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8.5 Illustrating Slot Description

To illustrate slot description, we can redefine the <my-complex> class seen before. A definition could be:

(define-class <my-complex> (<number>) 
   (r #:init-value 0 #:getter get-r #:setter set-r! #:init-keyword #:r)
   (i #:init-value 0 #:getter get-i #:setter set-i! #:init-keyword #:i))

With this definition, the r and i slots are set to 0 by default, and can be initialised to other values by calling make with the #:r and #:i keywords. Also the generic functions get-r, set-r!, get-i and set-i! are automatically defined to read and write the slots.

(define c1 (make <my-complex> #:r 1 #:i 2))
(get-r c1) ⇒ 1
(set-r! c1 12)
(get-r c1) ⇒ 12
(define c2 (make <my-complex> #:r 2))
(get-r c2) ⇒ 2
(get-i c2) ⇒ 0

Accessors can both read and write a slot. So, another definition of the <my-complex> class, using the #:accessor option, could be:

(define-class <my-complex> (<number>) 
   (r #:init-value 0 #:accessor real-part #:init-keyword #:r)
   (i #:init-value 0 #:accessor imag-part #:init-keyword #:i))

With this definition, the r slot can be read with:

(real-part c)

and set with:

(set! (real-part c) new-value)

Suppose now that we want to manipulate complex numbers with both rectangular and polar coordinates. One solution could be to have a definition of complex numbers which uses one particular representation and some conversion functions to pass from one representation to the other. A better solution is to use virtual slots, like this:

(define-class <my-complex> (<number>)
   ;; True slots use rectangular coordinates
   (r #:init-value 0 #:accessor real-part #:init-keyword #:r)
   (i #:init-value 0 #:accessor imag-part #:init-keyword #:i)
   ;; Virtual slots access do the conversion
   (m #:accessor magnitude #:init-keyword #:magn  
      #:allocation #:virtual
      #:slot-ref (lambda (o)
                  (let ((r (slot-ref o 'r)) (i (slot-ref o 'i)))
                    (sqrt (+ (* r r) (* i i)))))
      #:slot-set! (lambda (o m)
                    (let ((a (slot-ref o 'a)))
                      (slot-set! o 'r (* m (cos a)))
                      (slot-set! o 'i (* m (sin a))))))
   (a #:accessor angle #:init-keyword #:angle
      #:allocation #:virtual
      #:slot-ref (lambda (o)
                  (atan (slot-ref o 'i) (slot-ref o 'r)))
      #:slot-set! (lambda(o a)
                   (let ((m (slot-ref o 'm)))
                      (slot-set! o 'r (* m (cos a)))
                      (slot-set! o 'i (* m (sin a)))))))

In this class definition, the magnitude m and angle a slots are virtual, and are calculated, when referenced, from the normal (i.e. #:allocation #:instance) slots r and i, by calling the function defined in the relevant #:slot-ref option. Correspondingly, writing m or a leads to calling the function defined in the #:slot-set! option. Thus the following expression

(slot-set! c 'a 3)

permits to set the angle of the c complex number.

(define c (make <my-complex> #:r 12 #:i 20))
(real-part c) ⇒ 12
(angle c) ⇒ 1.03037682652431
(slot-set! c 'i 10)
(set! (real-part c) 1)
(describe c)
#<<my-complex> 401e9b58> is an instance of class <my-complex>
Slots are: 
     r = 1
     i = 10
     m = 10.0498756211209
     a = 1.47112767430373

Since initialization keywords have been defined for the four slots, we can now define the standard Scheme primitives make-rectangular and make-polar.

(define make-rectangular 
   (lambda (x y) (make <my-complex> #:r x #:i y)))

(define make-polar
   (lambda (x y) (make <my-complex> #:magn x #:angle y)))

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