[lisp] scheme学习2

1.在scheme中，为了效率，对序对的操作 cons car 和cdr是内部实现的，这里是scheme实现， 其中cons用到了闭包

 (define (cons a b)
     (define (dispatch m)
         (cond ((= m 1) a)
             ((= m 2) b)
             (else (error "index out of range")))
     )
     dispatch
 )

 (define (car d) (d 1))
 (define (cdr d) (d 2))

2.计算列表长度和叶子节点数目

 (define (count_leaf x)
     (cond ((null? x) 0)
           ((not(pair? x)) 1)
           (else (+
             (count_leaf (car x))
             (count_leaf (cdr x))
             ))
           )
 )

 (define (length items)
     (define (length_iter count x)
             (if (null? x)
                 count
                 (length_iter (+ 1 count) (cdr x))
         )
     )

     (length_iter 0 items)
 )

3.Honor规则计算多项式（SICP P80 2.34）

(define (accumulate op inital seq)
        (if (null? seq)
            inital
            (op (car seq) (accumulate op inital (cdr seq)))
            )
)

(define (honor_eval x coeff_seq)
        (accumulate
            (lambda (this_coeff highter_terms)
                (
                    + this_coeff
                      (* x highter_terms)
                )
            )
            0
            coeff_seq
        )
)