x))))
|
|
(define (make-from-mag-ang r a) (tag (cons r a)))
|
|
; interface to rest of the system
|
|
(put 'real-part '(polar) real-part)
|
|
(put 'imag-part '(polar) imag-part)
|
|
(put 'magnitude '(polar) magnitude)
|
|
(put 'angle '(polar) angle)
|
|
(put '=zero? '(polar) (lambda (z) (= (magnitude z) 0)))
|
|
(put 'make-from-mag-ang 'polar make-from-mag-ang)
|
|
(put 'make-from-real-imag 'polar make-from-real-imag)
|
|
(display "[install-polar-package]\n")
|
|
'done)
|
|
|
|
(define (install-complex-package)
|
|
;; imported procedures from rectangular and polar packages
|
|
(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))
|
|
;; getters
|
|
(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))
|
|
;; 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))))
|
|
(define (equ? z1 z2)
|
|
(and (= (magnitude z1) (magnitude z2))
|
|
(= (angle z1) (angle z2))))
|
|
;; interface to rest of the system
|
|
(put 'real-part '(complex) real-part)
|
|
(put 'imag-part '(complex) imag-part)
|
|
(put 'magnitude '(complex) magnitude)
|
|
(put 'angle '(complex) angle)
|
|
(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))))
|
|
(put 'equ? '(complex complex) equ?)
|
|
(put '=zero? '(complex) =zero?)
|
|
(display "[install-complex-package]\n")
|
|
'done)
|
|
|
|
;; constructors
|
|
(define (make-scheme-number n)
|
|
((get 'make 'scheme-number) n))
|
|
|
|
(define (make-rational n d)
|
|
((get 'make 'rational) n d))
|
|
|
|
(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 (real-part z) ((get 'real-part '(complex)) z))
|
|
(define (imag-part z) ((get 'imag-part '(complex)) z))
|
|
(define (magnitude z) ((get 'magnitude '(complex)) z))
|
|
(define (angle z) ((get 'angle '(complex)) z))
|
|
|
|
;; generic operations
|
|
(define (add x y) (apply-generic 'add x y))
|
|
(define (add3 x y z) (apply-generic 'add3 x y z))
|
|
(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 (equ? x y) (apply-generic 'equ? x y))
|
|
(define (=zero? x) (apply-generic '=zero? x))
|
|
(define (exp x y) (apply-generic 'exp x y))
|
|
|
|
(install-scheme-number-package)
|
|
(install-rational-package)
|
|
(install-rectangular-package)
|
|
(install-polar-package)
|
|
(install-complex-package)
|
|
|
|
(assert (add (make-scheme-number 10) (make-scheme-number 20)) (make-scheme-number 30))
|
|
(define p1 (make-complex-from-mag-ang 14.142135623730951 0.7853981633974483))
|
|
(define e1 (make-complex-from-real-imag 10 10))
|
|
(assert (add e1 e1) (make-complex-from-real-imag 20 20))
|
|
|
|
(newline) (display "ex-2.77 - see comments") (newline)
|
|
|
|
; real-part (and all other selectors are implemented via calls to apply
|
|
; generic. The first call to apply generic has the type 'magnitude '(complex).
|
|
; By adding the code from Alyssa that call gets dispatched a second time which
|
|
; results in a call to apply generic with 'magnitude '(rectangular). This calls
|
|
; the actual magnitude function from the rectangular package.
|
|
|
|
(newline) (display "ex-2.78 - simplify scheme number") (newline)
|
|
|
|
; Solution at the beginning of this file.
|
|
(assert (add 5 3) 8)
|
|
|
|
(newline) (display "ex-2.79 - equ?") (newline)
|
|
|
|
; Extended each of the packages and defined generic procedure
|
|
(assert (equ? (make-scheme-number 10) (make-scheme-number 10)) #t)
|
|
(assert (equ? (make-rational 3 4) (make-rational 6 8)) #t)
|
|
(assert (equ? (make-complex-from-mag-ang 3 4) (make-complex-from-real-imag 6 8)) #f)
|
|
(assert (equ? p1 e1) #t) ; define above
|
|
|
|
(newline) (display "ex-2.80 - =zero?") (newline)
|
|
|
|
; Extended each of the packages and defined generic procedure
|
|
(assert (=zero? 0) #t)
|
|
(assert (=zero? 1) #f)
|
|
(assert (=zero? (make-rational 0 1)) #t)
|
|
(assert (=zero? (make-rational 1 1)) #f)
|
|
(assert (=zero? e1) #f)
|
|
(assert (=zero? p1) #f)
|
|
|
|
(newline) (display "ex-2.81 - Louis trying things") (newline)
|
|
|
|
(define (scheme-number->complex n)
|
|
(make-complex-from-real-imag (contents n) 0))
|
|
|
|
(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
|
|
((eq? type1 type2) (error "No need to coerce identical types"
|
|
(list op type-tags)))
|
|
(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)))))))
|
|
|
|
(display "[see comments]\n")
|
|
(assert (exp 3 3) 27)
|
|
(assert (add (make-scheme-number 3) (make-complex-from-real-imag 3 4))
|
|
(make-complex-from-real-imag 6 4))
|
|
|
|
; a. This is an endless loop. Louis change is not necessary, because if we
|
|
; coerce the arguments into the same type we would have found the respective
|
|
; procedure already.
|
|
|
|
; (define (scheme-number->scheme-number n) n)
|
|
; (define (complex->complex z) z)
|
|
; (put-coercion 'scheme-number 'scheme-number scheme-number->scheme-number)
|
|
; (put-coercion 'complex 'complex complex->complex)
|
|
|
|
; (exp (make-complex-from-real-imag 3 4) (make-complex-from-mag-ang 2 3))
|
|
|
|
; b. apply-generic already handles arguments of the same type correctly. It
|
|
; will simply not find a coercion procedure and return.
|
|
|
|
; c. added check for identical types to apply-generic. The following now just
|
|
; causes an error and no endless loop.
|
|
; (exp (make-complex-from-real-imag 3 4) (make-complex-from-mag-ang 2 3))
|
|
|
|
|
|
(newline) (display "ex-2.82 - multi argument coercion") (newline)
|
|
|
|
|
|
(define (scheme-number->rational n)
|
|
(make-rational (contents n) 1))
|
|
(put-coercion 'scheme-number 'rational scheme-number->rational)
|
|
|
|
; Try to coerce all args into target-type. Returns list if successful and empty
|
|
; list otherwise.
|
|
(define (coerce-args target-type args)
|
|
(define (coerce-arg arg)
|
|
(let ((t1->t2 (get-coercion (type-tag arg) target-type)))
|
|
(if (procedure? t1->t2) (t1->t2 arg) arg)))
|
|
(map coerce-arg args))
|
|
|
|
(define (apply-generic op . args)
|
|
(define (try-args args-list)
|
|
(if (null? args-list)
|
|
(error "No method for these types" (list op (map type-tag args)))
|
|
(let ((proc (get op (map type-tag (car args-list))))
|
|
(args-contents (map contents (car args-list))))
|
|
(if (procedure? proc)
|
|
(apply proc args-contents)
|
|
(try-args (cdr args-list))))))
|
|
(define (coerce-to-arg arg)
|
|
(coerce-args (type-tag arg) args))
|
|
(try-args (cons args (map coerce-to-arg args))))
|
|
|
|
(assert (add3 (make-rational 1 3) 2 (make-rational 3 9)) (make-rational 8 3))
|
|
|
|
; This approach does not work if there exist procedures for mixed types or if
|
|
; the coerced type that would work is different from any of the existing
|
|
; arguments' types.
|
|
|
|
(display (coerce-args 'rational (list (make-rational 1 3) 2 3))) (newline)
|
|
|
|
(newline) (display "ex-2.83") (newline)
|
|
|
|
(newline) (display "ex-2.84") (newline)
|
|
|
|
|
|
(newline) (display "ex-2.85 - we are back!") (newline)
|