SICP勉強会について社内発表しました。 * SICPとは * SICP勉強用の環境構築(gauche/vim) * SICP勉強会について * SICPの内容紹介 * ディジタル回路のシミュレータ

1. SICP
2017/05/26

2. SICP
SICP
SICP
SICP
:

3. SICP
MIT
Structure and Interpretation of Computer
Programs ( :
)
Scheme

4. SCHEME
LISP
1998 `R5RS` 50
(Gauche, Racket, etc.)
Gauche

5. SICP - GAUCHE
# macOS, homebrewを想定
# Gaucheのインストール
```
brew install gosh
brew install rlwrap # いれておくと便利
```
# slibのインストール(`trace`のため)
```
curl -O 'http://groups.csail.mit.edu/mac/ftpdir/scm/slib-3b5.zip'
unzip slib-3b5.zip
mv slib /usr/local
cd /usr/local/slib
./configure
make
sudo make install
```

6. SCHEME HELLO WORLD
$ echo '(print "Hello World!")' | gosh
Hello World!

7. SICP -VIM
vim `:!gosh %`
`NeoBundle 'thinca/vim-quickrun'`
`silent! map <Space>q <Plug>(quickrun)` - <Space>q
`NeoBundle 'tpope/vim-surround'`
S
`NeoBundle ‘vim-scripts/vim-niji'`
`NeoBundle 'haruyama/vim-matchopen'`

8. TRACE :
; fib.scm
(use slib)
(require 'trace)
(define (fib n)
(cond ((= n 0) 0)
((= n 1) 1)
(else (+ (fib (- n 1))
(fib (- n 2))))))
(trace fib)
(fib 3)
; CALL fib 3
; CALL fib 2
; CALL fib 1
; RETN fib 1
; CALL fib 0
; RETN fib 0
; RETN fib 1
; CALL fib 1
; RETN fib 1
; RETN fib 2

9. SICP
https://sicp.connpass.com/
(http://sicp.iijlab.net/fulltext/xfore.html) HTML
7

10. SICP 4
https://web.archive.org/web/20150104041426/http://oss.timedia.co.jp/show/SICP/Answer%20Book
Excersize 3.26 ( )

11. 3
http://labs.timedia.co.jp/2014/11/reading-sicp-3.22-3.23.html
Exersise 3.22 Exersise 3.55 ( )

13. SICP
(lambda )
LISP ( )
SICP

14. 1
LISP(Scheme) lambda
2
( Huffman etc)
3 .
3.4.4 ←
4 - Scheme Scheme
5 - Scheme

15. 3.3.4
(wires)
(function boxes)
(event-driven simulation)

16. output = !(A) output = A || B output = A && B

17. . (HALF-ADDER)
2 (A B)
S: (sum)
C: (carry)
(D E: )

18. . (HALF-ADDER)
A B S C
0 0 0 0
1 0 1 0
0 1 1 0
1 1 0 1

19. (define a (make-wire))
(define b (make-wire))
(define c (make-wire))
(define d (make-wire))
(define e (make-wire))
(define s (make-wire))
(or-gate a b d)
(and-gate a b c)
(inverter c e)
(and-gate d e s)
. (HALF-ADDER)

20. (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))
. ( )

21. : (FULL-ADDER)
S:
Cout:

22. : (FULL-ADDER)
A B CI S CO
0 0 0 0 0
1 0 0 1 0
0 1 0 1 0
1 1 0 0 1
0 0 1 1 0
1 0 1 0 1
0 1 1 0 1
1 1 1 1 1

23. (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))
: (FULL-ADDER)

24. (get-signal ⟨wire⟩)
(set-signal! ⟨wire⟩ ⟨new value⟩)
(add-action! ⟨wire⟩ ⟨ ⟩)
.
(after-delay ⟨ ⟩ ⟨ ⟩)
add-action!

25. (define (inverter input output)
(define (invert-input)
(let ((new-value (logical-not (get-signal input))))
(after-delay inverter-delay ;遅延時間(定数)
(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))))

26. (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 ;遅延時間(定数)
(lambda ()
(set-signal! output new-value)))))
(add-action! a1 and-action-procedure)
(add-action! a2 and-action-procedure)
'ok)
-
(define (logical-and s1 s2)
(cond ((and (= s1 0) (= s2 0)) 0)
((and (= s1 0) (= s2 1)) 0)
((and (= s1 1) (= s2 0)) 0)
((and (= s1 1) (= s2 1)) 1)
(else (error "Invalid signal" s1 s2))))

27. 3.28
“ .
or-gate , and-gate . ”

28. 3.28
“ .
or-gate , and-gate . ”
(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)
(define (logical-or s1 s2)
(cond ((and (= s1 0) (= s2 0)) 0)
((and (= s1 0) (= s2 1)) 1)
((and (= s1 1) (= s2 0)) 1)
((and (= s1 1) (= s2 1)) 1)
(else (error "Invalid signal" s1 s2))))

29. 3.29 ( )
“ , ,
. or-gate .
and-gate-delay inverter-delay .”

30. 3.29 ( )
“ , ,
. or-gate .
and-gate-delay inverter-delay .”

31. 3.29 ( )
“ , ,
. or-gate .
and-gate-delay inverter-delay .”
A1 A2 A1 && A2 !A1 && !A2 !(!A1 && !A2)
0 0 0 1 0
1 0 0 0 1
0 1 0 0 1
1 1 1 0 1

32. 3.29 ( )
“ , ,
. or-gate .
and-gate-delay inverter-delay .”
(define (or-gate a1 a2 output)
(let ((i1 (make-wire))
(i2 (make-wire))
(a (make-wire)))
(inverter a1 i1)
(inverter a2 i2)
(and-gate i1 i2 a)
(inverter a output))
'ok)

33. 3.29 ( )
“ , ,
. or-gate .
and-gate-delay inverter-delay .”
(define (or-gate a1 a2 output)
(let ((i1 (make-wire))
(i2 (make-wire))
(a (make-wire)))
(inverter a1 i1)
(inverter a2 i2)
(and-gate i1 i2 a)
(inverter a output))
'ok)
:
2 * inverter-delay + and-gate-delay

34. 3.30
“ 3.27 n (ripple-carry adder) .
n . A1,A2,
A3, ...,An B1, B2, B3, ..., Bn ( Ak Bk 0 1).
n S1, S2, S3, ..., Sn , C .
ripple-carry-adder . n
--- Ak, Bk Sk--- , C .
,
. n , ,
, . ”

35. 3.30 (RIPPLE-CARRY
ADDER)

36. 3.30 (RIPPLE-CARRY
ADDER)
“ 3.27 n (ripple-carry adder) . n
. A1,A2,A3, ...,An B1, B2,
B3, ..., Bn ( Ak Bk 0 1). n S1, S2, S3, ..., Sn ,
C . ripple-carry-adder .
n --- Ak, Bk Sk--- , C
. ”

37. 3.30 (RIPPLE-CARRY
ADDER)
(define (ripple-carry-adder as bs ss c)
(define (iter as bs ss ck-1)
(if (not (null? as))
(let ((ak (car as))
(bk (car bs))
(sk (car ss))
(ck (make-wire)))
(full-adder ak bk ck sk ck-1)
(iter (cdr as) (cdr bs) (cdr ss) ck))))
(let ((c1 (make-wire)))
(full-adder (car as) (car bs) c1 (car ss) c)
(iter (cdr as) (cdr bs) (cdr ss) c-in)))
“ 3.27 n (ripple-carry adder) . n
. A1,A2,A3, ...,An B1, B2,
B3, ..., Bn ( Ak Bk 0 1). n S1, S2, S3, ..., Sn ,
C . ripple-carry-adder .
n --- Ak, Bk Sk--- , C
. ”

38. * 1インバータ遅延(Di)
* 1アンドゲート遅延(Da)
* 1オアゲート遅延(Do)
* Do >= Da + Di と仮定
半加算器の遅延:
Sの遅延(Dhs) = max(Do, Da + Di) + Da
= Do + Da
Cの遅延(Dhc) = Da
“ , . n
, , ,
. ”
3.30 (RIPPLE-CARRY
ADDER)

39. 3.30 (RIPPLE-CARRY
ADDER)
半加算器 Sの遅延(Dhs) = Do + Da
半加算器 Cの遅延(Dhc) = Da
全加算器の遅延:
Sの遅延(Dfs) = max(0, Dhs) + Dhs
= 2Dhs
= 2(Do + Da)
= 2Do + 2Da
Cの遅延(Dfc) = max(Dhs + Dhc, Dhc) + Do
= Dhs + Dhc + Do
= (Do + Da) + (Da) + Do
= 2Do + 2Da
“ , . n
, , ,
. ”

40. 全加算器 Sの遅延(Dfs) = 2Do + 2Da
全加算器 Cの遅延(Dfc) = 2Do + 2Da
n桁の繰上り伝播加算器:
S1の遅延 Drs = (n-1) * Dfc + Dfs
= (n-1) * (2Do + 2Da) + 2Do + 2Da
= n(2Do + 2Da)
= 2n(Do + Da)
Cの遅延 Drc = (n-1) * Dfc + Dfc
= n * Dfc
= 2n(Do + Da)
= n(2Do + 2Da)
= 2n(Do + Da)
例:
Di = 2, Da = 3, Do = 5 の時、
Drs = Drc = 2n(3 + 5) = 16n
3.30 (RIPPLE-CARRY
ADDER)
“ , . n
, , ,
. ”

41. - 3.3.5
2017/06/07( ) 19:30
21:00 @3F
- 🍕 🍣
connpass(http://sicp.iijlab.net/fulltext/x335.html )

42. SICP
Structure and Interpretation of Computer Programs https://mitpress.mit.edu/sicp/full-text/book/book.html - HTML
http://sicp.iijlab.net/fulltext/ - HTML
minghai/sicp-pdf: SICP PDF with Texinfo and LaTeX source https://github.com/minghai/sicp-pdf - minghai
hiroshi-manabe/sicp-pdf: SICP PDF with Texinfo and LaTeX source https://github.com/hiroshi-manabe/sicp-pdf - hiroshi-manabe
SICP
Lisper MIT SICP( ) - Qiita http://qiita.com/kaz-yos/items/d1ecd4bfe9989c290e99
SICP - sicp http://sicp.g.hatena.ne.jp/hyuki/
(SICP) - Higepon’s blog http://d.hatena.ne.jp/higepon/20061027/1161960363
(SICP) | http://kinokoru.jp/archives/794
( ) https://web.archive.org/web/20150104041426/http://oss.timedia.co.jp/
show/SICP/Answer%20Book
SICP-Solutions http://community.schemewiki.org/?SICP-Solutions