開発環境
- OS X Lion - Apple(OS)
- Emacs、BBEdit - Bare Bones Software, Inc. (Text Editor)
- プログラミング言語: MIT/GNU Scheme
計算機プログラムの構造と解釈(Gerald Jay Sussman(原著)、Julie Sussman(原著)、Harold Abelson(原著)、和田 英一(翻訳)、ピアソンエデュケーション、原書: Structure and Interpretation of Computer Programs (MIT Electrical Engineering and Computer Science)(SICP))の4(超言語的抽象)、4.2(Scheme の変形 - 遅延評価)、4.2.2(遅延評価の解釈系)、評価器の修正、サンクの表現、問題 4.29を解いてみる。
その他参考書籍
問題 4.29
フィボナッチ数を求める場合は、メモ化しないと、メモ化するよりプログラムは遥かに遅く走る。(n番目のnが大きければ大きい程。)
メモ化することにより、2回計算するところが1回で済むようになるからメモ化した方が速くなる。
n番目のフィボナッチ吸うを求める手続きの定義。
(define (fib n)
(cond ((= n 0) 0)
((= n 1) 1)
(else (+ (fib (- n 1))
(fib (- n 2))))))
メモ化した場合。
コード(BBEdit)
sample.scm
(define (eval exp env)
(cond ((self-evaluating? exp) exp)
((variable? exp) (lookup-variable-value exp env))
((quoted? exp) (text-of-quotation exp))
((assignment? exp) (eval-assignment exp env))
((definition? exp) (eval-definition exp env))
((if? exp) (eval-if exp env))
((lambda? exp)
(make-procedure (lambda-parameters exp)
(lambda-body exp)
env))
((begin? exp)
(eval-sequence (begin-actions exp) env))
((cond? exp) (eval (cond->if exp) env))
((application? exp)
(apply-in-eval (actual-value (operator exp) env)
(operands exp)
env))
(else
(error "Unknown expression type -- eval" exp))))
(define (actual-value exp env)
(force-it (eval exp env)))
;; 超循環表記ののapplyの定義の名前を替え、基本手続きの名前との衝突を避ける
(define (apply-in-eval procedure arguments env)
(cond ((primitive-procedure? procedure)
(apply-primitive-procedure
procedure
(list-of-arg-values arguments env)))
((compound-procedure? procedure)
(eval-sequence
(procedure-body procedure)
(extend-environment
(procedure-parameters procedure)
(list-of-delayed-args arguments env)
(procedure-environment procedure))))
(else
(error
"Unknown procedure type -- APPLY" procedure))))
(define (list-of-arg-values exps env)
(if (no-operands? exps)
'()
(cons (actual-value (first-operand exps) env)
(list-of-arg-values (rest-operands exps)
env))))
(define (list-of-delayed-args exps env)
(if (no-operands? exps)
'()
(cons (delay-it (first-operand exps) env)
(list-of-delayed-args (rest-operands exps)
env))))
(define (delay-it exp env)
(list 'thunk exp env))
(define (thunk? obj)
(tagged-list? obj 'thunk))
(define (thunk-exp thunk) (cadr thunk))
(define (thunk-env thunk) (caddr thunk))
(define (evaluated-thunk? obj)
(tagged-list? obj 'evaluated-thunk))
(define (thunk-value evaluated-thunk) (cadr evaluated-thunk))
(define (force-it obj)
(cond ((thunk? obj)
(let ((result (actual-value
(thunk-exp obj)
(thunk-env obj))))
(set-car! obj 'evaluated-thunk)
(set-car! (cdr obj) result)
(set-cdr! (cdr obj) '())
result))
((evaluated-thunk? obj)
(thunk-value obj))
(else obj)))
(define (eval-if exp env)
(if (true? (actual-value (if-predicate exp) env))
(eval (if-consequent exp) env)
(eval (if-alternative exp) env)))
(define (eval-sequence exps env)
(cond ((last-exp? exps) (eval (first-exp exps) env))
(else (eval (first-exp exps) env)
(eval-sequence (rest-exps exps) env))))
(define (eval-assignment exp env)
(set-variable-value! (assignment-variable exp)
(eval (assignment-value exp) env)
env)
'ok)
(define (eval-definition exp env)
(define-variable! (definition-variable exp)
(eval (definition-value exp) env)
env)
'ok)
(define (self-evaluating? exp)
(cond ((number? exp) true)
((string? exp) true)
(else false)))
(define (variable? exp) (symbol? exp))
(define (quoted? exp)
(tagged-list? exp 'quote))
(define (text-of-quotation exp) (cadr exp))
(define (tagged-list? exp tag)
(if (pair? exp)
(eq? (car exp) tag)
false))
(define (assignment? exp)
(tagged-list? exp 'set!))
(define (assignment-variable exp) (cadr exp))
(define (assignment-value exp) (caddr exp))
(define (definition? exp)
(tagged-list? exp 'define))
(define (definition-variable exp)
(if (symbol? (cadr exp))
(cadr exp)
(caadr exp)))
(define (definition-value exp)
(if (symbol? (cadr exp))
(caddr exp)
(make-lambda (cdadr exp)
(cddr exp))))
(define (lambda? exp) (tagged-list? exp 'lambda))
(define (lambda-parameters exp) (cadr exp))
(define (lambda-body exp) (cddr exp))
(define (make-lambda parameters body)
(cons 'lambda (cons parameters body)))
(define (if? exp) (tagged-list? exp 'if))
(define (if-predicate exp) (cadr exp))
(define (if-consequent exp) (caddr exp))
(define (if-alternative exp)
(if (not (null? (cddr exp)))
(cadddr exp)
'false))
(define (make-if predicate consequent alternative)
(list 'if predicate consequent alternative))
(define (begin? exp) (tagged-list? exp 'begin))
(define (begin-actions exp) (cdr exp))
(define (last-exp? seq) (null? (cdr seq)))
(define (first-exp seq) (car seq))
(define (rest-exps seq) (cdr seq))
(define (sequence->exp seq)
(cond ((null? seq) seq)
((last-exp? seq) (first-exp seq))
(else (make-begin seq))))
(define (application? exp) (pair? exp))
(define (operator exp) (car exp))
(define (operands exp) (cdr exp))
(define (no-operands? ops) (null? ops))
(define (first-operand ops) (car ops))
(define (rest-operands ops) (cdr ops))
(define (cond? exp) (tagged-list? exp 'cond))
(define (cond-clauses exp) (cdr exp))
(define (cond-else-clause? clause)
(eq? (cond-predicate clause) 'else))
(define (cond-predicate clause) (car clause))
(define (cond-actions clause) (cdr clause))
(define (cond->if exp)
(expand-clauses (cond-clauses exp)))
(define (expand-clauses clauses)
(if (null? clauses)
'false
(let ((first (car clauses))
(rest (cdr clauses)))
(if (cond-else-clause? first)
(if (null? rest)
(sequence->exp (cond-actions first))
(error "ELSE clause isn't last -- COND->IF"
clauses))
(make-if (cond-predicate first)
(sequence->exp (cond-actions first))
(expand-clauses rest))))))
(define (true? x)
(not (eq? x false)))
(define (false? x)
(eq? x false))
(define (make-procedure parameters body env)
(list 'procedure parameters body env))
(define (compound-procedure? p)
(tagged-list? p 'procedure))
(define (procedure-parameters p) (cadr p))
(define (procedure-body p) (caddr p))
(define (procedure-environment p) (cadddr p))
(define (enclosing-environment env) (cdr env))
(define (first-frame env) (car env))
(define the-empty-environment '())
(define (make-frame variables values)
(cons variables values))
(define (frame-variables frame) (car frame))
(define (frame-values frame) (cdr frame))
(define (add-binding-to-frame! var val frame)
(set-car! frame (cons var (car frame)))
(set-cdr! frame (cons val (cdr frame))))
(define (extend-environment vars vals base-env)
(if (= (length vars) (length vals))
(cons (make-frame vars vals) base-env)
(if (< (length vars) (length vals))
(error "Too many arguments supplied" vars vals)
(error "Too few arguments supplied" vars vals))))
(define (lookup-variable-value var env)
(define (env-loop env)
(define (scan vars vals)
(cond ((null? vars)
(env-loop (enclosing-environment env)))
((eq? var (car vars))
(let ((val (car vals)))
(if (eq? val '*unassigned)
(error "Unassigned variable" var)
val)))
(else (scan(cdr vars) (cdr vals)))))
(if (eq? env the-empty-environment)
(error "Unbound variable" var)
(let ((frame (first-frame env)))
(scan (frame-variables frame)
(frame-values frame)))))
(env-loop env))
(define (set-variable-value! var val env)
(define (env-loop env)
(define (scan vars vals)
(cond ((null? vars)
(env-loop (enclosing-environment env)))
((eq? var (car vars))
(set-car! vals val))
(else (scan (cdr vars) (cdr vals)))))
(if (eq? env the-empty-environment)
(error "Unbound variable -- SET!" var)
(let ((frame (first-frame env)))
(scan (frame-variables frame)
(frame-values frame)))))
(env-loop env))
(define (define-variable! var val env)
(let ((frame (first-frame env)))
(define (scan vars vals)
(cond ((null? vars)
(add-binding-to-frame! var val frame))
((eq? var (car vars))
(set-car! vals val))
(else (scan (cdr vars) (cdr vals)))))
(scan (frame-variables frame)
(frame-values frame))))
(define (setup-environment)
(let ((initial-env
(extend-environment (primitive-procedure-names)
(primitive-procedure-objects)
the-empty-environment)))
(define-variable! 'true true initial-env)
(define-variable! 'false false initial-env)
initial-env))
(define (primitive-procedure? proc)
(tagged-list? proc 'primitive))
(define (primitive-implementation proc) (cadr proc))
(define primitive-procedures
(list (list 'car car)
(list 'cdr cdr)
(list 'cons cons)
(list 'null? null?)
(list '* *)
(list '+ +)
(list '- -)
(list '/ /)
(list '< <)
(list '= =)
(list '> >)
(list 'apply apply)
(list 'atan atan)
(list 'cos cos)
(list 'display display)
(list 'eq? eq?)
(list 'error error)
(list 'eval eval)
(list 'list list)
(list 'log log)
(list 'max max)
(list 'min min)
(list 'newline newline)
(list 'not not)
(list 'number? number?)
(list 'pair? pair?)
(list 'quotient quotient)
;; (list 'random random)
(list 'read read)
(list 'remainder remainder)
(list 'round round)
;; (list 'runtime runtime)
(list 'set-car! set-car!)
(list 'set-cdr! set-cdr!)
(list 'sin sin)
(list 'symbol? symbol?)
(list 'vector-ref vector-ref)
(list 'vector-set! vector-set!)))
(define (primitive-procedure-names)
(map car primitive-procedures))
(define (primitive-procedure-objects)
(map (lambda (proc) (list 'primitive (cadr proc)))
primitive-procedures))
(define (apply-primitive-procedure proc args)
(apply
(primitive-implementation proc) args))
(define input-prompt ";;; L-Eval input:")
(define output-prompt ";;; L-Eval value:")
(define (driver-loop)
(prompt-for-input input-prompt)
(let ((input (read)))
(let ((output
(actual-value input the-global-environment)))
(announce-output output-prompt)
(user-print output)))
(driver-loop))
(define (prompt-for-input string)
(newline) (newline) (display string) (newline))
(define (announce-output string)
(newline) (display string) (newline))
(define (user-print object)
(if (compound-procedure? object)
(display (list 'compound-procedure?
(procedure-parameters object)
(procedure-body object)
'<procedure-env>))
(display object)))
(define the-global-environment (setup-environment))
(driver-loop)
入出力結果(Terminal, REPL(Read, Eval, Print, Loop))
$ scheme
MIT/GNU Scheme running under MacOSX
Type `^C' (control-C) followed by `H' to obtain information about interrupts.
Copyright (C) 2011 Massachusetts Institute of Technology
This is free software; see the source for copying conditions. There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
Image saved on Friday April 13, 2012 at 9:02:52 AM
Release 9.1.1 || Microcode 15.3 || Runtime 15.7 || SF 4.41 || LIAR/C 4.118
Edwin 3.116
1 ]=> (load "./sample.scm")
;Loading "./sample.scm"...
;;; L-Eval input:
(define (fib n)
(cond ((= n 0) 0)
((= n 1) 1)
(else (+ (fib (- n 1))
(fib (- n 2))))))
;;; L-Eval value:
ok
;;; L-Eval input:
(fib 20)
;;; L-Eval value:
6765
;;; L-Eval input:
End of input stream reached.
Moriturus te saluto.
$
ちょっと待ったら計算結果が出力された。(10秒以内くらい)
メモ化しなかった場合。
上記のforce-it手続きを修正。
コード(BBEdit)
sample.scm
(define (force-it obj)
(if (thunk? obj)
(actual-value (thunk-exp obj) (thunk-env obj))
obj))
入出力結果(Terminal, REPL(Read, Eval, Print, Loop))
$ scheme
MIT/GNU Scheme running under MacOSX
Type `^C' (control-C) followed by `H' to obtain information about interrupts.
Copyright (C) 2011 Massachusetts Institute of Technology
This is free software; see the source for copying conditions. There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
Image saved on Friday April 13, 2012 at 9:02:52 AM
Release 9.1.1 || Microcode 15.3 || Runtime 15.7 || SF 4.41 || LIAR/C 4.118
Edwin 3.116
1 ]=> (load "./sample.scm")
;Loading "./sample.scm"...
;;; L-Eval input:
(define (fib n)
(cond ((= n 0) 0)
((= n 1) 1)
(else (+ (fib (- n 1))
(fib (- n 2))))))
;;; L-Eval value:
ok
;;; L-Eval input:
(fib 20)
;;; L-Eval value:
6765
;;; L-Eval input:
End of input stream reached.
Moriturus te saluto.
$
メモ化しなかった場合は、体感的に明らかに結果が出力されるのにメモ化した場合より時間がかかった。
問題の対話。
メモ化した時。
;;; L-Eval input (square (id 10)) ;;; L-Eval value 100 ;;; L-Eval input count ;;; L-Eval 1
メモ化しなかった時。
;;; L-Eval input (square (id 10)) ;;; L-Eval value 100 ;;; L-Eval input count ;;; L-Eval 2
メモ化した場合は、square手続きで(id 10)は一度めはid手続きが実行されて、二度目はメモから取得するからcountは1になる。
メモ化しなかったときは、二度目も(id 10)が実行されるので、countは2になる。
確認。
メモ化した場合。
入出力結果(Terminal, REPL(Read, Eval, Print, Loop))
;;; L-Eval input: (define count 0) ;;; L-Eval value: ok ;;; L-Eval input: (define (id x) (set! count (+ count 1)) x) ;;; L-Eval value: ok ;;; L-Eval input: (define (square x) (* x x)) ;;; L-Eval value: ok ;;; L-Eval input: (square (id 10)) ;;; L-Eval value: 100 ;;; L-Eval input: count ;;; L-Eval value: 1
メモ化しなかった場合。
入出力結果(Terminal, REPL(Read, Eval, Print, Loop))
;;; L-Eval input: (define count 0) ;;; L-Eval value: ok ;;; L-Eval input: (define (id x) (set! count (+ count 1)) x) ;;; L-Eval value: ok ;;; L-Eval input: (define (square x) (* x x)) ;;; L-Eval value: ok ;;; L-Eval input: (square (id 10)) ;;; L-Eval value: 100 ;;; L-Eval input: count ;;; L-Eval value: 2
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