SICP問題3.28
ディジタル回路のシミュレータでand-gateと似ているor-gateを定義する問題。
まずは論理和(locgical or)の定義
(define (logical-or a b) (cond ((and (= a 0) (= b 0)) 0) ((or (and (= a 1) (= b 1)) (and (= a 1) (= b 0)) (and (= a 0) (= b 1))) 1) (else (error "Invalid signal" a b))))
or-gateの定義
(define (or-gate a1 a2 output) (define (or-action-procedure) (let ((new-value (logical-or (get-signal a1) (get-signal a2)))) (after-delay or-gate-delay (lambda () (set-signal! output new-value))))) (add-action! a1 or-action-procedure) (add-action! a2 or-action-procedure) 'ok)
で、解答は終わりなんだけど、このままだと動かないので、教科書の後の節に載ってる定義も写経。
; (get-signal <wire>) ; 回線の信号の現在の値を返す ; (set-signal! <wire> <new value>) ; 回線の信号の値を新しい値に変更する ; (add-action! <wire> <procedure of no argument>) ; 回線の信号が値を変えた時、指定した手続きが走ることを主張する。更に遅延時間と走らせるべき手続きを取り、遅延時間後に与えられた手続きを実行する手続きafter-delayを利用する (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!) ((eq? m 'add-action!) accept-action-procedure!) (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 (add-action! wire action-procedure) ((wire 'add-action!) action-procedure)) ; 次第書き(agenda) ; (make-agenda) (define (make-agenda) (list 0)) ; 新しい空の手続きを書き出す ; (empty-agenda? <agenda>) ; 指定した次第書きが空なら真 ; (first-agenda-item <agenda>) ; 次第書きの最初の項目を返す ; (remove-first-agenda-item! <agenda>) ; 最初の項目を削除し、次第書きを修正する ; (add-to-agenda! <time> <action> <agenda>) ; 与えられたアクション手続きが指定した時刻に走るように追加して、次第書きを修正する ; (current-time <agenda>) ; 現在のシミュレーション時刻を返す (define (current-time agenda) (car agenda)) (define (set-current-time! agenda time) (set-car! agenda time)) (define (make-time-segment time queue) (cons time queue)) (define (segment-time s) (car s)) (define (segment-queue s) (cdr s)) ; 3.2.2のキュー演算 (define (front-ptr queue) (car queue)) (define (rear-ptr queue) (cdr queue)) (define (set-front-ptr! queue item) (set-car! queue item)) (define (set-rear-ptr! queue item) (set-cdr! queue item)) (define (empty-queue? queue) (null? (front-ptr queue))) (define (make-queue) (cons '() '())) (define (front-queue queue) (if (empty-queue? queue) (error "FRONT called with an empty queue" queue) (car (front-ptr queue)))) (define (insert-queue! queue item) (let ((new-pair (cons item '()))) (cond ((empty-queue? queue) (set-front-ptr! queue new-pair) (set-rear-ptr! queue new-pair) queue) (else (set-cdr! (rear-ptr queue) new-pair) (set-rear-ptr! queue new-pair) queue)))) (define (delete-queue! queue) (cond ((empty-queue? queue) (error "DELETE! called with an empty queue" queue)) (else (set-front-ptr! queue (cdr (front-ptr queue))) queue))) (define (print-queue queue) (front-ptr queue)) (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 (after-delay delay action) (add-to-agenda! (+ delay (current-time the-agenda)) action the-agenda)) ; 次第書きにある手続きを順次に実行する手続き (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)))) ; 信号が値を変えた時には、新しい信号の値を、現在の時刻および回線を識別する名と一緒に印字するプローブ (define (probe name wire) (add-action! wire (lambda () (newline) (display name) (display " ") (display (current-time the-agenda)) (display " New-value = ") (display (get-signal wire))))) (define the-agenda (make-agenda)) (define inverter-delay 2) (define and-gate-delay 3) (define or-gate-delay 5) (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)) action) (let ((rest (cdr segments))) (if (belongs-before? rest) (set-cdr! segments (cons (make-new-time-segment time action) (cdr segments))) (add-to-segments! rest))))) (let ((segments (segments agenda))) (if (belongs-before? segments) (set-segments! agenda (cons (make-new-time-segment time action) segments)) (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))))) ; 半加算器(half-adder) (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)) ; 全加算器(full-adder) ; 二進数を足すのに使う基本的な回路 (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) 'ok)) ; インバータ(inverter) 否定 (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) 'ok) (define (logical-not s) (cond ((= s 0) 1) ((= s 1) 0) (else (error "Invalid signal" s)))) ; アンドゲート(and-gate) (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) 'ok) ; 論理積(logical and) (define (logical-and a b) (cond ((and (= a 1) (= b 1)) 1) ((or (and (= a 1) (= b 0)) (and (= a 0) (= b 1)) (and (= a 0) (= b 0))) 0) (else (error "Invalid signal" a b))))