PPL (201-1289101)

Solution to HW1

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From SICP: Section 3.3.4. This is the digital circuit simulation system. You need to implement the or-gate circuit yourselves (it is very similar to the and-gate).


  1. Using the system to create compound-gates
  2. Implementing primitive gates
  3. Implementing wires
  4. Implementing the agenda
  5. The simulation engine

Using the system to create compound-gates

(define (half-adder a b s c)
  (let ((d (make-wire)) (e (make-wire)))
    (or-gate a b d)
    (and-gate a b c)
    (inverter c e)
    (and-gate d e s)

(define (full-adder a b c-in sum c-out)
  (let ((s (make-wire))
        (c1 (make-wire))
        (c2 (make-wire)))
    (half-adder b c-in s c1)
    (half-adder a s sum c2)
    (or-gate c1 c2 c-out)

Implementing primitive gates

(define (inverter input output)
  (define (invert-input)
    (let ((new-value (logical-not (get-signal input))))
      (after-delay inverter-delay
                   (lambda ()
                     (set-signal! output new-value)))))
  (add-action! input invert-input)

(define (and-gate a1 a2 output)
  (define (and-action-procedure)
    (let ((new-value
           (logical-and (get-signal a1) (get-signal a2))))
      (after-delay and-gate-delay
                   (lambda ()
                     (set-signal! output new-value)))))
  (add-action! a1 and-action-procedure)
  (add-action! a2 and-action-procedure)

(define (logical-not s)
  (cond ((= s 0) 1)
        ((= s 1) 0)
        (else (error "Invalid signal" s))))

;;Note: logical-and should test for valid signals, as logical-not does
;;Fix it.
(define (logical-and x y)
  (if (and (= x 1) (= y 1))

Implementing wires

(define (make-wire)
  (let ((signal-value 0) (action-procedures '()))
    (define (set-my-signal! new-value)
      (if (not (= signal-value new-value))
          (begin (set! signal-value new-value)
                 (call-each action-procedures))
    (define (accept-action-procedure! proc)
      (set! action-procedures (cons proc action-procedures))
    (define (dispatch m)
      (cond ((eq? m 'get-signal) signal-value)
            ((eq? m 'set-signal!) set-my-signal!)
            ((eq? m 'add-action!) accept-action-procedure!)
            (else (error "Unknown operation -- WIRE" m))))

(define (call-each procedures)
  (if (null? procedures)
        ((car procedures))
        (call-each (cdr procedures)))))

(define (get-signal wire)
  (wire 'get-signal))

(define (set-signal! wire new-value)
  ((wire 'set-signal!) new-value))

(define (add-action! wire action-procedure)
  ((wire 'add-action!) action-procedure))

(define (after-delay delay action)
  (add-to-agenda! (+ delay (current-time the-agenda))

Implementing the agenda

(define (make-time-segment time queue)
  (cons time queue))
(define (segment-time s) (car s))
(define (segment-queue s) (cdr s))

(define (make-agenda) (list 0))

(define (current-time agenda) (car agenda))
(define (set-current-time! agenda time)
  (set-car! agenda time))

(define (segments agenda) (cdr agenda))
(define (set-segments! agenda segments)
  (set-cdr! agenda segments))
(define (first-segment agenda) (car (segments agenda)))
(define (rest-segments agenda) (cdr (segments agenda)))

(define (empty-agenda? agenda)
  (null? (segments agenda)))

(define (add-to-agenda! time action agenda)
  (define (belongs-before? segments)
    (or (null? segments)
        (< time (segment-time (car segments)))))
  (define (make-new-time-segment time action)
    (let ((q (make-queue)))
      (insert-queue! q action)
      (make-time-segment time q)))
  (define (add-to-segments! segments)
    (if (= (segment-time (car segments)) time)
        (insert-queue! (segment-queue (car segments))
        (let ((rest (cdr segments)))
          (if (belongs-before? rest)
               (cons (make-new-time-segment time action)
                     (cdr segments)))
              (add-to-segments! rest)))))
  (let ((segments (segments agenda)))
    (if (belongs-before? segments)
         (cons (make-new-time-segment time action)
        (add-to-segments! segments))))

(define (remove-first-agenda-item! agenda)
  (let ((q (segment-queue (first-segment agenda))))
    (delete-queue! q)
    (if (empty-queue? q)
        (set-segments! agenda (rest-segments agenda)))))

(define (first-agenda-item agenda)
  (if (empty-agenda? agenda)
      (error "Agenda is empty -- FIRST-AGENDA-ITEM")
      (let ((first-seg (first-segment agenda)))
        (set-current-time! agenda (segment-time first-seg))
        (front-queue (segment-queue first-seg)))))

The simulation engine

(define (propagate)
  (if (empty-agenda? the-agenda)
      (let ((first-item (first-agenda-item the-agenda)))
        (remove-first-agenda-item! the-agenda)

(define (probe name wire)
  (add-action! wire
               (lambda ()        
                 (display name)
                 (display " ")
                 (display (current-time the-agenda))
                 (display "  New-value = ")
                 (display (get-signal wire)))))

;;; Sample simulation

;: (define the-agenda (make-agenda))
;: (define inverter-delay 2)
;: (define and-gate-delay 3)
;: (define or-gate-delay 5)
;: (define input-1 (make-wire))
;: (define input-2 (make-wire))
;: (define sum (make-wire))
;: (define carry (make-wire))
;: (probe 'sum sum)
;: (probe 'carry carry)
;: (half-adder input-1 input-2 sum carry)
;: (set-signal! input-1 1)
;: (propagate)
;: (set-signal! input-2 1)
;: (propagate)

;; That's all folks

Last modified May 27th, 1997 Michael Elhadad