#lang sicp 

(define (accumulate op initial sequence)
  (if (null? sequence)
      initial
      (op (car sequence)
          (accumulate op
                      initial
                      (cdr sequence)))))
(define (horner-eval x coefficient-sequence)
  (accumulate 
   (lambda (this-coeff higher-terms) (+ this-coeff (* higher-terms x)))
   0
   coefficient-sequence))

; For example, to compute ${1 + 3x$ + {5x^3 + x^5}} at ${x = 2$} you

(horner-eval 2 (list 1 3 0 5 0 1))