sicp ex-2.57 多项式求导

(define (derive exp var)
  (define (=number? a b)
    (and (number? a) (= a b)))
  
  (define (make-sum a b)
    (cond ((=number? a 0) b)
          ((=number? b 0) a)
          ((and (number? a) (number? b)) (+ a b))
          (else (list ‘+ a b))))
  
  (define (make-product a b)
    (cond ((=number? a 0) 0)
          ((=number? b 0) 0)
          ((=number? a 1) b)
          ((=number? b 1) a)
          ((and (number? a) (number? b)) (* a b))
          (else (list ‘* a b))))
  
  (define (product? a)
    (if (eq? a ‘*)
        true
        false))
  
  (define (sum? a)
    (if (eq? (car a) ‘+)
        true
        false))
  
  (define (addend s) (cadr s))
  
  (define (make-sum-list a b)
    (if (= (length b) 1)
        (list ‘+ a (car b))
        (append (list ‘+ a ) b))
    )
  (define (augend s)
    (if (<= (length s) 3)
        (caddr s)
        (make-sum-list (caddr s) (cdddr s))))

  
  (define (make-product-list a b)
    (if (= (length b) 1)
        (list ‘* a (car b))
        (append (list ‘* a ) b))
    )
  
  (define (multiplier s) (cadr s))
  
  (define (multiplicand s) 
    (if (<= (length s) 3)
        (caddr s)
        (make-product-list (caddr s) (cdddr s))))
  
  (define (variable? a)
    (symbol? a))
  
  (cond ((number? exp) 0)
    ((variable? exp)
     (if (eq? exp var) 1 0))
    ((sum? exp) (make-sum (derive (addend exp) var) (derive (augend exp) var)))
    ((product? (car exp)) (make-sum (make-product (multiplier exp) (derive (multiplicand exp) var))
                       (make-product (derive (multiplier exp) var) (multiplicand exp))))))