### PPL (201-1289101)

#### Solution to HW1

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).

#### 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)
'ok))

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

#### 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)))))
'ok)

(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)))))
'ok)

(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))
1
0))
```

#### 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))
'done))
(define (accept-action-procedure! proc)
(set! action-procedures (cons proc action-procedures))
(proc))
(define (dispatch m)
(cond ((eq? m 'get-signal) signal-value)
((eq? m 'set-signal!) set-my-signal!)
(else (error "Unknown operation -- WIRE" m))))
dispatch))

(define (call-each procedures)
(if (null? procedures)
'done
(begin
((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 (after-delay delay action)
action
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 (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)))
(if (= (segment-time (car segments)) time)
(insert-queue! (segment-queue (car segments))
action)
(let ((rest (cdr segments)))
(if (belongs-before? rest)
(set-cdr!
segments
(cons (make-new-time-segment time action)
(cdr segments)))
(let ((segments (segments agenda)))
(if (belongs-before? segments)
(set-segments!
agenda
(cons (make-new-time-segment time action)
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)
'done
(let ((first-item (first-agenda-item the-agenda)))
(first-item)
(remove-first-agenda-item! the-agenda)
(propagate))))

(define (probe name wire)
(lambda ()
(newline)
(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
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
```