開発環境
- macOS Sierra - Apple (OS)
- Emacs (Text Editor)
- Scheme (プログラミング言語)
- kscheme (ksi)(github) (処理系)
計算機プログラムの構造と解釈[第2版](ハロルド エイブルソン (著)、ジュリー サスマン (著)、ジェラルド・ジェイ サスマン (著)、Harold Abelson (原著)、Julie Sussman (原著)、Gerald Jay Sussman (原著)、和田 英一 (翻訳)、翔泳社、原著: Structure and Interpretation of Computer Programs (MIT Electrical Engineering and Computer Science)(SICP))の第2章(データによる抽象の構築)、2.3(記号データ)、2.3.2(例: 記号微分)、抽象データによる微分プログラム、代数式の表現、問題2.56、57、58.を取り組んでみる。
その他参考書籍
問題2.56、57、58.
コード(Emacs)
(begin
(load "procedures.scm")
(newline)
(define (p obj) (display obj) (newline))
(define (deriv exp var)
(if (number? exp)
0
(if (variable? exp)
(if (same-variable? exp var)
1
0)
(if (sum? exp)
(make-sum (deriv (addend exp) var)
(deriv (augend exp) var))
(if (product? exp)
(make-sum
(make-product (multiplier exp)
(deriv (multiplicand exp) var))
(make-product (deriv (multiplier exp) var)
(multiplicand exp)))
(if (exponentiation? exp)
(make-product
(make-product (exponent exp)
(make-exponentiation
(base exp)
(make-sum (exponent exp)
-1)))
(deriv (base exp) var))
(error "unknown expression type -- DERIV" exp)))))))
(define (variable? x) (symbol? x))
(define (same-variable? v1 v2)
(and (variable? v1) (variable? v2) (eq? v1 v2)))
(define (sum? x)
(and (pair? x) (eq? (car x) '+)))
(define (make-sum a1 a2)
(if (=number? a1 0)
a2
(if (=number? a2 0)
a1
(if (and (number? a1) (number? a2))
(+ a1 a2)
(list '+ a1 a2)))))
(define (addend s) (cadr s))
(define (augend s) (caddr s))
(define (product? x)
(and (pair? x) (eq? (car x) '*)))
(define (multiplier p) (cadr p))
(define (multiplicand p) (caddr p))
(define (=number? exp num)
(and (number? exp) (= exp num)))
(define (make-product m1 m2)
(if (or (=number? m1 0) (=number? m2 0))
0
(if (=number? m1 1)
m2
(if (=number? m2 1)
m1
(if (and (number? m1) (number? m2))
(* m1 m2)
(list '* m1 m2))))))
(p 2.56)
(define (exponentiation? x) (and (pair? x) (eq? (car x) '**)))
(define (make-exponentiation base exp)
(if (= exp 0)
1
(if (= exp 1)
base
(list '** base exp))))
(define (base e) (cadr e))
(define (exponent e) (caddr e))
(p (deriv '(** x 10) 'x))
(p (deriv '(** x 0) 'x))
(p (deriv '(** x 1) 'x))
(p 2.57)
(define (make-sum a1 a2)
(if (=number? a1 0)
a2
(if (=number? a2 0)
a1
(if (and (number? a1) (number? a2))
(+ a1 a2)
(list '+ a1 a2)))))
(define (addend s) (cadr s))
(define (augend s)
(if (null? (cdddr s))
(caddr s)
(cons '+ (cddr s))))
(p (deriv '(+ x y 10) 'x))
(define (multiplier p) (cadr p))
(define (multiplicand p)
(if (null? (cdddr p))
(caddr p)
(cons '* (cddr p))))
(p (deriv '(* x y 10) 'x))
(p (deriv '(* x y (+ x 3)) 'x))
(p "2.58-a")
(define (sum? x)
(and (pair? x) (eq? (cadr x) '+)))
(define (make-sum a1 a2)
(if (=number? a1 0)
a2
(if (=number? a2 0)
a1
(if (and (number? a1) (number? a2))
(+ a1 a2)
(list a1 '+ a2)))))
(define (addend s) (car s))
(define (product? x)
(and (pair? x) (eq? (cadr x) '*)))
(define (multiplier p) (car p))
(define (make-product m1 m2)
(if (or (=number? m1 0) (=number? m2 0))
0
(if (=number? m1 1)
m2
(if (=number? m2 1)
m1
(if (and (number? m1) (number? m2))
(* m1 m2)
(list m1 '* m2))))))
(p (deriv '(x + (3 * (x + (y + 2)))) 'x))
(p "2.58-b")
(define (sum? x)
(if (and (pair? x) (memq '+ x))
#t
#f))
(define (addend s)
(define (iter s)
(if (eq? (car s) '+)
'()
(cons (car s)
(iter (cdr s)))))
((lambda (res)
(if (null? (cdr res))
(car res)
res))
(iter s)))
(define (augend s)
((lambda (res)
(if (null? (cdr res))
(car res)
res))
(cdr (memq '+ s))))
(p (deriv '(x + 1 + x) 'x))
(define (product? x)
(and (pair? x) (not (memq '+ x)) (memq '* x)))
(define (multiplier p) (car p))
(define (multiplicand p)
((lambda (res)
(if (null? (cdr res))
(car res)
res))
(cddr p)))
(p (deriv '(2 * x * 3) 'x))
(p (deriv '(x + 3 * (x + y + 2)) 'x))
'done)
入出力結果(Terminal(kscheme), REPL(Read, Eval, Print, Loop))
$ ksi < sample56.scm ksi> 2.56 (* 10 (** x 9)) 0 1 2.57 1 (* y 10) (+ (* x y) (* y (+ x 3))) 2.58-a 4 2.58-b 2 6 4 => done ksi> $
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