SICP 2.5.1 Generic arithmetic operations
In previous post I have used wrong StackOverflow answer. :) Or, to be more precise, right answer for that section, but useless here, as we want to store in table functions for multiple arguments.
Correct answer that supports lists looks like this:
(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))
Also I needed to copypaste a lot of code to be able to start working on first exercise:
(define (attach-tag type-tag contents)
(cons type-tag contents))
(define (type-tag datum)
(if (pair? datum)
(car datum)
(error "Bad tagged datum -- TYPE-TAG" datum)))
(define (contents datum)
(if (pair? datum)
(cdr datum)
(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 (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 (install-rectangular-package)
;; internal procedures
(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))))
;; interface to the rest of the system
(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 r a))))
'done)
(install-rectangular-package)
(define (install-polar-package)
;; internal procedures
(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)))
;; interface to the rest of the system
(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 r a))))
'done)
(install-rectangular-package)
(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))
;; 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))))
(put 'real-part '(complex) real-part)
(put 'imag-part '(complex) imag-part)
(put 'magnitude '(complex) magnitude)
(put 'angle '(complex) angle)
'done)
(install-complex-package)
Exercise 2.77
(define z (cons 'complex (cons 'rectangular (cons 3 4))))
(magnitude z)
It calls apply-generic
to do operation 'magnitude
with z
(apply-generic 'magnitude (cons 'complex (cons 'rectangular (cons 3 4))))
apply-generic
looks for operation 'magnitude
for 'complex
numbers, and applies it to value inside
(apply (get 'magnitude 'complex) (cons 'rectangular (cons 3 4)))
That operation, thanks to Alyssa P. Hacker, is just application of same magnitude
function, but this time for 'rectangular
object
(magnitude (cons 'rectangular (cons 3 4)))
apply-generic applies operation 'magnitude for 'rectangular type to content of rectangular "package":
(apply (get 'magnitude 'rectangular) (cons 3 4))
which is magnitude
function from inside rectangular package
(magnitude (cons 3 4))
(sqrt (+ (square 3)
(square 4)))
5
Exercise 2.78
(define (attach-tag type-tag contents)
(if (eq? type-tag 'scheme-number)
contents
(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))
)
)
To test:
(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)))
'done)
(install-scheme-number-package)
Exercise 2.79
(put 'equ? '(scheme-number scheme-number) =)
(put 'equ? '(complex complex)
(lambda (x y) (and
(= (real-part x) (real-part y))
(= (imag-part x) (imag-part y))
))
)
(define (equ? x y) (apply-generic 'equ? x y))
Exercise 2.80
(put 'zero? '(scheme-number)
(lambda (x) (= x 0))
)
(put 'zero? '(complex)
(lambda (x) (= (magnitude x) 0))
)
(define (zero? x) (apply-generic 'zero? x))