SICP 2.34多项式加法

对于一个多项式：

求值，我们可以化简找出其规律，利用Horner 规则化简：

可以明显看出多项式的递归规律：从an开始，(+ (* an x) a(n-1))，下一个也是如此，直到a0。
之前建立的accumulate过程，也有相似的递归性，应该是一类过程，accumulate的原始定义：

(define (accumulate op initial sequence)    (if (null? sequence)        initial        (op (car sequence)             (accumulate op initial (cdr sequence)))))

op 是对数据的操作，从简单的加减乘除到复杂的自定义运算。
initial是初始数据，说明它是个什么的累加，比如数或者表
sequence是待处理的数据

那么结合此多项式的计算规律，对于多项式的计算可以抽象成代码：

(define (hover_eval x sequence)    (accumulate (lambda (this_coeff higher_terms)        (+ (* x this_coeff) higher_terms))        0        sequence))

手动模拟线性递归过程：

(horner-eval  2 (list 1 3 0 5 0 1))(accumulate (lambda (this-coeff higher-terms) <??>)            0            (list 1 3 0 5 0 1))(+ 1 (* 2        (accumulate (lambda (this-coeff higher-terms) <??>)                    0                    (list 3 0 5 0 1))))(+ 1 (* 2        (+ 3 (* 2 (accumulate (lambda (this-coeff higher-terms) <??>)                              0                              (list 0 5 0 1))))))(+ 1 (* 2        (+ 3 (* 2                (+ 0 (* 2 (accumulate (lambda (this-coeff higher-terms) <??>)                                      0                                      (list 5 0 1))))))))(+ 1 (* 2        (+ 3 (* 2                (+ 0 (* 2                        (+ 5 (* 2 (accumulate (lambda (this-coeff higher-terms) <??>)                                              0                                              (list 0 1))))))))))(+ 1 (* 2        (+ 3 (* 2                (+ 0 (* 2                        (+ 5 (* 2                                (+ 0 (* 2                                        (accumulate (lambda (this-coeff higher-terms) <??>)                                                    0                                                    (list 1))))))))))))(+ 1 (* 2        (+ 3 (* 2                (+ 0 (* 2                        (+ 5 (* 2                                (+ 0 (* 2                                        (+ 1 (* 2                                                (accumulate (lambda (this-coeff higher-terms) <??>)                                                            0                                                            '())))))))))))))(+ 1 (* 2        (+ 3 (* 2                (+ 0 (* 2                        (+ 5 (* 2                                (+ 0 (* 2                                        (+ 1 (* 2 0))))))))))))(+ 1 (* 2        (+ 3 (* 2                (+ 0 (* 2                        (+ 5 (* 2                                (+ 0 (* 2                                        (+ 1 0)))))))))))(+ 1 (* 2        (+ 3 (* 2                (+ 0 (* 2                        (+ 5 (* 2                                (+ 0 (* 2 1))))))))))(+ 1 (* 2        (+ 3 (* 2                (+ 0 (* 2                        (+ 5 (* 2                                (+ 0 2)))))))))(+ 1 (* 2        (+ 3 (* 2                (+ 0 (* 2                        (+ 5 (* 2 2))))))))(+ 1 (* 2        (+ 3 (* 2                (+ 0 (* 2                        (+ 5 4)))))))(+ 1 (* 2        (+ 3 (* 2                (+ 0 (* 2 9))))))(+ 1 (* 2        (+ 3 (* 2 18))))(+ 1 (* 2 (+ 3 36)))(+ 1 (* 2 39))(+ 1 78)79