(sicp19)sicp問題2.56〜2.57

久しぶりに。

;;m.2.56
(define (deriv exp var)
  (cond ((number? exp) 0)
        ((variable? exp)
         (if (same-variable? exp var) 1 0))
        ((sum? exp)
         (make-sum (deriv (addend exp) var)
                   (deriv (augend exp) var)))
        ((product? exp)
         (make-sum
          (make-product (multiplier exp)
                        (deriv (multiplicand exp) var))
          (make-product (deriv (multiplier exp) var)
                        (multiplicand exp))))
        (else
         (error "unknown expression type -- DERIV" exp))))

(define (variable? e)
  (symbol? e))

(define (same-variable? v1 v2)
  (and (symbol? v1) (symbol? v2) (eq? v1 v2)))

(define (make-sum a1 a2)
  (cond ((=number? a1 0) a2)
        ((=number? a2 0) a1)
        ((and (number? a1) (number? a2)) (+ a1 a2))
        (else (list '+ a1 a2))))

(define (make-product m1 m2)
  (cond ((or (=number? m1 0) (=number? m2 0)) 0)
        ((=number? m1 1) m2)
        ((=number? m2 1) m1)
        ((and (number? m1) (number? m2)) (* m1 m2))
        (else (list '* m1 m2))))

(define (=number? exp num)
  (and (number? exp) (= num exp)))

(define (f? x symbol)
  (and (pair? x) (eq? (car x) symbol)))

(define (sum? x) (f? x '+))
(define (product? x) (f? x '*))

(define (addend s) (cadr s))
(define (augend s) (caddr s))

(define (multiplier p) (cadr p))
(define (multiplicand p) (caddr p))

;(deriv '(+ x 3) 'x) => 1

;;m2.56----
(define (exponetiation? exp)
  (f? exp '**))
(define (base e)  (cadr e))
(define (exponent e) (caddr e))
(define (make-exponetiation b e)
  (cond ((= e 0) 1)
        ((= e 1) b)
        (else (list '** b e))))

(define (deriv exp var)
  (cond ((number? exp) 0)
        ((variable? exp)
         (if (same-variable? exp var) 1 0))
        ((sum? exp)
         (make-sum (deriv (addend exp) var)
                   (deriv (augend exp) var)))
        ((product? exp)
         (make-sum
          (make-product (multiplier exp)
                        (deriv (multiplicand exp) var))
          (make-product (deriv (multiplier exp) var)
                        (multiplicand exp))))
        ((exponetiation? exp)
         (make-product
          (make-product (exponent exp)
                        (make-exponetiation (base exp) (- (exponent exp) 1)))
          (deriv (base exp) var)))
                                 
        (else
         (error "unknown expression type -- DERIV" exp))))

(deriv '(** x 3) 'x) ;;gosh> (+ 3 (** n 2))

;;m2.57
;;残りの項を再帰的にということなので…
(define (f g exp)
  (if (null? exp)
      0
      (g (car exp) (f g (cdr exp)))))
(define (augend exp)
  (f make-sum (cddr exp)))

(augend '(+ 1 2 3)) ;;5になってればいい
;;gosh> 5
(augend '(+ 2 3 4 x y 3 4)) ;;要素に文字が来ても
;;gosh> (+ 3 (+ 4 (+ x (+ y 7))))

;;fってaccumulateだ。
;;ということでこれだけで問題の回答になる。

(define (augend exp)
  (accumulate make-sum  0 (cddr exp)))
(define (multiplicand exp)
  (accumulate make-product 1 (cddr exp)))

(augend '(+ 1 2 3 4))
;;gosh> 9
(multiplicand '(* 2 3  x 4 5))
;;gosh> (* 3 (* x 20))


(deriv '(* x y (+ x 3)) 'x)
;;gosh> (+ (* x y) (* y (+ x 3)))

図形言語

何を使おう？
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