2.33

练习 2.33 请填充下面缺失的表达式，完成将一些基本的表操作看作累积的定义：

(define (map p sequence)
    (accumulate (lambda (x y) <??>) nil sequence)
)

(define (append seq1 seq2)
    (accumulate cons <??> <??>)
)

(define (length sequence)
    (accumulate <??> 0 sequence)
)

首先，定义 accumulate

 
(define (accumulate op initial sequence)
  (if (null? sequence)
      initial
      (op (car sequence)
          (accumulate op initial (cdr sequence))) 
      )
  )
​x
 
#<undef>

 
(define (map p sequence)
  (accumulate (lambda (x y) (cons (p x) y)) '() sequence)
  )
​
(map (lambda (x) (+ x 1)) (list 1 2 3 4))
 
(2 3 4 5)

 
(define (append seq1 seq2)
  (accumulate cons seq2 seq1) 
  )
​
(append (list 1 2) (list 3 4))
 
(1 2 3 4)

 
(define (length sequence)
  (accumulate (lambda (x y) (+ 1 y)) 0 sequence)
  ) 
​
(length (list 1 2 3 4 5))
 
5