9.5 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 magniture 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)))