D  A clock for infinity

The Guile [13] procedure alarm provides an interruptable timer mechanism. The user can set or reset the alarm for some time units, or stop it. When the alarm’s timer runs out of this time, it will set off an alarm, whose consequences are user-settable. Guile’s alarm is not quite the clock of sec 15.1, but we can modify it easily enough.

The alarm’s timer is initially stopped or quiescent, i.e., it will not set off an alarm even as time goes by. To set the alarm’s time-to-alarm to be n seconds, where n is not 0, run (alarm n). If the timer was already set (but has not yet set off an alarm), the (alarm n) procedure call will return the number of seconds remaining from the previous alarm setting. If there is no previous alarm setting, (alarm n) returns 0.

The procedure call (alarm 0) stops the alarm’s timer, i.e., the countdown of time is stopped, the timer becomes quiescent and no alarm will go off. (alarm 0) also returns the seconds remaining from a previous alarm setting, if any.

By default, when the alarm’s countdown reaches 0, Guile will display a message on the console and exit. More useful behavior can be obtained by using the procedure sigaction, as follows:

(sigaction SIGALRM
  (lambda (sig)
    (display "Signal ")
    (display sig)
    (display " raised.  Continuing...")
    (newline)))

The first argument SIGALRM (which happens to be 14) identifies to sigaction that it is the alarm handler that needs setting.¹ The second argument is a unary alarm-handling procedure of the user’s choice. In this example, when the alarm goes off, the handler displays "Signal 14 raised. Continuing..." on the console without exiting Scheme. (The 14 is the SIGALRM value that the alarm will pass to its handler. Don’t worry about it now.)

From our point of view, this simple timer mechanism poses one problem. A return value of 0 from a call to the procedure alarm is ambiguous: It could either mean that the alarm was quiescent, or that it was just about to run out of time. We could resolve this ambiguity if we could include “*infinity*” in the alarm arithmetic. In other words, we would like a clock that works almost like alarm, except that a quiescent clock is one with *infinity* seconds. This will make many things natural, viz.,

(1) (clock n) on a quiescent clock returns *infinity*, not 0.

(2) To stop the clock, call (clock *infinity*), not (clock 0).

(3) (clock 0) is equivalent to setting the clock to an infinitesimally small amount of time, viz., to cause it to raise an alarm instantaneously.

In Guile, we can define *infinity* as the following “number”:

(define *infinity* (/ 1 0))

We can define clock in terms of alarm.

(define clock
  (let ((stopped? #t)
        (clock-interrupt-handler
         (lambda () (error "Clock interrupt!"))))
    (let ((generate-clock-interrupt
           (lambda ()
             (set! stopped? #t)
             (clock-interrupt-handler))))
      (sigaction SIGALRM
                 (lambda (sig) (generate-clock-interrupt)))
      (lambda (msg val)
        (case msg
          ((set-handler)
           (set! clock-interrupt-handler val))
          ((set)
           (cond ((= val *infinity*)
                  ;This is equivalent to stopping the clock.
                  ;This is almost equivalent to (alarm 0), except
                  ;that if the clock is already stopped,
                  ;return *infinity*.

                  (let ((time-remaining (alarm 0)))
                    (if stopped? *infinity*
                        (begin (set! stopped? #t)
                          time-remaining))))

                 ((= val 0)
                  ;This is equivalent to setting the alarm to
                  ;go off immediately.  This is almost equivalent
                  ;to (alarm 0), except you force the alarm
                  ;handler to run.

                  (let ((time-remaining (alarm 0)))
                    (if stopped?
                        (begin (generate-clock-interrupt)
                          *infinity*)
                        (begin (generate-clock-interrupt)
                          time-remaining))))

                 (else
                  ;This is equivalent to (alarm n) for n != 0.
                  ;Just remember to return *infinity* if the
                  ;clock was previously quiescent.

                  (let ((time-remaining (alarm val)))
                    (if stopped?
                        (begin (set! stopped? #f) *infinity*)
                        time-remaining))))))))))

The clock procedure uses three internal state variables:

(1) stopped?, to describe if the clock is stopped;

(2) clock‑interrupt‑handler, which is a thunk describing the user-specified part of the alarm-handling action; and

(3) generate‑clock‑interrupt, another thunk which will set stopped? to false before running the user-specified alarm handler.

The clock procedure takes two arguments. If the first argument is set‑handler, it uses the second argument as the alarm handler.

If the first argument is set, it sets the time-to-alarm to the second argument, returning the time remaining from a previous setting. The code treats 0, *infinity* and other values for time differently so that the user gets a mathematically transparent interface to alarm.